Linear Structures and Fluid Salients
THE STRUCTURING OF MOVING FLUIDS
Linear Structures and Fluid Salients
(The Structuring of Moving Fluids) [5]
Michael A. Gorycki, Ph.D. (Revised August 19, 2018)
ABSTRACT
The importance of salients to the structuring of moving fluids in a number of natural and laboratory phenomena has been discussed in my other web sites. Included in the present web site are additional comments and simple experiments and/or arguments for additional phenomena which I believe also involve the mechanism of linear fluid salient formation. These additional phenomena include: the familiar pattern produced by rainwater running down a driveway (here termed runoff wave trains), rising smoke columns, periodic volcanic clouds, automobile dust cloud trails, bullet schlieren photography, the structuring of jet contrails and the formation of von Karman vortex streets. Meandering streams are also considered to be linear, but are discussed in a separate essay [6]. Doubtless, there are still other examples of the linear fluid salient mechanism to be recognized.
Current thought holds that laminar flow gives way to turbulence if the speed of a flow regime exceeds a certain limit, identified as the critical Reynolds number. A number of researchers also find that there is a phase between laminar flow and true (sensu stricto) turbulence, called transitional flow. These observations are often restricted to flow in pipes. I suggest that laminar flow gives way to a knobby structure (fluid salients) in water flowing through a pipe and also made visible as water flows out of a hose. This structuring is commonly considered to be turbulence [3]. The “conical” ribbon in a smoke column often exhibits drag folds (Couette flow) which I also consider to be fluid salients. It then becomes true turbulence at the highest point of the smoke column [4] when the drag folds enlarge, slow and collide. Since the phenomena in which the fluid salient mechanism appears are so diverse, I would suggest that fluid salients are, in fact, the transitional flow between laminar flow and true turbulence (sensu stricto). Also, the transition from laminar flow to the growth of fluid salients is achieved by the laminar flow reaching a critical speed. The formation of the fluid salient structure, which often takes up a large volume, causing a later reduction in the overall speed of flow in some phenomena, which then deteriorates into true turbulence.
INTRODUCTION
As described in this and my other web sites,
[1] Fluid Salients and the Structuring of Moving Fluids
[2] Fluid Salients and the Formation of Beach Cusps
[3] Fluid Salients and Spiral Galaxies and Other Vortices
[4] Fluid Salients and the Formation of Round Phenomena
[5] Fluid Salients and Linear Structures
[6] Fluid Salients and Stream Meandering
[7] Fluid Salients and the Jet Stream
[8] Fluid Salients and Planar Structures
a variety of natural or laboratory phenomena can be attributed to what I call the fluid salient mechanism. These are evenly spaced salients, separated by zones of retarded/reversed flow, which form in fluids when the laminar flow velocity is exceeded [4], [6]. I would additionally suggest that turbulence develops as a consequence of the slowing and deterioration of the developed fluid salient structuring. This sequence is seen in driveway runoff, in a column of smoke rising from a cigarette, as a straight stream develops sinuous flow on the stream plate, or during the development of what is considered turbulence in the flow within pipes. That is, in some instances, it seems that fluid salient structuring is both a forerunner to, and is responsible for, turbulence.
General Remarks
For convenience, some general remarks will be repeated here. As mentioned in my web sites, individual salients themselves can take on various shapes including: having parabolic tips as seen in beach swash [2], with curled edges as in density currents or Taylor vortices [8], as generated from descending drop toroidals in a fluid, ink splotches, shield-shaped as in Bènard structuring, and cumulous as in clouds of various origins (volcanic, atmospheric, explosive, dust, debris, etc. [4]).
Overrolling of laminar flow is important to fluid salient production and depends upon the conditions of formation of each phenomena produced, as well as the observer’s perspective. Underrolling may also occur, but the end result is the same: extension at right angles to the direction of motion which then leads to compression causing the production of evenly spaced salients with intervening retarded zones of reverse flow. Consequently, the terms overrolling and underrolling can often be used interchangeably. Extension/compression can occur in axial, planar, and circumferential structural conditions.
Various names have been applied in the literature to what I call fluid salients. These include Bénard circulation cells, Langmuir circulation cells (paired counter-rotating horizontal vortices), tectonic arcs, Taylor vortices, turbidity current lobes and associated clefts and tunnels, fingering patterns or rim perturbations of impacting drops, longitudinal vortices, reversing helicoidal flow, hairpin vortices, cumulous structure, wind shear, circular and polygonal hydraulic jumps, von Karman vortex streets, Hele-Shaw flow, etc. I consider some of these designations to be discredited because the mechanism originally invoked does not seem to be operating, and all seem to be variations of the evenly spaced salients separated by zones of retarded flow which I originally described in an earlier paper (Gorycki, 1973a).
I also suggested in my earlier web site [1] that fluid salients are ubiquitous and legion, and that the list presented of phenomena generated by the operation of fluid salient formation was probably incomplete. Following are several I would like to add to the list as linear phenomena, along with some already described that require additional comments. As a conceit, a number of asides have been included in the discussions of the various phenomena. It is hoped they add to the argument. In summary, most, if not all, repeated structures (periodicities) involving moving fluids, seem to be the result of the operation of the fluid salient mechanism.
