Michael A. Gorycki, Ph.D., June, 2001

The development of aligned, evenly-spaced lobate salients, separated by zones of retarded flow, can be observed at the interface of a fluid traversing a planar surface in many natural environments and during certain man-made events. Physical models presented here reveal the mechanism of salient formation and associated processes. Salients can be recognized in diverse phenomena including hairpin vortices (which are transitional between laminar flow and turbulence), beach cusp series, most types of sand dunes, gravity currents, haboobs, and turbidites. It is suggested here that they are responsible for Langmuir circulation. They also may be recognized in thunderstorm squall lines, tornado swarms, wind shear, and haboobs. Taylor vortices and the large-scale structure of Jupiter’s atmosphere may result from salient formation acting against cylindrical or spherical surfaces. All cumulous and related structures, including hurricanes, cloud rows, and Bénard cells appear to derive from fluid salients, as do falling drop patterns. It is also argued here that primary and secondary tectonic arc series may owe their general structure to fluid salients forming lithospheric plates. Salients, therefore, range in size from a few mm to thousands of km and can take from a few milliseconds to millions of years to form.

INTRODUCTION

The recognition and study of the structuring of moving fluids derive from an early observation of the leading edge of a small amount of water moving across the bottom of a small, flat-bottomed tray. As the fluid is frictionally impeded, it’s edge overrolls, thins, and, restrained from extending axially, is thrown into a series of evenly-spaced salients if the energy of the system is sufficient. Adjacent salients mutually interfere, producing rearward-pointing zones of retarded flow between each salient (Gorycki, 1973a). If flow continues, weaker salients can become cannibalized and become absorbed as they are overwhelmed by the overrolling sides of adjacent salients which then become larger and less numerous.

Continued discernment of fluid structuring in a variety of natural and experimental environments reveals that it is ubiquitous, legion, and likely responsible for a variety of geologic, marine, and atmospheric phenomena. Additionally, they may be discerned in laboratory and even some kitchen phenomena.

Depending on the environment of formation, aligned, evenly-spaced salients and zones of retarded flow exhibit diverse morphologies. In addition, second-, third-, and even higher order (smaller) salients can develop on primary salients. Fluid salients and zones of retarded flow can: 1) occur aligned at the leading edge of a fluid overriding a planar surface, 2) be generated against a cylindrical or spherical surface, 3) form radially either centrifugally or centripetally, 4) develop globoidally as cumulous structures diverging from a central point, and 5) be uniformly distributed on a two-dimensional plane which is perpendicular to salient motion. Following are a variety of phenomena in which fluid salients may be recognized.

The Mechanism of Salient Formation

A Physical Model

A simple physical model to demonstrate aligned, evenly-spaced salients involves placing a straight 5 cm length of 0.4 mm diameter cylindrical rubber monofilament (taken from a new elastic cloth waistband) between two pieces of plate glass. The apposed glass surfaces are first coated with a thin film of light mineral oil to reduce friction between the glass and the monofilament. Pressing down on the upper glass, the monofilament is flattened to about half its diameter. At this point, a spherical tri-axial ellipsoid in the monofilament becomes oblate. If the upper plate is translated in a direction perpendicular to the monofilament’s axis, one would expect the cylinder to overroll and remain straight. Instead, it extends axially (as the oblate spheroid becomes prolate in that direction) and forms a series of nearly identical waves (salients) with amplitude parallel to the motion of the upper plate (Fig. 1), but with virtually no change in the straight-line distance between its ends. Obviously, the monofilament greatly increases its length at the expense of a reduction in cross-sectional area. More familiarly, rolling dough by hand across a flat surface thins the worked material and causes it to lengthen, but, lacking axial constraint, without the production of salients.

The anterior salients of the rubber cylinder closely resemble a uniform series of hairpin vortices, detected in the laminar flow of fluids. All overrolling in the monofilament is in the same direction. In a discussion of the generation of turbulence in fluids, Tesar (1997) [1] (see his figures I-26 and I-27) describes

a hairpin vortex as forming from a roller vortex, becoming elevated, thinning, and forming a number of thinner secondary salients (his instabilities), which degenerate, into turbulent spots. He describes a cascade as the energy in turbulence being continuously transferred from large vortices to smaller ones. In the context of this paper, I would describe cascading as second- and higher-order salients forming on primary salients as is commonly seen in the swash zone of beaches (Fig. 2). Second- and higher-order salients also suggest chaos theory fractals [2].

The most obvious illustration in nature of the action of aligned, evenly-spaced salients would be in the formation of beach cusps (Gorycki, 1973a). Beach cusps have been found to vary in size from a few cm up to 360 m apart and are separated by bays which oppose submerged seaward deltas. Various authors have presented disparate, conflicting observations and theories concerning the process of beach cusp formation over the years. They involve such parameters as cusp shape, size and spacing, sediment particle size, erosion versus deposition, wave refraction, swash directions, effects of long-shore currents, beach face irregularities, angle of wave fronts, and two-wave cycles. Russell & McIntire’s (1965) early study is detailed, but still leads them to conclude that they have not been able to explain the reasons for cusp spacing.

Later research by Inman and Guza (1982), based on a standing wave model, is in conflict with the more recent self-organization computer simulation model of Werner and Fink (1993). However, both teams also admit that their studies have not provided a solution to the cause of beach cusp series [3]. Werner feels that an understanding as to how local interactions between fluid and sediment leads to globally uniform patterns is lacking in the standing wave model, but also admits that more detailed observations of morphology and swash flow during cusp formation are needed for the self-organized theory. In still later work on cusps, Masselink (1998) concludes that the cause of beach cusp formation requires "...further numerical and experimental investigations..."’ and, finally, Coco, O’Hare and Huntley (1999), assert that, "...it is not possible to produce conclusive support for one theory above the other...".

Examination of air photos of well-formed beach cusps series strongly suggest that plunging waves, which directly impinge and bottom on the submerged portion of the beach face, apparently are essential to the formation and maintenance of cusp series [4] and are reminiscent of the simple

action seen in the rocking trough (Gorycki, 1973a).

A thin layer of sand and silt, strewn on the trough bottom, quickly forms rearward-projecting deposits (Fig. 4) as a line of salients flows over the sediment. The sand is frondescently swept bilaterally to the sides of each salient, depositing in the inter-salient zones of retarded flow. In nature, the evenly-spaced rearward projections develop into the submarine deltas with overdeepening of the beach face just seaward of each cusp. Well-developed deltas can be seen to impede their portion of the incoming wave (Fig. 5) and lie midway between salients. Water, flowing from the cusps into the intercusp areas and back to the sea, further erodes the beach face to deepen the bays and add sediment down-slope to the submarine deltas. Once partially developed, the inter-cusp deltas (and associated return flow of water) and the fore-cusp overdeepening would continue to control the location of retarded zones and salients, respectively, as they develop from successive waves of similar strength and adequate wavelength (Fig. 6). As a consequence, evenly-spaced cusps, bays, and deltas would continue to develop and be maintained (Fig. 7). If a larger set of waves reaches the beach face, established cusps and deltas would be replaced by a larger set. If wave action becomes random, established cusps might initially control the swash, causing larger waves to passively rush up the beach face in the intercusp bays and refract toward the beach cusps (Gorycki, 1973a). Weaker waves would have little effect. In time, however, established cusps and deltas would be destroyed, particularly if the wave period shortens.

