A couple of weeks ago I was delighted to find myself an invited guest on the BBC Radio 4 show, The Museum of Curiosity. It’s pure entertainment – hosted by John Lloyd, the comedy writer and producer of, for example, Not The Nine O'Clock News, Spitting Image and Blackadder, it features three guests who, after an introductory session of general discussion and humour, are invited to submit their nomination for inclusion in the mythical museum. Such donations can be real or imaginary but they must be curious and they should be funny; previous items have included The Big Bang, a Yeti, Silence, Father Christmas, and the Battle of Waterloo. Knowing that the museum is vast, I donated a Sand Dune Choir, a group of dunes, each selected for emitting a representative note from the musical scale (as individual dunes around the world really do); my assumption was that these dunes would migrate around the museum, spontaneously booming, squeaking, and singing, until, one day, they would get their act together and burst into a rendition of the theme from Lawrence of Arabia, or perhaps Gone With the Wind.
I enjoyed, amongst other aspects of the concept, the idea of indoor dunes, simply because it’s so absurd; but it’s also something of a problem for serious scientific research. Dunes and the laboratory environment simply don’t mix – for any number of reasons. Primarily, of course, it’s a problem of scale, in the sense not only of the size of a typical sand dune (never mind a dune field), but also of time: the evolution of a single dune takes place on a scale of years. Small-scale features of windblown sand – ripples etc. – can be reproduced and analysed in the laboratory, and they have been for decades. Ralph Bagnold (“the man who figured out how deserts work”) was doing this kind of fundamental research in his self-designed and -constructed wind tunnels seventy-five years ago, but scaling up to dunes was out of the question. Even the largest-scale experiments have produced moving piles of sand, but nothing resembling a dune.
The science of understanding how dunes work has thus relied on two entirely separate approaches: field observations, measurement, and description of real dunes, and attempts to scale things down in the laboratory. Scaling up and scaling down are, of course, standard operating procedure in many research laboratory disciplines, and the approach can produce powerful insights. But every step taken, however carefully and proportionately calculated, that departs from the natural scale, changes the calibration to reality. The complexity and dynamics of something like a field of sand dunes – for example, the Saharan dunes in the image above - are extraordinary, and the natural processes involved operate on a multiple orders of magnitude range in scale: from nano-scale interactions between individual grains to regional scale feedback between geomorphology and atmospheric boundary layers. Modelling such a system with accuracy is simply out of the question, whether the models are physical or mathematical.
But that’s not to say that such approaches are not worthwhile – they can shed light on the complexity. A fascinating example of this has just been published in the new issue of the Geological Society of America’s journal, Geology. “ Formation and stability of transverse and longitudinal sand dunes” reports the results of modelling by three researchers at laboratories in Paris (full reference below). Dunes come in all shapes and sizes and varying degrees of complexity. Perhaps the most familiar, and apparently the simplest, is the crescent-shaped barchan dune, commonly occurring in groups of different sizes, a herd moving slowly across the desert floor as sand is blown across their upwind slopes and avalanches down the steep front; the “horns” point in the direction of movement. Ralph Bagnold recognised that barchans tend to form in a setting where one wind direction is dominant year-round, a relatively simple situation – but he also recognised their complexity, smaller dunes travelling faster than larger ones, catching up with and merging with them, only to eventually “reappear” on the downwind side. This gives the strange appearance of parental dunes “breeding” offspring – a process that has been much-studied and remains the subject of scientific debate (and a separate post).
There are many areas of the world’s deserts where the wind directions vary, depending on the time of year, often with two distinct directions dominating equally. Under these circumstances, long, linear dunes form, sometimes at right angles to the average wind direction (transverse dunes), sometimes roughly parallel (longitudinal dunes, image below); it is these types that the French researchers set out to understand better, remarking, with some degree of understatement, in the paper’s abstract that “In both cases, their large width (hundreds of meters) and evolution time scale (years) strongly limit the investigation of their dynamics and thus our understanding of such structures.”