I have grouped these linear phenomena under several headings. They are:
Runoff Wave Trains
Speech, Bodily, and Other Sounds
Rising Smoke Columns and Meanders
Flickering Candles
Periodic Volcanic Clouds
Periodic Volcanic Clouds
Car Dust Trails
Bullet Schlieren Photography
Jet Contrails
von Karman Vortex Streets
Fluttering Flag
Runoff Wave Trains
As the result of runoff during heavy rains, gently sloping to steep roads and driveways often exhibit a familiar succession of similar, evenly spaced waves running downslope (Fig. 1)
Fig. 1. Photo of familiar driveway runoff wave train formed on a paved surface, and moving toward the observer. The waves are evenly-spaced and separated by zones of retarded flow.
Commonly, the runoff water becomes directed into narrow, smoothed, elongate, channels or troughs, formed by repeated contact of car tires with the pavement. I have observed this phenomenon for a number of years, and I suggest that its cause is due to the fluid salient mechanism.
For convenience, I would like to introduce the term runoff wave train for an evenly spaced series of identical water waves that bodily move downslope under the influence of gravity. Each wave in a runoff wave train on a driveway can be broken into four portions. Just downslope of any wave crest the surface of the channel is covered with a relatively slow moving, thin layer of water exhibiting laminar flow. Due to shearing, faster moving upper level water from that first region drains downslope into an increasingly thicker layer of laminar flowing water. This second portion is transitional with (and contributes downslope to) the overrolling and slowed third portion, the cascading wave crest. This combination of evenly-spaced salients separated by zones of retarded flow is the definition of fluid salients. This thickest portion may or may not show a second order array of fluid salients, separated by zones of retarded flow, that is formed when a critical velocity and thickness of the primary (first order) fluid salient is attained. These salients result from overrolling and inhibited lateral extension of the forward edge of the wave due to the constricting cross-sectional profile of the tire-formed trough and the contact with the slow moving thin zone of the preceding wave. This zone of secondary fluid salients can give rise to a slowing, fourth, turbulent, forward edge, if the flow is sufficient, thus exhibiting the transition from laminar to fluid salients to turbulent flow.
Again, each wave on the driveway is slowed because of the expenditure of energy in primary salient formation, leading to the possible turbulence in the forward region of the wave. The slowing of each crest allows the zone of the wave just ahead to become effectively drained as its water is conferred downslope to the crest in front of it. Thus, the leading edge of any crest is provided with a drained region upon which slowing, overrolling, possibly salient formation, and turbulence may develop. It is obvious that flow is insufficient, the surface of the driveway is not hydrophobic and a meandering stream will not be produced as with the stream plate [6].
The spacing between wave crests and water volume of each wave likely are functions of runoff volume, depth, slope, speed, viscosity, channel smoothness, channel (trough) profile, etc. An excess of water will simply produce a heavy, turbulent, continuous stream; too little water will produce a thin, continuous laminar flow. If the channel becomes constricted for a short distance, a runoff wave train deteriorates to form a continuous turbulent stream until the effective channel cross-section is resumed at which the runoff wave train will resume. Apparently, the flow regime for fluid salients has been temporarily exceeded in the constricted region so that a structuring cannot occur. Each wave is usually crescent-shaped (convex downslope) due to the greater depth of the trough at its center and the consequent minor increase in velocity in that region. The edges of the crest can be slowed because of lesser water depth in those regions.
The Llyn Brianne dam slipway on the River Towy in Wales produces evenly-spaced runoff wave trains (fluid salients) on a grand scale as opposed to those seen on a typical driveway. The reduction in slope further down the spillway leads to the production of the overrolling, slowed, waves. Because of the broad, flat cross-section of the slipway, a few second-order salients may be seen across the width of each wave, but the runoff wave train structure is unmistakable <A>.
The above discussion of driveway runoff offers a clear, readily observed, and easily studied example of the transition from laminar flow (with increasing thickness), to overrolling with lateral extension, to slowing, due to a possible array of second-order fluid salients followed by turbulent flow. This allows the preceding wave to drain. This structuring is dispersed downstream within each wave if a critical flow regime is attained. Runoff wave trains do not seem to be recognized in the literature.
As an aside, a stream of water running down a hydrophilic surface such as rain on a car windshield produces a simpler flow pattern. If a hydrophilic glass plate is used as a stream plate [6], the first part of the flow can be featureless. Further downstream evenly spaced waves form. If ink is injected with a micropipette, a single, straight ink filament forms close to the glass surface along the whole length of the stream. The filament is very slow moving and is unaffected as it is overridden by the waves above it. The even spacing of the waves suggests that an array of fluid salients do form in this phenomena. The flow is not fast, the substrate is smooth and not too steep (about 30 degrees), and the waves widen downstream by lateral extension (Fig. 2).
Fig. 2. Runoff wave train of fluid salients running down a mirrored hydrophilic glass stream plate. Depending on the flow rate and angle of flow, the upper half of the flow may not exhibit waves. The waves present may be single and evenly spaced or, as shown here, accompanied by preceding capillary ripples along the length of the stream. Notice the widening downstream. There is no array of secondary fluid salients in each main wave, but the pattern is very similar to driveway runoff wave trains.
As a wave flows, it becomes wider, and drains the area behind it, causing the laminar flow there to be thinner and slow. At the head of the wave, where the water is thicker, it may be overrolling because it is slowed, and encounters the drained area of the preceding wave. There, the water is thinnest, slowest moving, and also acts to retard the overrolling flow of the following wave. Capillary ripples may precede each main wave.