Werner and Fink (1993) find that cusps are rare on most beaches, but tend to form when normally incident, nonbreaking waves surge against high beach slopes in regions where the range between high and low tide is small. Rudowski (1964) notes that beach cusps form readily in the relatively restricted Baltic Sea, where the tidal range is very small. After exhaustive field observations, he concludes that beach cusps usually form as the result of erosive activity, when the force of the surf is not too strong, and when waves approach parallel to the beach. He finds that cusps can form if the wave front is not parallel to the shore, but that the angle to the shoreline must be less than 40 degrees and the resulting cusps would be asymmetrical.

By observing aligned, evenly-spaced salients operating on the beach face and considering the rubber monofilament model and the rocking trough salients with their ability to organize sand on the trough bottom into spaced "deltas", we have a simple and obvious mechanism for beach cusp formation. As a consequence, the diverse, often contradictory field observations of many workers can be readily accommodated (Gorycki, 1973a). It appears, then, that the initial incoming wave can become intrinsically structured, initializing the formation and location of a series of cusps and deltas. These incipient cusps and deltas then control the location of later salients and retarded zones, resulting in the further development of the cusp series. Cusp spacing would be determined by a combination of such parameters as water density, beach face slope, wave size, etc., but the role played by sediment during cusp initiation, erosion, transportation, and deposition, would seem to be essentially collateral.

Other Sedimentary Structures

Sand Dunes

Folk (1971) describes great chains of incredibly parallel dunes which dominate the vast inland deserts of the world and extend over areas of as much as 100,000 sq mi. They follow the orientation of the great geostrophic trade wind systems, are widely spaced if large, are narrow compared to the interdune space, have tuning fork junctures invariably in an upwind direction, and, "...like stripes in a convict suit...", exhibit uniform lateral spacing in any one area.

These dunes and a variety of other, more or less parallel, evenly-spaced structures such as sand strips, parabolic, and possibly barchan sand dunes, as well as a variety of elongate subaqueous structures (Folk, 1971), could be attributed to salients developing in the wind or water along a straight front just as sand is moved into streaks on the rocking trough (Fig. 4). The dunes would determine the location of developing retarded zones, with salients forming in the interdune areas (Fig. 8). The spacing of dunes, whether they are the result of erosion or deposition, would be a function of an optimal, consistent wind velocity and persistent direction. Folk’s observation (1971) that the processes which formed and maintain the Simpson Desert dunes are fixed because the dunes have cores of old alluvial sediment and "...thus have not shifted laterally in position since dune formation began...", supports the control which established structures may have on the positioning of fluid salients.

Folk (1971), however, referencing Bagnold (1953), ascribes the uniform spacing of dunes to paired horizontal roller vortices in the wind and attributes it to Langmuir circulation operating in the atmosphere, but admits there is no satisfactory explanation for the uniform spacing or the "... vitally important junctures." Also, in a personal (Internet) communication Husar [5] agrees with Tsoar

that helicoidal flow is not a proven explanation for long km-spaced dunes, and Tsoar, in that communication, maintains that no one has ever observed or measured helicoidal flow in connection with the formation of dunes in deserts. He offers his own smoke candle experiments as proof. Sparrow and Husar’s figure 1 (1969) showing black dye moving up the upper surface of a submerged, heated, inclined plate mimics my observations on the rocking trough experiments (Gorycki, 1973a). The dye appears to be gently swept by salients into evenly-spaced, thin, dark streaks which then become more widely spaced and fewer in number in a process similar to the cannibalization of water salients in the rocking trough and the lateral movement of sediment into zones of retarded flow (Gorycki, 1973a). As a consequence, up-current tuning fork junctions are also present in the dye streaks of Sparrow and Husar’s (1969) figure 1. Hanna (1969) discusses counter-rotating horizontal helical vortices observed in the trajectories of simultaneously released neutral density balloons moving downwind, but these might be explained by a detail of salient formation described in the following section.

Aligned, evenly-spaced salients may be observed in a slow-moving gravity current formed by pouring 10 ml of a saturated sodium chloride solution, colored with ink, down an 8 by 40 cm trough (Gorycki, 1973a). The trough has walls 3 cm high, is filled with standing fresh water, and is tilted 3 degrees. As it travels downslope, (Fig. 9) the leading edge of the current is modified by the retarding effect of the overlying water into a head, neck, and body region (Komar, 1972). Elevation of the head region, caused by interaction with the invaded fluid, is similar to that seen in hairpin vortices [1]. The current also forms long salients separated by retarded zones (Komar, 1972) and the leading portion of the flow can be seen to lighten in color by incorporation of the fresh water through which is flows. Allen (1971) describes the well-known admixing of the ambient medium at the upper surface of gravity currents, but he pointedly describes additional inmixing, with a spatial periodicity, of ambient medium into what he calls clefts and tunnels (here, retarded zones) between fingers or lobes (here, salients) at the head of a gravity current, which also serves to increase the total volume of the current. This sub-current addition finds its way "...into the body of the flow...close to the lower boundary..." where it "...can be transported upward through the effects of shearing and buoyancy much more readily than fluid mixed at the upper surface can be transported downward." (Allen, 1971).

Hanna’s (1969) comments on balloon trajectories might be explained by the paired, oppositely rotating structuring within a single cleft as presented by Simpson (1969, 1972).

Allen’s (1971) depiction (his figure 3) of a hypothetical gravity current is typical of salient formation discussed in this section, but he deduces an implied spatially periodic variation of the bed shear stresses across the region of the head resulting in "...very probably a system of oppositely rotating (horizontal) longitudinal vortices...", again suggestive of Langmuir circulation acting within a moving fluid. He maintains that these vortices must operate in the head of turbidity currents in order to explain the criss-crossing of tool marks commonly observed in turbidites (Allen, 1971). However, the intrinsic structure of fluid salients as described in the present paper (Fig. 4) would explain the morphology of gravity currents and also the uniform spacing of flute marks and the criss-cross of tool marks seen in some turbidites. [7]

The plumose flow of sand in each salient [8] would explain the

development of frondescent sole markings seen in other turbidites. It should also be noted that mud and lava flows can exhibit evenly-spaced salients.

Following is a discussion of Langmuir circulation and the evidence which supports fluid salients as the operative mechanism for that phenomenon.

Langmuir Circulation Cells

Langmuir (1938) describes relatively narrow (2 to 6 m wide) streaks of seaweed on the surface of the ocean having spacings of approximately 100 to 200 m and smaller-scale (1-10 m) alignments of floating debris (streaks) on Lake George. He ascribes the streaks to multiple, paired horizontal cylindrical roller-vortices developing within the water caused by ostensibly structureless wind blowing across the water parallel to the streaks. Paired vortices would roll the surface water toward the streaks, thus sweeping floating debris together. Interestingly, a number of later workers describe mixing of upper surface lake or sea water with deeper water as being very important to the distribution of heat, oxygen, plankton, organic matter and nutrients, and also to oil spill dispersion, organization of bubble clouds, etc. The mixing is usually ascribed to Langmuir’s roller vortices operating in the water.

