To: Professor Haim Tsoar, BGU, IL

CC: Wind Erosion List

Dear Dr. Tsoar,

Thank you for your informative response. Although I was not aware of it, I am not at all surprised that the thermal, helicoidal flow explanation of long, km-spaced dunes has been treated by many over the past century. As you say, it is an intuitively plausible but hardly a proven explanation.

Based on your comments and your reference to a lack of supporting experimental evidence, I am quite sure that a ‘simple’ free-convection flow explanation will not provide a full answer. Nevertheless, I thought that I might show you the key features of such free convection flow pattern, just in case it provides some clues.

The flow visualization images below are from E.M. Sparrow and R.B. Husar: Longitudinal vortices in natural convection flow on inclined surfaces. J. Fluid Mech. (1969), Part 2 pp 251-255. Today, I have scanned in the old images and annotated them a bit for clarity.

Figure 1 Heated inclined plate viewed from above. Black dye is released uniformly from the surface. Regions of convergence at the surface are black streaks in direction of the main boundary layer flow up the plate. [If applicable, the black streaks of the dye would correspond to the crest of the ripples.]

Figure 2. Longitudinal thermals along the surface of the inclined plate viewed from the bottom of the plate. The flow is helicoidal only near the surface of the plate. Once the thermal separates from the surface, it keeps rising in the neutrally buoyant fluid. This is different then the frequently observed helicoidal flows visualized by cloud streaks. In that case flow is confined to two flat surfaces ( the ground and the top of the mixing layer) and the spacing of the convergence zones is about the same as the spacing of the two horizontal surfaces.

Fig 3. Flow visualization in the boundary layer with a wire releasing the dark dye. The sharp upward flows away from the surface are the longitudinal thermal sheets. There is slower downward flow between the thermal sheets. However, there is no obvious recirculation as part of the vortex.

The real big problem with this laminar, 20 cm size water analog to the dune flow is the scaling to the large-scale, turbulent atmosphere. Today I checked out Steve Hanna’s paper that you have listed– he was wrestling with the same puzzling question. If there is any need to continue this discussion, we might ask Steve to step in.

I also meant to comment on your observation that smoke candle visualizations do not support the existence of secondary flows. Maybe it’s the intermittency of thermal flows that makes it tough to visualize them.

Fig 4 On heated horizontal surfaces, thermals are not constant flows but rise periodically with rather uniform frequency. The life of periodic thermals is made of the 3 phases, (1) the conduction phase when the layer heats up, (2) the separation phase when it reaches sufficient buoyancy to rise and (3) the mixing phase when the rising thermal ‘bubble’ mixes up the fluid near the surface and makes it ready for a renewed conduction cycle.

So, maybe it is the periodicity of such thermal flows that precludes a simple smoke visualization over the dunes.

Regards,

Rudy Husar

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From: Haim Tsoar <tsoar@bgumail.bgu.ac.il
To: "'wind_erosion@ttacs6.ttu.edu'" <wind_erosion@ttacs6.ttu.edu
Subject: RE: Desert Ripples
Date: Tue, 24 Nov 1998 11:43:02 -0800
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Dear Dr. Husar,

I read with great interest your note about desert ripples that you referred to a cork screw-like secondary flow. It's the first time that I hear about the formation of sand ripples by helical roll vortices. I am an aeolian geomorphologist and my knowledge of fluid mechanical is minimal. In my long reply I would like to show you that the literature of aeolian geology and geomorphology has referred to this type of flow (helical roll vortices) for a very long time (I enclose a long list of some of the professional literature) but only for the formation of sand dunes. However, no one was able to measure this secondary flow over and around sand dunes in the field.  

Bagnold, the founder of the field of aeolian sand transport and desert dunes, speculated in 1953 that the atmosphere over a sandy plain, heated by the sun, is so unstable that it begins to rotate as a continuous series of long helical vortices alternately right and left, in horizontal fashion parallel to the wind. The right is having a clockwise rotation and the left a counterclockwise one. By that mechanism, Bagnold thought that sand is swept up until forming ridges where the two roll vortices meet and ascend.

In fact, Bagnold was not the first to assert the helicoidal flow hypothesis and its results on the environment. It has been used to explain the long formation of clouds, streaks of seaweed in the ocean (Langmuir, 1938), the presence and sequence, in a ridge of very small scale, of turbid material (Folk, 1977) and the preservation of dune shape (Douglass, 1909). In spite of the impact it should have deserved, Bagnold's (1953) theory was only published in symposium proceedings that had a relatively small distribution. It also happened that, during the 1950's and 1960's there was very little interest in desert sand dunes. Only during the end of the 1960's and the beginning of 1970's was the helicoidal flow theory resurrected (Hanna, 1969; Mabbutt et al., 1969; Wippermann, 1969; Glennie,1970; Hastings, 1971; Folk, 1971; Wilson, 1972; Warren 1974; 1979). Some of the renewed ideas of atmospheric helicoidal flow, as the cause and effect of dune formation, were raised again in analogy with the theory of subaqueous ripple formation through pairs of spiral flows as described by Allen (1968). Warren (1979) worked wonders by synthesizing the formation of most dune patterns as resulting from longitudinal vortex. According to him and Warren and Knott (1983), longitudinal vortices are formed at the lee of a dune and are propagated undisturbed to deform the next dune downwind, in self-generating processes.