The wave is rounded and widens downstream as it spreads. Less mass at the edges results in thinning and slower forward motion on the planar glass surface. With driveway runoff, a thicker central flow can be aided by a depressed trough produced by tires and also by contribution of water from the edges to the central flow. The result, again, is a curved wave that is slowed while moving downslope and, possibly, a slowing turbulence.
A structuring similar to runoff wave trains can be seen in evenly spaced ocean waves, under constant prevailing wind. This is also the result of drag folding (planar fluid salients [8]). Here, the waves are not constrained laterally so as to cause extension/compression, but spread and increase their lengths at right angles to their direction of motion (see Current Ripples and Drag Folds [8]). The motivating force of the ocean waves is the wind; for driveway, or windshield runoff, it is gravity.
What is of interest in Fig. 2 is that this flow pattern is similar to the driveway runoff pattern (Fig. 1). They conform to the definition of fluid salients in being evenly spaced, and alternating with intervening zones of retarded flow in the ratio of 1:1 [2]. Again, I suggest that it is the thickening, overrolling, and slowing of fluids that leads to the development of fluid salients. True turbulence does not occur in this experiment.
Runoff wave trains may also be seen in decorative Gardenfall fountains.
Speech, Bodily, and Other Sounds
It seems that human speech and the other sounds that our bodies can produce are the result of the fluid salient mechanism. To briefly defer, the emptying of a 4 fl oz Ocean Spray® juice container simulates this. If we peel back the opening tab so that it forms an equilateral triangle with its base measuring 2 cm, the foil cover oscillates to produce a long stream of evenly spaced fluid salients that empties the container, but at an inaudible pitch.
Human speech and the action of the vocal cords has been likened to air escaping from the laterally stretched neck of an inflated balloon. Here, the fluid (air) is expelled in evenly spaced, equal amounts that are controlled by the air pressure in the balloon, tension of the rubber neck, and the time it takes for each salient to be ejected. Unlike the juice, the bursts of air can produce an audible pitch that can be varied by the tension of the rubber. The intensity depends on the force or pressure of each salient, and the intermittent cessation of sound is part of the definition of the mechanics of fluid salients. I think we can permit the “Bronx cheer” to be included as a part of human speech. Its mechanism occurs solely in the mouth, but it does convey a simple thought, and its mechanism of origin is similar.
Esophageal and anal sphincter muscles have a different anatomy and action when compared with the vocal cords, but I suggest that the fluid salient mechanism is still operational. The vibrations are caused by the alternation of high and low air pressure and we must conclude that speech as well as the sounds most musical instruments make are related to the other phenomena listed here ([1]-[4], [6]-[8]).
Rising Smoke Columns and Meanders
A pattern of dispersion, in which laminar flow, fluid salient formation, and true turbulent flow appear in sequence, similar to driveway runoff may also be observed in smoke columns. Smoke, rising in still air from a cigarette, is usually described as having an initially laminar, straight portion that gives way aloft to turbulence (Fig. 3a).
Fig. 3a. Photo from Resnick (et al.,) which ignores the middle, most interesting (fluid salient) portion, of the smoke column. True turbulence, just beginning to form at the very top of the plume is also ignored. Other workers have recognized the fluid salient portion as being transitional flow, but do not offer an explanation for its production. Salients, in the form of incomplete toroidals, look to be forming a spiral just above the laminar plume because the hottest part of the plume is on the right of a cone that has been formed and the salients are tilted down to the left. The fifth salient seems to form a complete circle, but the cone is really a curved ribbon (see Figs. 4 and 5 which also show near-conical ribbons). The laminar flow portion has widened and slowed by cooling and friction with the ambient air which also causes the formation of the conical ribbon of fluid salients. The overrolling fluid salients rise further, include cooler ambient air, loose buoyancy, collide, and produce a small overlying zone of true (sensu stricto) turbulence.
As an aside, note that this image is analogous to the sinuous stream (Fig. 3b) (shown as Fig. 3 in [6]), which shows a straight, laminar stream developing fluid salient sinuosities as friction slightly slows the flow of water. Turbulence downstream is not seen.
Fig. 3b. Sinuous stream (Fig. 3 [6]) formed due to slowing of laminar flow and development of fluid salients (compare with Fig. 3a above).
Simple experimentation affords some insight with regard to revealing the fluid salient mechanism in the smoke column phenomenon. Initially, a plume of smoke, rising from the smoldering end of a length of 5-mm diameter cotton rope, is centered at the base of a vertical, open-ended, transparent cylinder about 11 cm in diameter and 15 cm high. A suitable cylinder can be cut from a clear plastic two-liter soft drink bottle with its label and top and bottom removed. The cylinder and smoke source both rest on an elevated, horizontal, wire mesh surface. The mesh allows entrained clear air from underneath eventually to rise vertically with the smoke through the cylinder. The plume initially produced tends to be narrow, but widens and slows slightly with distance traveled as it also cools and is affected by friction with surrounding air. It can extend a distance beyond the top of the chimney (depending on the speed of the associated clear, laminar air), where it eventually becomes turbulent without the formation of fluid salients, even in a still atmosphere. If the chimney is extended to a height of 60 cm, by nesting four cylinders together, the plume will eventually attain that height undisturbed, again, continuing to expand slightly as it rises and becomes turbulent above the cylinders. Obviously, the chimney protects the plume from extraneous air currents, and the plume ascends in a laminar fashion as it is contained by the surrounding and enclosing column of entrained, laminar, rising, clear air. When the plume and entrained laminar clear air exit the cylinders they encounter overlying air that is not part of the system. This leads to true turbulence.