Similarly, evenly-spaced, streaks of trade wind cumulus clouds over the ocean are common and have been attributed to Avsec rolls (1939) by Malkus (1963) who presents schematic maps of evenly-spaced cloud rows which are considered to require strong vertical wind shear as in plane Couette flow (Brown, 1991). She also suggests that the cloud rows are the result of vertical displacement of warm moist air (to colder regions) between apposed, elongate, helical, Avsec rolls (Avsec, 1939) or Ekman helical vortices generated in the plane Couette flow of the planetary boundary layer (Brown, 1991). These cloud rows are interpreted here as due, rather, to vertical displacement of air in zones of retarded flow between fluid salients (Fig. 10) operating in a moving layer of the atmosphere, rather than Langmuir-like helical roller vortices. Hanna (1969) similarly describes longitudinal vortices in the atmosphere and couples longitudinal dune formation and cloud row formation to the same mechanism operating where vortices are thought to converge toward each other near the ground and diverge at altitude.

These observations, and recalling Folk’s (1971) and Bagnold’s (1953) suggestion that some sort of structuring must be present in the wind blowing over land, leads to the conclusion that Langmuir circulation in sensu stricto, that is, only within the water, is not necessarily responsible for the development of streaks on the surfaces of bodies of water. Also, importantly, no evidence as to why evenly-spaced, paired horizontal roller vertices should develop, in any medium, to produce the various structures is presented by Folk (1971), later workers (Allen, 1971), [5] or even by Langmuir (1938) himself.

I have noted fog blown from a quiet pool surface and snow crystals blown across a frozen lake surface becoming organized into elongate streaks, parallel to wind direction (McLeish, 1968). Any aerial, sub-aerial, or sub-aqueous aligned structures may be more simply ascribed to the essentially two-dimensional, lateral component of motion of structured air in the evenly-spaced fluid salients operating above an interface in the atmosphere; on the surface of water or land; or within the moving water acting on subaqueous surfaces, as experimentally shown here. The lateral component of flow of a supposed pair of roller vortices, with bases rotating away from each other, would comprise a single fluid salient. Adjacent, converging bases, would comprise a retarded zone for the location of a streak, dune, or cloud row. Consequently, the upper half of the more elaborate, presumed system of paired horizontal roller vortices could thus be eliminated (Fig. 10), resulting in the simpler mechanism experimentally described here with the rubber monofilament, the rocking trough, or the gravity current. As a consequence, any evidential structuring of the near-surface water ascribed to Langmuir circulation would be passive and shallow.

It should be noted here that Langmuir himself provides strong evidence for fluid salients and against his horizontal roller vortices. Using his "velocity indicator", he observed that shallow water at depths of less than 5 m drifted under a streak, whereas water at 10 m "...had no tendency to do so." He only assumes that "...perhaps at a greater depth the indicator would move into a position midway between streaks since there must be horizontal currents which converge under the rising currents between the streaks." He "...never observed in Lake George any reverse flow in the lower part of the epilimnon..." except a (usually windless) nocturnal flattening (leveling) of the epilimnon along the lake’s axis, which is also parallel to the usual, daily wind direction (Langmuir, 1938). Langmuir also notes that the longitudinal and transverse velocities of the water have their maximum values at the surface and gradually decrease to zero as his vortices become "...increasingly diffuse at greater depths." He additionally mentions that the surfaces of larger vortices contain smaller and shallower vortices, reminiscent of second- and higher-order salients as described here.

Also, if steaks and adjacent interstreak surface waters are generated by a series of paired, subaqueous horizontal roller vortices, it would seem streaks and interstreak areas should both be conveyed in a downwind direction at the same speed (see Hanna’s (1969) figure 4a which diagrammatically shows longitudinal vortices acting in the wind to produce evenly-spaced longitudinal dunes. These simplistic vortices must retain the same velocity throughout). In this respect, Langmuir, again, provides evidence against his horizontal roller vortices acting in the water. Employing a string with floats stretched across streaks, he describes water motion in the streaks to be faster downwind than in the broader areas between (Langmuir, 1938). If, instead, we assume that it is aligned wind salients which are centered on the broad inter-streak areas, they would push surface water and debris bilaterally and downwind toward the streaks and expose relatively still subsurface water underneath the salients. Since the debris would present a frictional drag on the wind, the wind would also preferentially move the streak areas more quickly downwind compared to the upwelling water in intervening areas which would initially have comparatively little of a down-wind component to its velocity.

The lack of evidence for return water flow, the diminution of assumed horizontal roller vortex structure at depth, and the variation in velocity of surface water strongly suggest that, as stated previously, paired horizontal roller vortices (Langmuir circulation cells) within the water apparently do not exist. It would seem that the accumulation, spacing, and motion of seaweed streaks are, therefore, dependent on evenly-spaced fluid salients and retarded zones developing in the wind just above the water’s surface.

ALIGNED PLANAR SALIENTS

Thunderstorm Squall Lines

Powerful cold fronts are known to generate rather evenly-spaced thunderstorms (Fig. 11) along squall lines located just forward of the fronts (Strahler, 1969). This spacing strongly suggests the development of aligned planar salients providing clefts or tunnels (Allen, 1971; Simpson, 1969, 1972) (zones of retarded flow) which can engulf warmer, moist air which then rises as thunderheads, at spaced intervals, through the colder air.

Tornado Swarms

Accumulating data concerned with the structure of tornadoes and their development in the mid-western and southeastern United States strongly suggests that a complicated process based on the production of planar salients may also be responsible. In a typical scenario, tornadoes commonly develop at the leading edge of a massive, easterly-moving cold front as it invades a region overlain by warm, moist air which is itself usually moving in a northerly direction from the Gulf of Mexico. This normally results in a front moving to the east-northeast. Some of the warm air near the ground will be trapped within overriding and overrolling cooler air and will, in conjunction with opposition from the invaded warm air mass, as in the head region of turbidity currents (Komar, 1972), form a series of elevating hairpin vortices. Idso (1974) observed, on two occasions, an elevated hairpin vortex which visibly formed at the fronts of dust-laden wind. He maintains, however, that the overrolling vortices require a topographic disturbance, such as a mountain, to uplift and form the twin, oppositely-rotating funnels. No such topography would be necessary in the production of a fluid salient series as described here. Also, the counterclockwise rotation of the southern limb of each vortex would tend to be enhanced by the northward flowing warmer air at the eastern edge of the front and it is this direction of rotation which is most commonly observed in tornadoes, whereas, conversely, the clockwise rotating northern limb of each vortex would tend to be inhibited (Fig. 12) [9]. This limb is also "...generally in the storm’s precipitation downdraft.", (Snow, 1984). As the southern limb of a hairpin vortex assumes a vertical axis (Snow, 1984), it would entrain rising warmer air engulfed by the tunnel or cleft structure from which it emanates, and this would increase its vorticity and generate a tornado. It is also the weight of the overlying colder air pressing down which facilitates upward motion of the warmer air near the ground.

It is this combination of events, as suggested here, which may explain the parallel, and often uniformly-spaced, paths of destruction generated by swarms of counter-clockwise-rotating tornadoes so often seen as a single cold front traverses the Midwest or southeastern U.S. Four evenly-spaced tracks produced by seven tornadoes in east-central Florida on Feb. 22-23, 1998; four tracks produced by 15 tornadoes on March 1, 1997 in central Arkansas; and a similar swarm on May 3, 1999 in Oklahoma City, are good examples of spaced swarms. An explanation for, and even the recognition of the even-spacing in thunderstorm squall lines and tornado swarms, is generally lacking in the literature.