 There are two conjectural explanations for the formation of helicoidal flow in deserts, such as differential heating between the atmospheric layers of the sandy surface (hotter) and the interdune area (cooler), thus giving origin to instability and convective currents (Douglass, 1909; Bagnold, 1953; Hanna, 1969; Mabbutt et al., 1969; Folk, 1971), or the creation of pressure gradients between the axes of interdune areas and the crests of dunes, such pressure build-up being caused by resistance to wind by the dune itself (Glennie, 1970, 1985).

 Bagnold (1941) considers that, in strong wind, blowing sand has a transverse instability so that sand tends to deposit in longitudinal strips, a process suggested by Glennie (1970) for the initiation of linear seif dunes. Hanna (1969) believes that conditions similar to those suggested by Kuettner (1959) for the formation of cloud streaks is the most likeable theory for the boundary layer of deserts. Field geomorphologists, like me, find that helicoidal flow theory is only valid for vegetated-linear dunes since linear seif dunes are formed by bi-directional winds with almost no wind parallel to dune alignment. Vegetated-linear dunes are exceptional with respects to linear seif dunes by being partly or wholly covered by vegetation. The helicoidal flow hypothesis was developed without any reference to vegetation cover as a determining factor in dune formation.

 In conclusion, the helicoidal flow theory for the formation of sand dunes arose intuitively from the visual impression that dunes made on the researcher. No one has ever observed or measured helicoidal flow in connection with the formation of dunes in deserts. Wind environments of dunes show great directional variability. Wind direction records and sand movement tracing on dunes seems to contradict the helicoidal flow theory for the formation of sand dune. I used many smoke candles on and around desert sand dunes when the sand temperature was 70C and did not trace any cork screw-like secondary flow.

Haim Tsoar

Professor

BGU

Reference list

Allen, J. R. L. (1968) Current ripples? North Holland, Amsterdam.

Bagnold, R. A. (1941) The physics of blown sand and desert dunes? Methuen, London.

Bagnold, R. A. (1953) The surface movement of blown sand in relation to

meteorology. In: Desert research, Vol. 2, pp. 89-96. Research Council of

Israel, Jerusalem.

Douglass, A. E. (1909) The crescentic dunes of Peru. Appalachia, 2, 34-45.

Folk, R. L. (1971) Genesis of longitudinal and oghurd dunes elucidated by

rolling upon grease. Bull. Geol. Soc. Am, 82, 3461-3468.

Folk, R. L. (1977) Longitudinal ridges with tuning fork junction in the

laminated interval of flysch beds: Evidence for low order helicoidal flow

in turbidities. Sed. Geol, 19, 1-6.

Glennie, K. W. (1970) Desert sedimentary environments. Developments in

Sedimentology? Elsevier, Amsterdam.

Glennie, K. W. (1985) Early Permian (Rotliegendes) palaeowinds of the North

Sea - Reply. Sed. Geol, 45, 297-313.

Hanna, S. R. (1969) The formation of longitudinal sand dunes by large

helical eddies in the atmosphere.J. Appl. Meteorol., 8, 874-883.

Hastings, J. D. (1971) Sand streets. Meteorol. Mag, 100, 155-159.

Kuettner, J. (1959) The band structure of the atmosphere. Tellus, 267-294.

Langmuir, I. (1938) Surface motion of water induced by wind. Science, 87,

119-123.

Mabbutt, J. A., Wooding, R. A. & Jennings, J. N. (1969) The asymmetry of

Australian desert sand ridges. Aust. J. Sci., 32, 159-160.

Warren, A. & Knott, P. (1983) Desert dunes: A short review of needs in

desert dune research and a recent study of micrometeorological

dune-initiation mechanics. In: Eolian sediments and processes (Ed. by M. E.

Brookfield and T. S. Ahlbrandt), pp. 343-352. Elsevier, Amsterdam.

Warren, A. (1974) Desert dunes. Geography, 59, 127-133.

Warren, A. (1979) Aeolian processes. In: Process in Geomorphology (Ed. by

C. Embleton and J. Thornes). Edward Arnold, London.

Wilson, I. G. (1972) Sand waves. New Scientist, 53, 634-637.

Wipperman, F. (1969) The orientation of vortices due to instability of the

Ekman boundary layer. Beitr. Phys. Atmos., 42, 225-244.

First I must confess that my knowledge of sand physics is minimal, and that I am looking at the sand ripples mainly from a heat transfer and fluid mechanics point of view. Worst yet, my comments are just untested opinions.

could be caused by secondary flows from thermal winds. As the hot air rises along the slope, at some point it separates from the surface as thermals. However, up-slope thermals are not mushroom-like round buoyant elements (like convective clouds over a flat surface), but they are equally spaced vertical sheets of rising air aligned with the up-slope flow. So, there is a cork screw-like secondary flow that converges at these sheets. (E.M. Sparrow and R.B. Husar: Longitudinal vortices in natural convection flow on inclined surfaces. J. Fluid Mech. (1969), Part 2 pp 251-255. )

The converging secondary flow could be sufficiently strong to move the sand into a pile along the line of convergence. But is it? A simple smoke visualization experiment on sand dunes could confirm or reject this entire idea. Flow visualization experiments in water tank (above reference) also show that some of the thermal sheets along heated inclined plates tend to merge along the slope occasionally yielding fingerprint-like merging pattern that has also been observed in the sand.

I think that such longitudinal vortices might develop over flat desert surfaces as well, provided that there is a prevailing wind. In that case again, the thermals would be stretched into elongated sheets of rising air and pile up the sand at the linear convergence zones.

Rudy Husar