In a second experiment, if the supporting screen is eliminated so that the smoke source and cylinder both rest directly on a tabletop, a very short laminar plume may form. The smoke above generates only a confused, turbulent cloud within the chimney because of the lack of any entrained ascending laminar flow of air in the system. That is, the still, ambient air slows what could be a smoke column exhibiting rising laminar flow, and the ascending smoke only causes turbulence. This experiment will be mentioned later.
In the third experiment, if the smoldering rope rests on the elevated wire mesh, and a chimney is not employed, a straight, laminar flow portion of the plume and associated entrained laminar air rises from the burn. The plume’s length can vary, depending on local conditions such as temperature of the burn, plume, and ambient air temperature and extraneous currents. If the ambient air is very still, the hot plume often forms a flat ribbon in its upper reaches because, as it rises, the plume is subject to a shearing stress caused by warmer smoke on one side to move faster than on the other. This shearing causes the formation of evenly spaced overrollings of uniform diameter (fluid salients). These overrollings incorporate ambient air along with the smoke so that the ribbon is also slowed compared to the straight, laminar, lower portion. The initial overroll is at a point where the laminar flow is overwhelmed by friction. Because of the dynamics of shearing, the overrollings maintain their similar diameters because they are constrained between the two walls of moving air having upward speeds that differ. This causes the plume of overrollings to extend along their horizontal axes, thus causing the ribbons to widen as they rise. The smoke on the hot side of the plume overrolls upward towards the cool side, whereas the surface on the cool side overrolls downward towards the hot. This shearing effect is similar to the drag folding one sees in metamorphic rocks. Commonly, the rising plume forms an incomplete, widening cone (Perry and Lim, 1978) because as additional smoke and air continue to be incorporated in the overrollings with height, the warmer axis, rising faster than the ambient air, creates a vertical draw that causes the ribbon to be everywhere pulled in towards the central axis.
I consider these overrollings to be fluid salients because they are uniform, evenly spaced, and have zones of retarded/reversed flow in the ratio of 1:1 with the salients (Figs. 4 and 5
Fig. 4 Conical, incomplete (split) column of laminar smoke which forms evenly spaced overrolls or toroidals (fluid salients) higher up in the plume. These give way to true turbulence (Perry and Lim, J. Fluid Mech. v. 88) because they loose buoyancy with height, slow, and suffer collisions. Note that the salients form from a curved ribbon.
Fig. 5. Similar to Fig. 4, but with a plume that is “s-shaped” in cross-section. The edge of the plume provides a cross-section of the evenly spaced overrolls (fluid salients). Note zone of retarded/reversed flow between each salient, with downward rotation on the outside of the plume, and upward rotation on the inside. Again, the salients do not form a spiral or a complete cone, but derive, in this case, from an s-shaped ribbon with faster upward flow along the central axis.
As an aside, when a drop of ink falls through water [4], the globule descends due to the higher density of the ink compared to the water. As a result, a single toroidal is formed. It increases its major diameter because the underrolling causes water to become entrained in the toroidal, but the toroidal ring maintains its minor diameter as it falls because the underrolling compresses the circular cylinder due to shearing. This is similar to a wave advancing up a beach face. A combination of overrolling and the shearing effect due to gravity (the weight of the wave against the beach face) causes extension/compression and thinning along the length of the wave resulting in fluid salient formation and the production of beach cusps [2]. However there is no thinning of the ring of the ink toroidal because the toroidal’s major diameter is free to enlarge. As the primary ink drop toroidal underrolls, extension/compression causes the outer portion of the underrolling ring to have a larger diameter than the inner. This cramping causes the development of downward moving salients and higher order toroidals to form at the base of the primary toroidal (see Vortex Ring Toroidals and Salient Formation, [4]. The toroidals also become slowed by the incorporation of less dense clear water. In the case of the smoke column, a widening ribbon forms because of inclusion of ambient air into the overrolling, and a closed toroidal form is lacking.
As shown in driveway runoffs (Fig. 1), laminar flow thickens as overriding occurs and may be replaced by a front of overrolling, progressively slowed, fluid salients that can become turbulent as it encounters and overwhelms the thin laminar flow of the preceding wave. This is due to water being unaffected by the overlying air. Looking at the smoke column (Fig. 3a), we see that the laminar flow portion becomes wider and is replaced by a growing, slow moving fluid salient structure. This, then deteriorates into a slowed cloud of turbulence as the fluid salients mix with the ambient air and collide with each other. Also, in the second experiment where the smoke source and cylinder rest directly on a tabletop, a short length of laminar flow smoke turns into turbulent flow without first producing fluid salients. This is because the laminar flow immediately thickens and slows as it rises a very short distance through the ambient air, involves a large volume of space, and turbulence ensues. Here, the ambient air has a great effect on the moving air. Also, in this instance, it is contrary to popular thought which has the transition from laminar flow to turbulence being caused by an increase in flow.
Increasing the flow on the tilted surface of the stream plate (Fig. 3b), causes the laminar, straight portion to generate (due to friction) a more slow moving sinuous structure caused by reversing helical flow produced by a stretching out of a series of fluid salients (see Reversing Helical Flow [6]). That is, a particle in the straight stream moves a distance downstream more quickly than a particle in the sinuous portion moving the same straight line distance. Also, in another stream plate experiment, rapid flow, coming directly from a straight nozzle, leads to braided flow (see Straight, Sinuous, Meandering, and Braided Streams [6]), which might be considered turbulent because of its erratic behavior, constantly changing course on the stream plate, and causing a number of sub-parallel channels, most of which become abandoned, as seen in braided streams in nature. A similar argument for the increase in speed of laminar flow, leading to the development of fluid salients that can be described as turbulence in pipes, is discussed in “Spheroidal, Cumulous Formation” [4].