Wind Shear

Examining information and data related to aircraft disasters attributed to near-ground-level clear air wind shear suggests that aligned planar salients could also be responsible for this phenomenon. Wind shear can be defined as any fast and dramatic variation in wind speed, or horizontal or vertical wind direction, such that the velocity of air moving over a plane’s wings is swiftly changed. Disasters are commonly the consequence of three sequential factors: 1) increased lift caused by a sudden headwind for which the pilot compensates by a decrease in power, 2) a sudden downward flow of air, and 3) a sudden tail wind. As a result, the plane will drastically lose altitude and may also catastrophically stall.

Wind shear can occur at or near the ground, and often involves a plane attempting either to take off or land into the wind on fixed runways and at near-stall velocity. It is suggested here that under conditions during which aligned fluid salients can develop, the plane will likely traverse a salient at an angle to the salient’s axis. This encounter will initially result in an increase on the air-speed indicator as the plane approaches the head region of a salient for which the pilot compensates with a decrease in power and elevation to reduce the effects of the increased lift. Continuing on a straight flight path, however, the plane would enter the portion of the salient where overrolling, or downward motion of the air might cause the plane to again loose altitude. (This downward motion is often attributed to a localized, single, inopportune, "microburst" of downward-moving air.) Continued traverse of the salient will cause the plane to cross the opposite edge of the salient where it encounters a tail wind and enters the region of retarded flow between two salients where slow-moving turbulent air would be encountered. This last factor will further reduce the plane’s altitude and velocity.

A schematic diagram (Fig. 13) shows a plane experiencing the sequence of events normally attributed to wind shear as it traverses one of a series of fluid salients. It is suggested here that at least some wind shear occurrences may be attributed to "clear air" fluid salients, similar in size and structure to dust-laden haboobs (which also usually exhibit salients), but which are invisible to both pilot and radar. Possibly, as the angle between the line of flight and the general wind direction increases, the more likely a plane will traverse salients and encounter a greater risk of windshear.

TAYLOR-COUETTE FLOW

Fluid salient formation may also be invoked to explain the development of Taylor vortices formed in the annulus fluid between two vertical, concentric cylinders [10]. In the situation where

the outer cylinder is stationary and the inner cylinder is rotating, there is a diminution in the rotational velocity (circular Couette flow) as the outer wall is approached, and the subsequent development of vortices if a given rotational rate (Reynolds number) is attained. To understand this process in light of fluid salient formation, it helps to consider a quickly-stirred cup of coffee. The spoon acts as the inner cylinder. The stirring generates a coffee "annulus" having an angular velocity which, through wall shear, diminishes as the wall of the cup is approached (Taylor-Goertler instability). That is, the fluid moving over the cup wall is frictionally slowed. There is also an elevation (axial extension) of the coffee at the wall of the cup produced by the outward radial (centrifugal) motion of the fluid. In the closed Taylor-Couette apparatus, this extension would be inhibited, generating compressional axial stresses relieved by salient formation on the concave surface of the outer cylinder. This would result in quickly-formed, continuous, evenly-spaced, annular rings (Taylor vortices) if the energy of the system is sufficient. Since plane Couette flow is defined as flow in a fluid between two plates on which a force is applied to move one plate, this definition is identical to my rubber monofilament model which generates aligned salients in the rubber monofilament sheared between two glass plates, one of which moves in a direction perpendicular to the long axis of the monofilament (and the axes of the salients). Paired rings or ring portions which rotate away from each other (at the outer glass wall) would represent a salient; each pair rotating toward each other, a zone of retarded flow. Also, extrapolation of salient formation with the rubber monofilament would have adjacent arms of an elongated salient close together and rotating away from each other. Conversely, adjacent arms of a zone of retarded flow would rotate toward each other. The requisite features, therefore, of salient formation as seen on the beach face (overrolling of a frictionally impeded liquid moving over a surface and inhibited lateral extension) are present in the Taylor-Couette apparatus.

To support this concept, it has already been experimentally shown, using a porous inner cylinder (Lueptow and Min, 1994a), that fluid pumped axially inhibits the development of vortices (salients), at a given Taylor number. Pumping and fluid transfer into the inner cylinder would diminish the prerequisite inhibited axial extension in the fluid so necessary to salient formation. Alternatively, employing two porous cylinders where any radially inward flow or strong radially outward flow of annular fluid occurs also inhibits vortex formation (Lueptow and Min, 1994b) apparently by destroying the incipient structuring necessary for inhibited axial extension and fluid salient formation. The same is true if the speed of the inner, rotating cylinder is modulated, or if the cylinder is moved up and down in a sinusoidal fashion, or, again, if fluid is pumped in an axial direction. In most experiments, Taylor vortices are initiated near the ends of the cylinders where the additional drag at the ends of the annulus may induce incipient salient formation. However, in one experiment, the early development of Taylor vortices occurs at the base of the annulus. These early vortices may be explained by the hydrostatic head inducing greater axial pressure, friction, and salient formation in that region (Weisberg, Kevrekidis, and Smits, 1997). [11]

Taylor vortices become wavy if the Reynolds number is increased. Sinuosity has been displayed in a physical model for the mechanism of stream meandering (Gorycki, 1973b) where a straight rubber monofilament, flattened between two lightly-oiled glass plates, becomes structured from slightly to strongly sinuous if the upper glass plate is translated in a direction parallel to the monofilament’s axis (Fig. 14). The sinuosity results from inhibited axial extension of the monofilament. The initially spherical tri-axial ellipsoid in the monofilament obviously eventually becomes prolate with the long axis parallel to that of the monofilament upon relative translation of the plates. This extension should be relieved by a sinuous distortion perpendicular to the glass surfaces but, instead becomes parallel to them because of the constraint which the glass plates impose. In natural streams the constraint is imposed by gravity. Sinuous flow in an initially straight, 4 mm wide, sediment-free stream of water flowing down an inclined, smooth, planar, hydrophobic surface (stream plate) can be demonstrated by injecting multiple ink filaments, simultaneously produced from a single micropipette orifice, into the stream of water. Sinuosity is shown to be due to the presence of increasingly frictionally slowed and sinuously distorted water filaments progressively deeper in the stream (hydraulic drag)(Gorycki, 1973b). By increasing the flow of water, the maximum sinuosity of the stream (stream distance/λ) in one experiment reached at least 1.79, indicating it is possible to demonstrate true meandering under laboratory conditions. Sediment added to the stream also deposits point bars and reveals a meandering thalweg where these are normally observed in the field. These laboratory streams bear the closest of relationships to sinuous and meandering streams, of any size, in nature (Gorycki, 1973b). The distortion in the stream, with downstream overrolling at each bend, mimics the distortion seen in Fig. 14.

The point of this is that once Taylor vortices become established in the Taylor-Couette apparatus and the rotation is increased, they can become elongated and, therefore, sinuously distorted in a fashion similar to that of the rubber monofilament, by differential motion (hydraulic drag = Couette flow) on the vortices held between the surfaces of the cylinders. In the situation where Taylor vortices become merely tilted with respect to the axis of rotation, the circular vortices deform to ellipses by simple elongation prior to becoming sinuous.

In spherical flow, Taylor-like vortices (Fechtmann, Wulf, Egbers, and Rath, 1997) [12],

may be seen in the belts and zones of Jupiter and are considered here to also be the result of fluid salient formation in that planet’s atmosphere. The planet is a large oblate spheroid (PD/ED = 0.93) due to its rapid rate of rotation and 1000 km thick, helium-hydrogen, gaseous atmosphere. Equatorial winds reach 600 km/h and shift eastward 11 degrees in 24 hours relative to the planet’s supercritical fluid interior. As a consequence, there is both a compression of the atmosphere (due to gravity), a circumferential restriction (from pole to pole), and a relative eastward motion of the atmosphere over the planet’s interior. As discussed here, with regard to Taylor vortices, these, again, are the requisites for salient formation. A similar vortical wind motion also exists in the region close to the earth’s equator.