It has been established for some time that the specifics of the shapes of these dunes, and their evolution, depends on sand supply versus wind direction, and the angle between the two directions. Transverse dunes often appear to be unstable, developing into sinuous shapes and eventually, if the supply of sand is too low breaking up into “barchanoid ridges” or, ultimately, true barchans. But sorting out the details is difficult: the physics of sand dunes (as originally established by Bagnold, whose work is still referenced in this paper) reflects the coupling of sediment transport by a fluid and the modification of the flow by the resulting shape of the bedform. Critically, the whole process, and in particular the minimum size of a dune, depends on the density ratio between the grains and the fluid. For quartz sand grains and air, this ratio is, of course, very large and so the minimum size of a dune is measured in meters – difficult to replicate in a laboratory. But change the fluid to water, and the ratio and hence the scale of everything, reduces by a factor of a thousand; here’s a way of scaling things down and making sand dunes indoors. But surely changing the fluid from air to water changes the whole game? Well, yes and no – sand dunes on all scales occur under water where strong currents operate, including the gigantic dunes on the floor of San Francisco Bay, and they share many of the features and behaviours of desert dunes. But they are also, inevitably, different. However, there have been a number of research projects that have successfully modelled dunes in the lab on a very small scale under water, and the paper in Geology is but the latest example.
The apparatus designed to model dune formation under two different wind directions is clever (diagram below). The plate is 90 cm wide and 1m long, and includes a circular rotatable element on which sand, a couple of millimeters thick is placed. The whole thing is immersed in a water tank and driven quickly forwards, replicating the fluid flow over the sand. The plate is then withdrawn to its original position, but very slowly so as not to disturb the sand, the circular part is rotated by a few degrees and the whole thing moved forward again, this time under a different “wind” direction. Repeating this over long periods of time – typically several days - and with varying angles between the two “winds” allows a wide variety of sand geometries to be produced; the bedforms created in the sand are illuminated by laser and photographed.
Here’s one of the illustrations from the paper, the top images being satellite views of transverse dunes “degenerated into barchanoid ridges” (White Sands), oddly mixed patterns showing both longitudinal and transverse forms (Taklamakan, China) longitudinal dunes extending for several tens of kilometers (Saudi Arabia). The lower three images are of experimental results that replicate these patterns on a small scale, the blue arrows and the angle θ showing the two wind directions in each case.
The experiments demonstrate that an initially flat sand bed first develops structures that are perpendicular to each wind direction, a complex pattern of superimposed forms that then evolves into dunes that progressively align perpendicularly to the mean wind direction if θ is less than 90 degrees (transverse) or parallel to the wind if the angle is greater than 90 degrees. But the transverse dunes often quickly disintegrate into barchanoid ridges. The longitudinal (sometimes also referred to as “seif”) dunes are stable and long-lasting, as long as an ample supply of sand continues to be available.
The paper, and its ancillary “data repository,” both available online but unfortunately only to GSA subscribers, contains much additional information and further detail, including numerical modelling work that supports the results of the physical experiments.
This is interesting work, but it does raise a few questions. For a start, the experiment used ceramic beads rather than real sand – not a problem in itself, but, after all the scaling down achieved in the overall model, these beads were between 65 and 120 micrometers – 0.065 to 0.12 mm – in diameter; this is the size range of fine real sand – but everything else is scaled down. Surely this is yet another step away from reality? The dunes produced experimentally range up to 3mm high, in other words, a pile 40 or so grains thick…. And yes, nature tends to enjoy patterns that are independent of scale (fractals and so on) but looking at the results shown in the “ABCD” figure above, the scale contrast is a factor of 400,000. There is much to think about in self-similar natural patterns that seem scaleless – but if we are producing patterns on the miniature scale that simply look like those on the scale of landscapes, are we reading too much into this, are we bewitched by appearances? And there remains the question of water versus air – yes, the basic physics of the transport of granular materials can be described simply in terms of fluid properties, but on the nano-scale could there not be important differences? All in all, I can’t help remembering the words of the great Werner Heisenberg, he of quantum physics and the uncertainty principle:
What we observe is not nature itself but nature exposed to our method of questioning.
So my indoor singing sand dunes in the Museum of Curiosity must remain there. One of the authors of the paper I have described has been a leading researcher on how dunes spontaneously emit sound – for a long time he was doing this in collaboration with a colleague, but their ideas diverged and they fell out. It’s reported that they now ignore each other completely.
[The Geology paper is: Geology 2010;38;491-494, E. Reffet, S. Courrech du Pont, P. Hersen and S. Douady; Formation and stability of transverse and longitudinal sand dunes. For a spectacular gallery of the diversity, complexity, and wondrous beauty of dune patterns, see http://www.wired.com/wiredscience/2009/12/deserts-gallery-1/]