A shear pattern similar to Figs. 1-5 develops if a 60 by 3 by 0.5 mm rectangular strip of fugitive hot melt adhesive is pressed between clean plate glass surfaces. The strip is cut from a film produced by gently melting and cooling the adhesive between spaced, plate glass sheets, using adequate ventilation. If the upper plate is translated in a direction parallel to the long axis of the strip, it forms evenly spaced salients similar to drag folds. I suggest that Couette flow is a version of fluid salients. While drag folds may be the result of Couette flow (Fig. 4), it is obvious that, given the chance, each drag fold will extend at right angles to the direction of flow. This gives rise to the lateral extension of current or oscillation ripple marks which widen at right angles to the flow as well as evenly-spaced salients (Fig. 6).
Fig. 6. Enlargement of a 60 by 3 by 0.5 mm rectangular strip of fugitive hot melt adhesive pressed between clean (unlubricated) plate glass surfaces (see Fig. 1) [8]. The upper plate has been translated (left) in a direction parallel to the long axis of the strip. Note the periodic rolls (and their dark shadow) which have formed due to Couette distortion of the strip. They have also widened (elongated) at right angles to the direction of flow. The rolls represent locations between ridges in current sand ripples and resemble a 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. The strip produces evenly spaced blebs separated by zones of stretching. The shearing effect is similar to the overrollings seen in the conical plumes of smoke (see Figs. 3 and 4). See also Figs. 1-3 [8].
The same pattern is produced by an unlubricated rubber cylinder in “Current Ripples and Drag Folds” in [8].
As an aside, in the case of beach cusps, the long dimension of the fluid salients are parallel to the direction of wave motion. The fugitive hot melt, rubber cylinder (and smoke overrollings, ripples, etc.) are at right angles to that direction. Note that for the fluid salients on the beach, the smoke overrollings, rubber cylinder, and the adhesive strip, a zone of retarded/reversed motion is present, also in the ratio of 1:1 with each fluid salient. Additionally, as mentioned in [3], the geosynchronous satellite loop of the whole 2010 Atlantic Hurricane Season <B>
<B> www.youtube.com/watch?v=o_YyTW5bjbU (see minutes 2:10-3:00)
early hurricanes; Danielle, Earl, Fiona, and Gaston are all about 5-6 seconds apart (2.10-2.26 minutes) on the video, and later hurricanes; Igor, Julia, and Lisa are all about 9 seconds apart (2.39-2.55 minutes). This even spacing of the two groups of hurricanes suggests that they originate as easterly waves, troughs of low pressure produced by shearing of the Northeast Trade Winds against the warm moist air ascending near the equator, called the Intertropical Convergence Zone (ITCZ). As a result, I feel they also might be considered to be evenly-spaced drag folds produced by the fluid salient mechanism.
Flickering Candles
Candles are designed to burn evenly, but if a candle burns unsteadily, it should be considered to flicker if the ambient air is still. If the ambient air is not still, the candle should be considered to flutter. By analogy, a flag on a pole flutters if there is a wind, but if there is no wind, the flag will not flutter, nor flicker. Flickering in a candle is obviously due to the energy provided by the flame.
Little effort has been made to explain flickering in candles, but I suggest that the width and length of the wick is critical. If the wick is of thick thread (0.4 m in diameter) and is inserted into the horizontal top (at least 10 cm across) of a large mass of wax, its burning will form a slow growing circular depression in the wax beneath the flame. It will also cause a thin layer of melted wax to achieve an equilibrium with the flame. The flame can be extremely small and steady, spherical and dim. It will merely glow without flickering or fluttering. This, because it does not have enough convective energy to noticeably disturb the ambient air around it. It simply melts the combusting wax by infrared radation. Eventually the tip of the wick will disintegrate as it turns to ash and the flame will extinguish. I had a small (3 mm in diameter), dim, spherical, blue/white flame burn for 8.5 hours which consumed 3 ml of wax. Another burned for more than 24 hours. With time, the diameter of the pool periodically lowered and decreased in size, depending on the condition, structure and orientation of the wick. To construct this candle, an awl is heated in the flame of a candle, thrust up and down until the melted wax solidifies, and a vertical shaft is formed. This is repeated until a shaft 4 cm deep is produced. A 5 cm length of wax-stiffened wick is inserted, and the candle is primed with wax from the lit candle which is caused to drip onto the shaft and inserted wick. The created candle is now ready to light. Different cotton wicks may have to be tested for this experiment.
To construct a candle which will flicker every time, the heated awl is inserted close to the wick of a half-burnt, second candle that is 2 cm diameter. The awl should form a hole about 4 cm deep along the side of the second candle’s wick. A 3 mm thick cotton string, made straight and rigid with melted and cooled wax, is inserted into the hole and cut so that a 5 mm length protrudes. Wax from the first candle is again caused to drip onto the inserted wick and hole, before it is lit.
If the wick is too stout for the diameter of the candle, it will burn fiercely and produce smoke. The pool of wax produced will overflow and pour down the side of the candle, being unable to fully rise up the wick by capillary action. This will cause the wick to lengthen and possibly collapse down the side of the candle.