RADIAL, PLANAR SALIENTS

Centrifugal Radial Salients

Centrifugal, radial salients develop due to lateral extension along a circular periphery when a frictionally impeded fluid spreads across a flat surface from a central point. They can be observed as the scalloped exhaust cloud of a rocket radially dilates against the earth’s surface (Fig. 15) and also in some nuclear explosions as the rising cloud, at a great height, flattens and spreads radially as it’s specific gravity matches that of the adjacent ambient atmosphere, or dilates at the earth’s surface [13]. (see 1945, Fatman; 1953, Annie; and 1955, Apple II).

For the smooth wax or glass, the expanding, toroidal lamella is featureless, but for the rough wax or glass, evenly-spaced perturbations (salients) are obvious in the lamellae. The rough surface apparently inhibits (frictionally impedes) the advance of the overrolling edge and thus induces salient formation. If we assume these salients are the result of surface tension only, then the "perturbations" should also be induced on the smooth surfaces.

In the kitchen, a much larger (20 cm diameter) version of Figure 16 can form on the bottom of a hydrophobic plastic sink if the faucet is very quickly turned on and off. Centrifugal salients may also be produced by quickly pouring a thin stream of milk, from a height of 10 cm, into a 1 cm deep layer of the "heavy" syrup from canned fruit. The point to be made, in this instance, is that the centripetal, radial milk salients obviously form without the influence of surface tension. Incidentally, centrifugal salients can also form at the edges of omelet’s and thin-batter pancakes if fried on a well-oiled skillet.

Centripetal Radial Salients

Folk (1971) maintains that star-shaped oghurd (star) sand dunes apparently form by radially inblowing wind converging as vertical drafts. This is consistent with radial centripetal salient formation, with apparent concomitant salient cannibalization or expulsion (Gorycki, 1973a). Some of these dunes are stationary for periods of time long enough for them to have long-lived geographic names given them indicating that once formed, they are capable of maintaining their structure and location. Folk, however, maintains that the dunes are created by rising air setting up roller vortices having vertical axes, another version of Langmuir paired circulation cells shown here as not being a viable mechanism.

Additionally, the gross, counter-clock-wise structure of cyclonic air masses and hurricanes, common to the Caribbean, develop when surface air tangentially approaches a central area of low-pressure, increases its angular velocity, and accordionizes due to mutual peripheral compression. This causes spaced upwellings of warm air into colder regions of the atmosphere where moisture then condenses and forms the familiar spiral clouds or rain feeder bands.

A solid model of the radial centripetal salients of a hurricane can be generated using a pencil and an inflated balloon. The tip of the eraser (first made sticky with rubber cement) is pressed into the side of an inflated balloon, and the pencil is then twisted.

CUMULOUS SALIENTS

Globoidal Cumulous Structures

Cumuli exhibit first-, second-, third- and higher order salients which, in each category, tend to be uniform in size and spacing. This structuring suggests an equant, three-dimensional version of salient formation generated from one or more points operating without interaction with a planar substrate. Cumuli occur when a rapidly expanding gas forms mutually interfering spherulitic, globoidal first-order salients which displace and distort the interfacing atmosphere and are comprised of second-order and smaller salients. Adding milk to a cup of tea produces the same structuring. To quote Benoit Mandlebrot, regarding fractal geometry, "... clouds are not spheres...".

Planar Cumulous Structures and Bénard Convection Cells

Cumulostratus and mammatus clouds commonly exhibit evenly-spaced two-dimensional arrays of salients associated with the essentially planar atmospheric interface at which condensation occurs. Cumulostratus clouds are similar to experimentally produced Bénard convection cells (1901) which are evenly-spaced, vertically-moving, fluid salients exhibiting a horizontal, two-dimensional, mutual interference due to radial extension from each of their centers. Concurrent downward motion occurs at the edge of each cell where mutual interference results in a zone of retarded flow. It is suggested here that Bénard cells are globoidal cumuli confined to a planar distribution. [17]

The plane along which Bénard cells form and are viewed is perpendicular to their direction of motion as opposed to most fluid structures which develop in a plane parallel to their direction of motion. A similar Bénard convective pattern of warm patches of ocean surface water surrounded by cold has been shown using infrared imagery (Stewart, 1969). Also, elongate, wind-generated, warm and cold streaks may be the result of stretching of the Bénard pattern, or due to fluid salient formation at the ocean surface. In addition, Husar [5] describes the periodic rising of groups of thermals in a liquid above a heated, horizontal hot surface. This, again, suggest a Bénard convective pattern. If the hot surface is tilted, these cells could give rise to longitudinal thermals, as described by Sparrow and Husar (1969) just as Bénard convection cells, if sheared, can give rise to elongate cloud rows.

Planar salient formation may also be responsible for the relatively uniform, random outcrop pattern exhibited by non-tectonic salt dome swarms seen in various regions. Large regions of oghurd (star) dunes such as at the eastern edge of Grand Erg Oriental, Algeria-Tunisia-Libya, also suggest a Bénard convection cell forming above each dune because it becomes hotter than the surrounding denuded desert floor. The radially inblowing winds, which shape the dune and support the cell above, are derived from the zone of retarded flow which surrounds each Bénard convection cell. Bénard convection has also been considered to be the mechanism for convection within the earth’s mantle which is responsible for plate tectonics.

Another version of this instability is also considered responsible for the "pillars of creation" seen in the Eagle Nebula.

[19] The New York Times, Tuesday, January 16, 2001, p. F1.

These pillars are considered to be generated as the surface of a dense molecular cloud is heated by nearby stars and, being less dense penetrates the underlying, cooler portion of the cloud which mutually responds by producing salients.

It should also be noted that snow avalanches may exhibit a planar cumulous structure in the central mass of the flow as air becomes increasingly incorporated into the snow.

Linear Cumulous Structures

Burning fuels from ruptured pipes also produce similar plume structures. All of these first order cumuli are similar to bubbles escaping from the end of submerged tubing where parameters such as the difference in specific gravity, bubble size, orifice size, velocity, pressure, viscosity, ambient currents etc., all control bubble size and spacing.

A simple experiment reveals an interesting aspect of this kind of linear flow which bears on 1st order cumuli. If the end of a 1 cm diameter length of tubing is positioned at the bottom of a 2 liter graduated cylinder and the flow of nitrogen (or likely any other) gas is increased to generate an ascending stream of 1 cm diameter bubbles spaced at 10 cm intervals, each bubble disturbs the water column due to the large difference in specific gravity between the gas and water. As a consequence of the turbulence, each bubble takes a separate, slightly erratic path to the surface. Interestingly, if the gas flow is slightly increased, every third or fourth bubble can be seen to accelerate, follow, overtake, and merge with the one just above it. This is apparently due to a funnel-like channel of upward-moving water created by the captured bubble which entrains the pursuing bubble. The coalesced (enlarged) bubble often then immediately breaks into smaller bubbles. The bubble cannibalization process described here apparently is unique to the literature and it is suggested here that the implied channeling structure in the water should be considered the cause of the linear cohesiveness of the volcanic plume cumuli or the smoke from a chimney or fire. Apparently, it is this type of channel which racing car drivers and ice skaters utilize (drafting) as they more easily follow leading competitors. Additionally, the contrails of jet planes often exhibit a periodicity similar in origin to bubbles leaving a submerged tube, except that the tube (jet) is moving and the "bubbles" are stationary. This contrail periodicity is also generally ignored in the literature. [22]

A similar pattern, produced by dust, is all too often seen in television commercials for fast-moving cars racing across playa lakebeds in the American southwest. Of greater importance, however, are the linear patterns which develop in natural clouds as previously described [23].

Malkus (1963) describes polygonal arrangements of cumuli, similar to experimentally derived Bénard convection cells which apparently can elongate into cloud rows if a minimal wind speed is achieved. Significantly, each cloud row is itself commonly comprised of evenly-spaced first-order cumulus clouds, here considered to be the result of axial compression of each row, with periodic upwelling of warm moist air into the colder zone of condensation as the cumuli expand against each other. The distortion imposed by Couette flow may be similar to that generated within the rubber monofilament model, as described here for stream meandering, except the sinuosity generated is in the vertical plane (into colder regions) because of the lack of any constraint (the glass plate surfaces (or gravity for the stream)). To demonstrate this, another physical model comprised of a 50 by 3 by 0.5 mm thick strip of hot melt adhesive flattened between clean plate glass surfaces can be distorted, due to spaced overrolling, into thickened and thinned portions as the upper glass plate is moved parallel to the long dimension of the strip (Fig. 17). This model mimics wind or water current structure during the development of ripple marks in sand, rippled altocumulus clouds (mackerel sky), ascending evenly-spaced cumulus clouds in cloud rows, or drag folds in rock strata. It is important to note that the thickened, clearer portions elongate axially, due to overrolling, perpendicular to the motion of the upper plate, and represent ripple troughs deepening and elongating in a direction perpendicular to the direction of the current. The elevated, thinner regions represent ripple crests.

As with my beach cusp and stream meander observations and the ripple model mentioned here (Fig. 17}, it appears that the incoming wave, the flowing stream, or the surface wind can become intrinsically structured, and the role played by sediment in all three environments during erosion, transportation, and deposition is essentially collateral.

TECTONIC ARC SERIES

Another familiar phenomenon that could be ascribed to aligned salient formation is the development of island arcs and associated structures. If we consider that a series of arcs is the result of extensive tectonic plates overriding a portion of the crust, and that salients of a similar magnitude all point toward the overridden surface and are separated by angular, rearward-pointing zones of retarded motion, we then have the definition of fluid salient formation operating on a grand scale over millions of years.

Arcuate tectonic structures of similar size have long been recognized but no satisfactory explanations were provided prior to the general acceptance of plate-tectonics (Jacobs, Russell, and Wilson, 1974). The familiar suggestion that an arc is structurally similar to a portion of the circular indented surface of a ping pong ball (Frank, 1963) may account for the general shape and cross-sectional structure of an arc in light of plate tectonics, but it does not explain the development of a connected series of segments of circles (arcs) of similar size and orientation.

Scholz and Page (1970) suggest that the surface area of the lithosphere must be reduced either by thickening of the downthrust plate or conserved by lateral buckling. They prefer buckling, similar to that seen at the edge of an old-fashioned bottle cap, as the cause of the development of island arc series in the North Pacific. Utilizing earthquake foci to contour the tops and bottoms of descending lithospheric plates, Stoiber and Carr (1971) indicate that the resulting downplunging folds in the plates represent a (lateral) shortening of the plates. Both papers, therefore, are not in conflict with the concept of lateral compression being involved in the development of salient-like arcs in the overriding plates.

Scholz and Page (1970) also argue that if one end (edge) of the downgoing slab is free, the result would be a straight hinge line ("arc") as in the case of the Tonga-Kermadec arc. In a similar fashion, the unusually straight coast of Chile, with its lack of a southern off-shore trench or deep focus earthquakes to the east, the presence of islands in the sinking portion of the coast in the south, and the southern tapering of the continent could all be attributed to a lack of lateral (northward) compression of the southern end of the Chilean "arc". This is apparently due to the separation of southern Chile from Antarctica as evidenced by the eastward thrust of the intervening Scotia plate. This plate abuts the southern free edge (Scholtz and Page, 1970) of the Chilean slab resulting in the straight hinge ("arc") and coastline, and may represent the return flow of Pacific mantle material into the expanding Atlantic Ocean basin. The motion of the Scotia plate only modestly affects the shapes of both Cape Horn and the Antarctic Peninsula. The arcuate shape of the west coast of South America from Peru northward would result from the lateral compression of the northern portion of the continent, between Chile and the Nazca and Caribbean plates. Interestingly, the last salient and the adjacent straight portion at either end of the distorted rubber monofilament, where there is also little axial compression, (Fig. 1) strongly resemble, in form and proportion, the Pacific coastline of South America.

Continuing the analogy with evenly-spaced fluid salients, the zones of retarded flow (retarded forward motion) between primary arcs, assisted by the underthrusting plate in the interarc region, might act to develop rearward-thrusting crustal stresses (Figs. 18-19). This would result in the development of secondary arcs (Jacobs, Russell, and Wilson, 1959; Scheidegger, 1958), as on the west coast of North America, which lie well inland between the primary arcs and point in the opposite direction (Fig. 20). These secondary arcs are shorter than associated primary arcs, appear as discontinuous inland mountain ranges or folded basins running from central Alaska to southern Mexico, are not associated with deep-seated earthquake activity or volcanoes, and are considered to be near-surface decollement (Badgley, 1965), produced by gravity gliding (Bally, Gordy, and Stewart, 1966) or strike-slip motion along lineaments which radiate rearward from primary arc junctions (Jacobs, Russell, and Wilson, 1959; Scheidegger, 1958).

Tentatively, the rather even spacing of the inner island belt of the Lesser Antilles, running from Grenada (including The Grenadines) to Saint Kitts ("ignoring" Nevis), suggests possible locations of secondary salients (or retarded zones), involved in the generation of localized volcanism, on the primary salient of the Lesser Antilles arc.

Finally, several uniform series of salient-like structures (ice cusps) separated by rearward-pointing junctions have been detected on the surface of Europa, one of Jupiter’s moons, suggesting another extraterrestrial version of fluid structuring.

CONCLUSIONS

and the plunge pools of waterfalls come to mind, but Allen (1971) also mentions his clefts and tunnels appearing in fresh-water plumes and salt wedges in estuaries and in carbon dioxide and methane flows on the floors and roofs of tunnels.

The glass plate-rubber monofilament models presented here (as related to rocking trough and stream plate experimentation) to explain salient formation or stream meandering are simple, easily observed, persuasive arguments which cannot be ignored. Additionally, the hot melt strip model is a simple and obvious explanation for the production of cloud rows with periodic cumuli, ripple marks, or drag folds in rock strata. A dimensional analysis study to explain the spacing of the rolls would be of interest. The production of evenly-spaced water salients and intervening sand "deltas" in the rocking trough are also simple mechanisms which are easily produced and studied.

The lack of any recent, definitive explanation for the formation of beach cusp series is significant as is the lack of observational evidence, in any environment, for Langmuir’s horizontal, paired roller vortices. One most also remember Langmuir’s own observations which support fluid salients and which detract from the concept of paired roller vortices. The monofilament model is also useful in demonstrating series of hairpin vortices and an understanding of the parameters involved in their formation in that model would be of interest.