When the side-by-side wicks of appropriate diameters are lit, they eventually lengthen to about 2 cm. At first, the flame will be steady and very pointed in still air, and the flame can be as tall as 20 cm. In time, a tight column of smoke, exhibiting laminar flow, will form above the flame because the candle’s new design causes a large amount of wax to melt and enter the double wick by capillarity where the wax undergoes incomplete combustion. This produces the longer flame and the smoke. The smoke can more easily be seen using a bright light and a white background. The smoke column rises, cools, slows, and broadens to form an overlying conical cloud of confused tendril-like toroidals which interfere with each other as they overroll. Above the conical cloud, the smoke becomes turbulent and then disburses. When the cone forms, the flame develops a broad, sinuous flickering structure near its top and an oscillation in thickness near the wick. This trend in the smoke from laminar flow to toroidals (fluid salients) to turbulence is suggestive of that more easily seen by the less energetic smoke column seen in Fig. 3a, where laminar flow, slowed by friction, produces a cone of fluid salients, in the form of toroidals, followed by overlying turbulence. It is also similar to von Karman vortex street, <D>
where a sinuosity originates downstream (the upper portion of the candle flame) and approaches the blunt body (the wick) because the still air is caused to form drag folds made visible in the laminar flow. Downstream broadening is also seen in von Karman vortex streets (see Wikipedia, von Carman vortex streets, “Images”).
Candle flickering can also be caused in a different manner. If, at the base of the flame, impurities collect on the wick, this can draw additional wax into the flame. This can cause flickering as the excess wax periodically and vigorously vaporizes.
I suggest that the sinuous waves of the flickering flame are similar to the smoke overrolls seen in Figs. 4 and 5, and are caused by circular drag folds (toroidals) in laminar flowing air, a linear version of the fluid salient mechanism. They surround the flame and possibly the upper part of the candle, rise due to the heat of the flame, and continue to the space above the candle where they enlarge due to incorporation of ambient air into the overrolling. Studying Fig. 3a, the lower portion of the rising smoke column represents the laminar flow at the upper part of the candle flame. The fluid salients are analogous to the toroidals around and above the flame. The confused zone at the top of the smoke column are where the toroidals increase in size by overrolling and are slowed in their ascent, collide, produce the turbulence above, and cause the inter-sporadic halt to the flickering further down at the level of the flame.
Examining the lower portion of a flickering flame during a video (see Flickering Candle Flame HD - YouTube), we see that the diameter of the wick is very large compared to the diameter of the candle. Also, the flame exhibits a uniform rhythm that causes its lower portion to thin and thicken in cadence with the upper portion that extends vertically upward a short distance and then retreats to a more stable height (use Settings Speed set to 0.25). This oscillation at the base appears to be caused by the formation of a sinuosity in the flame rushing upward. Apparently, the laminar flow portion above the flame is slowed by the overlying cone of toroidals. This slowing has a braking effect on the flame similar to the friction between the stream of water flowing down the stream plate seen in Fig. 3b.
Flickering often occurs in sporadic episodes. As the flame exhibits sinuosity it has destroyed the overlying laminar flow and toroidal structuring. When this occurs, the flame resumes its steady aspect, grows in length, and the cycle of laminar flow, etc., resumes.
Periodic Volcanic Clouds
Volcanic clouds are discussed in [4]. They exhibit a continuous cumulus flow version of fluid salients. Volcanic plumes can sometimes be periodic, which would require an uncommon eruptive mechanism. Instead, imagine a crater slowly, and continuously, filling with a pyroclastic cloud that is heavier than the ambient air. There may come a point where the hot cloud both attains a propitious size while the pyroclastics also have precipitated out. This would leave a large, less dense cloud of hot gas. The cloud will exit the crater, leaving a void to be replaced by the next, growing, dense pyroclastic cloud. If there is a steady wind, the exiting cloud will be carried from the crater’s location, leaving room for the next cloud of hot gas to continue the periodic cycle. This would explain the stretch of evenly spaced clouds exiting Popocatepetl in December of 2000 (NY Times, Tuesday, 1/2/2001). However, this periodicity, while resembling salient activity, it depends on steady volcanic activity interrelating with steady winds of an appropriate velocity.
Car Dust Trails
As described in my earlier web site [1], TV commercials often show cars traveling quickly over desert (playa lake) surfaces creating trailing plumes near the ground which immediately exhibit a linear spheroidal periodicity (Fig. 7a and 7b).
Fig. 7a and b. Repeated dust cloud trails behind cars crossing a playa lake.
A similar situation occurs if one is standing at a red light, in the rain, at the intersection of a fast-moving highway. As the cars quickly go by, a structuring of the air, similar to the dust cloud trails in Figs. 7a and 7b are seen. That is, evenly-spaced, thinner clouds of denser clusters of drops, separated by large, tenuous clouds of rain drops, appears behind each car. I suggest that each dense cloud represents a compressed volume of air from the front of the car, and the tenuous cloud may represent a low pressure volume of air containing dispersed drops that forms behind the car.
Bullet Schlieren Photography
A pattern similar to Fig. 7a and b, of axial pressure variations behind a bullet traveling through the air can result, as revealed by schlieren photography (Fig. 8).
Fig. 8. A repeated pattern of axial pressure variations in the schlieren figure behind a speeding bullet.