Because of the destructive nature of wind shear, thunderstorms, and tornadoes, their re-examination in the light of what has been discussed here seems warranted. With a view toward predictability, a measure of salient size and strength and observed spacing along squall lines and within tornado swarms might be useful.

I would also emphasize that the salients generated by a fluid moving across a planar surface are essentially two-dimensional, distorted versions of the more primitive equant structures seen in cumuli. A less than striking display of salients in any situation suggests an environment of formation involving a less than optimum release of energy.

The importance of Taylor vortices to turbulence cannot be understated. To reduce the drag on an airplane wing or within an oil pipe requires an understanding of how and why Taylor vortices and ensuing turbulence form. It is hoped that a consideration of fluid salients will aid in that pursuit since little has been suggested in the literature as to the cause of Taylor vortices. With increasing energy, laminar flow induces salient formation which can give rise to wavy (meandering) flow. Variations in the Taylor-Couette apparatus and increase in rotational speed can induce, among other phenomena, secondary vortices suggestive of the development of at least second-order salients as a system proceeds to fully turbulent flow.

Returning to the kitchen briefly, the planar and globoidal (cumuli) salient models described there offer homey reminders of the ubiquitous nature of fluid salients.

Regarding the general structure of tectonic arc series and the various associated arguments presented here, if we accede to Occam’s injunction that we not multiply entities, it would appear then, that arcs, and all the diverse phenomena discussed in this paper, derive from the same mechanism.

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Michael A. Gorycki, Ph.D.

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New York, New York 10010

REFERENCES

Allen, J. R. L., 1971, Mixing at Turbidity Current Heads, and

Avsec, D., 1939, "Thermoconvective Eddies in Air. Application to

Meteorology." Air Ministry Works, Institute of Fluid

Badgley, P. C., 1965, Structural and Tectonic Principles, Harper

and Row, New York, pp. 521.

Bagnold R. A., 1953, The Surface Movement of Blown Sand in

Relation to Meteorology: Desert Research (UNESCO Symposium),

Jerusalem, Israel. p. 89-96.

Bally, A. W., Gordy, P. L., and Stewart, G. A., 1966, Structure,

Bénard, H., 1901, Les Tourbillons Cellulaires dans une Nappe

Liquide Transportant de la Chaleur par Convection en Regime

Brown, R. A., 1991, Fluid Mechanics of the Atmosphere

(International Geophysics Series, ed. 1, p. 47.

Coco, G., O’Hare, T. J., and Huntley, D. A., 1999, Beach

Fechtmann, C., Wulf, P., Egbers, C., and Rath, H. J., 1997

Folk, R. L., 1971, Genesis of Longitudinal and Oghurd Dunes

Frank, F. C., 1963, Curvature of Island Arcs: Nature, v. 20, p.

363.

Gorycki, M. A., 1973a, Hydraulic Drag: A Meander-Initiating

Mechanism: Geol. Soc. America Bull., v. 84, p. 175-186.

Gorycki, M. A., 1973b, Sheetflood Structure: Mechanism of Beach

Cusp Formation and Related Phenomena: J. Geol., v. 81, p.

109-117.

Hanna S., 1969, The Formation of Longitudinal Sand Dunes by

Idso, S. B., 1974, Tornado or Dust Devil: The Enigma of Desert

Whirlwinds: American Scientist, v. 62, p. 530-541.

Inman D. L., and Guza R. T., 1982, The Origin of Swash Cusps on

Beaches: Mar. Geol., v. 49, p. 133-148.

Jacobs, J. A., Russell, R. D., and. Wilson, J. Tuzo, 1959, Physics

and Geology, McGraw-Hill, ed.1, pp. 424.

Jacobs, J. A., Russell, R. D., and. Wilson, J. Tuzo, 1974, Physics

and Geology, McGraw-Hill, ed.2, pp. 622.

Komar P. D., 1972, Relative Significance of Head and Body Spill

Langmuir I., 1938, Surface Motion of Water Induced by Wind:

Science, v. 87, p. 119-123.

Lueptow, R. M, and Min, K., 1994a, Circular Couette Flow with

Lueptow, R. M, and Min, K., 1994b, Hydrodynamic Stability of

Viscous Flow between Rotating Porous Cylinders with Radial

Flow: Physics of Fluids v. 6, p. 144-151.

Malkus, J. S., 1963, Cloud Patterns over Tropical Oceans: Science,

v. 141, p. 767-778.

Marmanis, H., and Thoroddsen, S. T. 1966, Scaling of the Fingering

Masselink, G., and Pattiaratchi, C. B., 1998, Morphological

McLeish, W., 1968, On the Mechanism of Wind-Slick Generation: Deep

Sea Research, v. 15, p. 461-489.

Rudowski, S., 1964, Beach Cusps on the Polish Coast of the

Russell, R. J., and McIntire, W. G., 1965, Beach Cusps: Geol.

Soc. America. Bull., v. 76, p. 307-320.

Scheidegger, A. E., 1958, Principles of Geodynamics, Springer-

Verlag, Berlin ed. 1, pp. 280.

Scholtz, C. H., and Page, R., 1970 Buckling in Island Arcs: Amer.

Geophys. Union, Trans., v. 51,p. 429.

Simpson, J. E., 1969, A Comparison between Laboratory and

Simpson, J. E., 1972, Effects of the Lower Boundary on the Head of

a Gravity Current: J. Fluid Mech., v. 53, p. 759-768.

Snow, J. T., 1984, The Tornado: Scientific American, v. 250, p. 86-

97.

Sparrow, E. M., and Husar R. B., 1969, Longitudinal Vortices in

Stewart, R. W., 1969, The Atmosphere and the Ocean, p. 27-38, in

Stoiber, R. E., and Carr, J., 1971 Lithospheric Plates, Benioff

Strahler, A. N., Physical Geography (John Wiley & Sons, New York,

ed. 3, 1969), Figs. 12.4, 12.5, P. 202.

Tesar V., 1997, Basic Fluid Mechanics (Hypertext Textbook for

CVUT Engineers, Czech Technical University in Praha) 1.

Weisberg, A. Y., Kevrekidis, I. G., and Smits, A. J., 1997,

Werner, B. T., and Fink T. M., 1993, Beach Cusps as Self-

Organized Patterns: Science, v. 260, p. 968-971.

FOOTNOTES and WEBSITES

[3] The New York Times, Tuesday, August 10, 1993, p. C4.

[9] The New York Times, Tuesday, May 11, 1999, p. F1.

[19] The New York Times, Tuesday, January 16, 2001, p. F1.

[21] The New York Times, Tuesday, January 2, 2001, p. F1.

EXPLANATION OF FIGURES

Fig. 1. A 0.4 mm diameter cylindrical rubber monofilament pressed between two glass plates. The flattened filament here is 1 mm wide. Motion of the upper plate, perpendicular to the length of the originally straight monofilament, causes sinuous, evenly-spaced curves to be simultaneously generated in the monofilament. This is the model for aligned, evenly-spaced, salient formation generated by a fluid moving across a plane. All rotation of the cylinder is in the same direction (see Fig. 14). Note the similarity of the straight portion and first salient (at either end) with the Pacific Coast of South America where it is suggested that a lack of compression, due to the Scotia plate, has caused the coastline of Chile to remain straight.