Jet Contrails
In my earlier web site [1] I also suggested that the periodic and spheroidal stream of first order cumuli, exhibited by the contrails of jet planes (and rocket exhausts), were examples of linear salient formation, and are examples of von Karman vortex streaks. I suggest that the bodies of jet engines and rockets produce a periodic axial expansion/collapse of the air and exhaust just behind the bulk of the engine in flight just as the cars and bullet in Figs. 7a, 7b and 8 show. See also Fig. 5 in [4].
A scenario for the development of visible contrails from a plane requires that conditions must be suitable. That is, there should be little or no shearing winds accompanying the contrails, the exhaust must contain sufficient water vapor, the atmosphere must be cold, and it should also contain a reasonable amount of water vapor. In addition, a further cooling effect is provided by expansion of the exhaust gases themselves. The exhaust is initially invisible just behind the jet engines because the gases have not cooled sufficiently to form ice crystal condensate. The two contrails behind each wing very quickly can coalesce and increase in diameter due to expansion of the hot gases. Continued expansion of the contrail gases is then expressed, along the flight path, of a linear version of a Bènard-like structure with the formation of cumulous clouds of similar size, which may eventually form second order salients (Fig. 9).
Fig. 9. A jet plane showing four contrails composed of evenly spaced, clouds of similar size. Note the absence of contrails just behind the engines due to the heat of the exhaust. Often the contrails merge producing two and sometimes one contrail far behind the plane.
It should also be noted that a pendant cloud can often be seen extending downward from each of the primary cumulous clouds in the contrail (Fig. 10).
Fig. 10. Pendant clouds of ice crystals precipitating from repeated pattern of cumuli in single contrail composed of 4 fused contrails.
These pendant clouds appear to result from subsequent precipitation and descent of accumulations of excessive ice crystals. They form if there is sufficient moisture and cooling in the expanding exhaust and in the surrounding atmosphere. Of interest here is the discreet even periodicity of the pendant clouds along a straight line because they suggest the operation of the fluid salient mechanism with intervening retarded/reversed flow for the row of single linear cumuli. This is similar to (linear) Bènard-like structuring which also exhibit retarded/reversed flow at their peripheries. Of importance here is that the car dust cloud trail, bullet schlieren figure, and jet contrail patterns are all expansion/collapse mechanisms and are similar in that they are all stationary, and the axial pressure structures created (the fluid salients) are also stationary (see my aside on standing waves in [3] Water Vortices. The point to be made here is that all these examples exhibit linear fluid salient formation as they undergo alternating axial compression/expansion and release.
von Karman Vortex Streets
Von Karman vortex streets are described as “a repeating pattern of swirling vortices caused by the unsteady separation of flow of a fluid around blunt bodies.” That is, the blunt body is the cause of the vortices. On a number of points, von Karman vortex streets are a veritable antithesis of the flow of water on the stream plate [6]. In a sense, they are a converse, or opposite version of the stream plate’s operation. This concept explains the source of the “unsteady separation of flow” mentioned in the quote.
Following is a list of corresponding, but opposing features of these two phenomena;
1) The nozzle of the stream plate dispenses a fast stream of water of finite depth down the center of a dry hydrophobic surface (Gorycki, 1973b) (and see [6]), whereas the blunt body of a von Karman vortex street creates a slowed flow, the separation, between two flowing sheets of fluid of indeterminate thickness.
2) On the stream plate the fastest flow is along the midline, furthest away from the stream’s banks. In the von Karman vortex street the slowest flow is along the midline of the separation.
3) The moving stream of water on the stream plate has mass compared to the empty region lying beyond its “banks”, while the flow of fluid on either side of the separation in the von Karman vortex street has greater mass compared to the separation.
4) Meander formation is caused by friction with the horizontal surface of the stream plate. I termed this meandering hydraulic drag (Gorycki, 1973b). The von Karman vortex street forms vortices due to friction with the two vertical surfaces of the separation. Both situations could be termed drag folding.
5) The meanders widen and migrate downstream of the nozzle as the flow is increased. The von Karman vortex street can widen downstream of the blunt body as the flow is fixed. In time, their enlargement causes them to work their way upstream as they dwindle in size until they reach the blunt body.
6) The stream of water matures from laminar flow to sinuous to meandering as the flow increases. The stream flows more quickly and the stream width also increases a modest but relevant amount, [6]. Even as the flow remains constant, the vortices and the separation in the von Karman vortex street enlarge downstream suggesting that the larger vortices of the street are slowed.
7) As the flow is held constant, the meanders cease growing and moving downstream. Again, the swirling vortices of the von Karman vortex street get larger downstream as the flow is held constant,
8) A sinuous meandering thalweg can be seen in the straight flow of water as it emerges from the nozzle (see Fig. 7, [6]). As the flow is increased, it morphs into sinuous and then meandering flow. Within the bends, evenly-spaced reversing helical flow occurs where there is “downward...overrolling” (see Fig. 10, [6]). All this is made visible by injection of ink filaments. In the von Karman vortex street, friction of the flow at the separation causes evenly spaced reversing swirling vortices to form. They are drawn from either side of the separation, toward the central low-pressure region, and form between the bends. This causes the “unsteady separation of flow”. Going downstream, the swirls alternatively reverse direction of rotation.
9) Friction of the moving stream’s mass against the bottom of the stream plate initiates the central meandering thalweg at the nozzle and reversing helical flow downstream. This meandering process shapes both banks. The von Karman vortex street is shaped by friction of the flow against the separation which then causes the reversing swirling vortices and alteration of the banks. This interaction with the banks produces the von Karman vortex street which advances upstream where it varies from side to side of the blunt body.
10) The meandering thalweg forms simultaneously along the stream which matures to meander bends, just as fluid salients form simultaneously in a wave on the beach face which starts the formation of a beach cusp series. The reversing swirling vortices start as a single, authentic perturbation on one side of the separation that initiates a series of vortices on both sides that leads to the maturation of a vortex street, (see a discussion of perturbations after the Introduction to Beach Cusps) [2].
As an aside, meandering streams exhibit reverse whorls that are evidence of retarded/reversed flow. They are the locations of point bars (see Point Bars in [6]), and indicate where sediment is able to accumulate. These are a component of the fluid salient mechanism.
The following are computational fluid dynamic simulations of turbulent von Karman vortex streets, behind obstructive cylinders. The vortex streets exhibit laminar, sinuous and meandering flow (<D>, <E>). In <D> the sinuous flow advances slowly upstream to the blunt body. In <E>, the alternating flow, advancing upstream to the blunt body, is more pronounced.
I consider von Karman vortex streets to be a combination of evenly spaced fluid salients (the curves) and associated retarded/reversed zones (the reversing swirling vortices), in the ratio of 1 to 1 (see <E>). This again is the definition of the fluid salient mechanism [6]. One should be struck by the similarity in appearances of the vortex street and a meandering stream, but observe the converse differences in the components of the two mechanisms. A comparison of the two should lead to a better understanding of both.
Fluttering Flag
The von Karman vortex street can be seen in a fluttering flag when the observer looks down the length of the flagpole. If the flagpole (blunt body) is replaced with a halyard, the flag continues to flutter. This indicates, therefore, that it is the frictional drag of the wind on both sides of the flag that causes the flutter (see Google, “Why do flags flutter?-Aerodynamic Engineering), and not the presence of a blunt body that causes the repeating pattern of swirling vortices (caused by the “unsteady“ separation of flow of a fluid). This is similar to the development of vortices on both sides of von Karman vortex streets. That is, it is the friction of the fluid flow against the separation (the flag) that produces the “repeating pattern of swirling vortices” (see Google, “Air Show Misty Blues”, on Videos). They appear to be drag folds reciprocally lifting away from both sides of the flag, similar to the one-sided fugitive adhesive seen in Fig. 6. In the video, as the folds in the flag move downstream toward the end of the flag, we note that the free end of the flag exhibits larger flutters than the attached edge. This suggests that the large flutters form first and are larger (like the downwind vortices seen in many natural or computational fluid dynamic simulations of turbulent von Karman vortex streets). In some videos these flutters (reversing swirling vortices} slow both surfaces of the separation and grow in numbers [as they decrease in size) toward the attached end of the flag, suggesting that the vortex street structuring is initiated downstream, as previously stated.
The flag may be replaced by a ribbon, thus reducing the thickness (height) of the von Karman vortex street. (This brings its mechanism closer to the structure of the stream plate supporting a sinuous or meandering stream exhibiting reversing helical flow.) Again, in the von Karman vortex street, it is the friction of the moving air against the ribbon that leads to the development of vortices (folds or fluid salients) in the air, and not “by the unsteady separation of flow of a fluid around blunt bodies.” These vortices then produce the vortex street in the fluttering ribbon or flag.
CONCLUSIONS
The varied phenomena discussed here all seem to suggest that the fluid salient mechanism is in operation. It also seems that any fluid motion between laminar flow and turbulence tends to form evenly spaced salients, including reversing helical flow, separated by zones of retarded flow. Runoff wave trains and rising smoke columns can exhibit: laminar flow, fluid salient formation and turbulent flow simultaneously along their lengths. Salients form in response to axial or lateral extension/compression within the moving fluid producing patterns; which can form at the edge of a plane, be planar, radial, cylindrical, spherical, linear, or result from a couple. Stationary salients may also be formed by moving objects. Frictional drag can produce reversing helical flow or vortices in meandering streams of von Karman vortex streets. Individual salients may exhibit a variety of shapes depending on their environment of formation. Material acted upon by fluid salients behaves in a passive manner, serving mainly to reveal the structuring of the fluid.
The point to be made here is that the concept of fluid salient formation, as a mechanism in the movement of fluids, remains a fertile ground for further thought, experimentation, and, hopefully, independent confirmation. All the experiments described here, and in my earlier web site and published papers, can be performed in a modestly equipped laboratory. That von Karman vortex streets can be thought of as an opposite version of stream meandering attests to the disparate nature of the fluid salient mechanism.
Questions, comments and criticism are welcomed and may be addressed to me at: gorycki@yahoo.com
REFERENCES
Donn, W. L., 1965, Meteorology: McGraw-Hill, Inc., Third Edition, pp. 484.
Gorycki, M. A., 1973a, Sheetflood Structure: Mechanism of Beach Cusp Formation and Related Phenomena: J. Geol., v. 81, p. 109-117.
Gorycki, M. A., 1973b, Hydraulic Drag: A Meander-Initiating Mechanism: Geol. Soc. America Bull., v. 84, p. 175-186.
Houze, Jr., R. A., 2014, Cloud Dynamics: Academic Press, pp. 496.
New York Times, Tuesday, January 2, 2001, F 1
Perry, A. E. and Lim, T. T., 1978, Coherent Structures in Coflowing Jets and Wakes: J. Fluid Mech. V. 88, p. 451-463.
Resnick, R., Halliday, D. and Krane, K. S., 1992, Physics: 4th ed., v. 1, pp. 592.
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