Fig. 2. A portion of the arcuate leading edge of a first-order salient (1) in the swash zone of a beach face. Note that three second-order salients (2) are present in one area, and third-order salients (3) fringe most of the first-order salient. This suggests a fractal-like structure, and that fluid salients are equivalent to hairpin vortices at the leading edge of a moving fluid (see footnote 1).

Fig. 3. Fluid salient formation at the leading edge of water flowing over the surface of rocking trough inclined 3 degrees. The salients at this moment are about 7 cm apart and are separated by turbulent zones of retarded flow. Scale line is 10 cm long; arrow shows direction of water motion.

Fig. 4. Sand, strewn upon the trough surface becoming organized into evenly-spaced rearward-pointing structures (submarine "deltas" seen between cusps) as the moving salients bilaterally and frondescently sweep the sand aside to generate the deltas or forward to add sand to a cusp. Note that similar wind action would produce longitudinal dunes grading into parabolic dunes. Salients are about 5 cm apart. Scale line represents 20 cm; arrow shows direction of water motion.

Fig. 5. Zone of retarded flow centered between two large primary salients and cusps. Note "V" shape of mutually interfering edges of adjacent salients and the small waves seaward, generated by bottoming over the submarine delta centered between cusps.

Fig. 6. View of a series of evenly-spaced primary salients advancing on Jone’s Beach, Long Island, New York. Submarine deltas, located between the salients, control the location and spacing of the salients.

Fig. 7. An idealized diagram showing three primary salients (S) approaching an established cusped beach. Lateral spreading of the salients produces turbulent zones of retarded flow (TZ) between the salients. Arrows indicate upbeach direction of water motion. Sand particles are moved frondescently and become deposited in the turbulent zones to form submarine deltas (SD), seaward of the bays. Return flow of water from the cusp areas is rapid, shapes the cusps, and also causes excavation of the bays. The return flow, in combination with the submarine deltas, also initiates development of retarded zones (which determines the location and spacing of the salients) in the next wave. On an initially uncusped beach face, it is the development of fluid salients and associated retarded zones in an approaching wave which initiates a cusp series. Note the higher-order (smaller) salients on the edges of the primary salients and that water motion in the salients on the cusps is opposite to what it would be if simple wave refraction were taking place.

Fig. 8. A; Idealized diagram showing longitudinal sand dunes (and associated parabolic dunes) (stippled) formed as the result of fluid salients developing in a persistent wind blowing across a sandy desert. Fluid salients (S) are located on the axes of the parabolic dunes (or between longitudinal dunes). Sand is swept frondescently onto the dunes (compare with Fig. 4). B; Section across the ridges at right angles to the direction of persistent wind motion showing the lateral component of wind motion in the salients (arrows) which may also produce evenly-spaced cloud rows at height above the ridges. Once established, the ridges determine the location of retarded zones (and, therefore, salients) in subsequent winds of similar velocity and direction. Other longitudinal, evenly-spaced subaerial and subaqueous structures may be similarly formed. Fluid salient structuring of wind appears to be responsible for what is called Langmuir circulation cells (more complicated, long helical-vortex rolls with axes parallel to the wind flow) ostensibly operating in the upper layer of the ocean or large lakes.

Fig. 9. Evenly-spaced salients seen in a density current produced by colored, saturated salt solution moving beneath standing water. Fresh water enters the flow both along its upper surface and within the retarded zones (clefts or tunnels) between the salients. Intermixing of current and standing water is apparent as elongate variations in color density of the current. Bar is 1 cm long.

Fig. 10. Relationship between fluid salients described in this paper and assumed paired horizontal roller vortices from the literature. (A) Elongate, evenly-spaced sand dunes in cross-section accumulating as lateral components of the structurally more simple salients denude the inter-dune surface, sweep sediment down-wind and deposit it in zones of retarded flow. The same components would comprise a retarded zone for the location of a streak on water. (B) An assumed series of more complicated, Langmuir-like, paired horizontal roller vortices from the literature inferred to have the same effect. (C) Cloud rows generated by updraft of mutually interfering salient edges. Aligned fluid salients, acting at altitude, may also produce cloud rows. See Figure 8.

Fig. 11. Thunderstorm squall lines seen on a radar screen. Note evenly-spaced patches in the upper right depicting individual cells. (after Strahler, 1969).

Fig. 12. A diagram showing fast-moving wind overrolling air near earth’s surface. If energy of the system is sufficient so that fluid salients form due to axial extension of the overrolling cylinder, the salient would tend to experience uplift as suggested by Komar (1972) and Allen (1971) at the head of a density current due to interaction with an invaded fluid. Warm air in the cylinder would then rise into the hairpin-like vortex to produce a tornado. [9]. As described in the text, conditions tend to promote the tornado forming from the counterclockwise-rotating limb, as the clockwise-rotating limb is suppressed.

Fig. 13. Schematic diagram of a plane attempting to land, traversing a zone of wind shear due to an encounter with a fluid salient. The plane encounters uplifting headwinds at the edge of the salient (head region) causing the pilot to reduce power and speed to reduce lift. The plane then enters the region of overrolling and looses altitude further. The plane then reaches the other edge of the salient (combined with a zone of retarded flow) and encounters tailwinds which cause the plane again to loose speed and altitude. The plane may then stall and/or not reach the runway.

Fig. 14. A cylindrical rubber monofilament pressed between two glass plates. Motion of the upper plate, parallel to the originally straight monofilament’s length, causes sinuous, evenly-spaced curves to be simultaneously generated in the monofilament. This is the model for hydraulic drag which apparently is responsible for sinuous and meandering flow in streams and wavy Taylor vortices. While it looks very similar to Figure 1, the distortion of the monofilament is quite dissimilar. There is an alternation in the direction of overrolling between the bends on one side of the sinuous filament compared with those on the other, with alternate twisting of the monofilament at successive bends.

Fig. 15. Dilational, centrifugal cumulous cloud formed by rocket exhaust spreading on ground surface. Note evenly-spaced scalloped cumulous salients at the periphery.

Fig. 16. Centrifugal (radial) salients forming ink splotches. The difference in splotch appearance is merely a function of the distance each drop has fallen (25 cm versus 180 cm) onto heavy paper resting on a shock-absorbing substrate.

Fig. 17. A 60 by 3 by 0.5 mm rectangular strip of hot melt adhesive (LITE-LOK 70-003A, National Starch & Chemical Company, Bridgewater, N.J.) pressed between plate glass surfaces. The upper plate has been translated in a direction parallel to the long axis of the strip. Note the periodic rolls which have developed due to Couette distortion of the strip. The rolls represent locations between ridges in sand ripples and could be the cause of mackerel sky or drag folds in rock. The strip is cut from a film produced by gently melting and cooling the adhesive between spaced, plate glass sheets, using adequate ventilation.

Fig. 18. Diagram showing the relationship between primary and secondary arcs (from Badgley, 1965).

Fig. 19. Diagram showing the relationship between primary and secondary arcs (from Badgley, 1965).

Fig. 20. Diagram showing relationship between coastal primary and inland secondary mountain arcs (here, salients and zones of retarded flow) for the west coast of North America. Strike-slip motion along lineaments (not shown) or gravity gliding, aided by possible landward underthrusting, responsible for the secondary arcs situated along conflicted retarded zones between salients (derived from Figs. 18 and 19).