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In Retrospect: the physics of sand dunes

Nature volume 457, pages 10841085 (26 February 2009) | Download Citation

Ralph Bagnold's wartime posting to map the dunes of North Africa was like a desert epic — and it inspired his classic text on how wind-blown grains self-organize into regular patterns, explains Philip Ball.

Physics of Blown Sand and Desert Dunes

By

Methuen: 1941. 265 pp.

“We forgave Bagnold everything for the way he wrote about dunes. 'The grooves and the corrugated sand resemble the hollow of the roof of a dog's mouth.' That was the real Bagnold, a man who would put his inquiring hand into the jaws of a dog.”

Ralph Bagnold intuited that regular dune and ripple shapes embody the physics of complex systems. Image: F. LEMMENS/GETTY IMAGES

This is the voice of Hungarian explorer László Almásy, as fictionalized in Michael Ondaatje's 1992 novel The English Patient. The remark is a piece of authorial indulgence, for Ondaatje's readers could hardly be expected to know of this Bagnold who flits across a few pages of the desert epic. Ondaatje, however, clearly knew his man, hinting at the groundbreaking way in which Ralph Alger Bagnold studied and wrote about the major obsession of his life: desert sands.

Bagnold did so with such perception and insight that his 1941 book The Physics of Blown Sand and Desert Dunes became the standard work on dune formation for many decades. Informed by observations in Libya and wind-tunnel experiments in the United Kingdom, Bagnold set out to explain how sand grains are organized by wind into structures ranging from ripples the width of a finger to undulations several kilometres across.

“The observer never fails to be amazed at a simplicity of form, an exactitude of repetition.”

His book is more than an exploration of a hitherto-neglected aspect of geomorphology. In hindsight, Bagnold's work can be seen as a landmark in a much broader vista: the investigation of complex, self-organizing systems, in which order and regularity emerge from interactions of components that seem to prescribe nothing more than chaos and disorder. As Bagnold wrote of dunes:

“The observer never fails to be amazed at a simplicity of form, an exactitude of repetition and a geometric order unknown in nature on a scale larger than that of crystalline structure.”

Thus he perceives that the problem is not simply to explain the size, shape and variety of dune-like formations, but to account for the more general phenomenon of regularity arising from a system that is initially featureless.

Sand ripples and dunes are conspiracies of grains that arise from the interplay of windborne transport, collision-driven piling up, and slope-shaving avalanches. They are an archetype for the self-organized patterning of systems of many interacting components. Interest in granular complexity has blossomed over the past decade, exemplified by the appearance of stationary-wave arrays in shaken, shallow layers; grain-size stratification in avalanches and rotating drums; and the use of sand piles as a model of 'scale-free' dynamics known as self-organized criticality. Such behaviour lies squarely in the domain of the physicist; Bagnold's prescience is located in his intuition that wind-formed geomorphology embodies the physics of complex systems writ large in nature.

There is a long tradition of army and naval engineers whose scientific legacy implies that their minds were on matters other than the military. Bagnold joined the British Army's Royal Engineers in 1915 and fell in love with the deserts during postings to Egypt and India. By the 1920s he was spending his leave exploring these 'seas of sand', joining Almásy's 1929 expedition in search of the legendary city of Zerzura west of the Nile.

Before Bagnold, the transport of small particles by fluids — not just sand in wind, but sand and silt in water, wind-blown snow and industrial processing of grains such as cereal and coal dust — was afforded little more than a few empirical formulae used by engineers. But Bagnold claimed that “the subject of sand movement lies far more in the realm of physics than of geomorphology”. He began from an aerodynamic perspective, conducting wind-tunnel studies in the mid-1930s to map the trajectories of individual sand grains in moving air. The key to the transport process is that the grains bounce when they hit the desert floor, and are carried along in a series of little jumps — known as saltation — that ultimately determine the length of sand ripples.

But the central issue was why wind-borne sand produces roughly regular ridges. Bagnold showed that this was caused by a self-amplifying growth instability, now recognized to drive patterning in systems such as snowflakes and dendrites, fractal aggregation and viscous fingering. He showed that a single, chance irregularity on a smooth desert floor stimulates growth and multiplication of bumps of more or less equal size and spacing.

He began fieldwork in Libya in 1938, funded by Britain's Royal Society. His book was published three years later, while he was conducting reconnaissance in the North African conflict during the Second World War. He deduced the wind conditions that produced different dune types, such as crescent-shaped barchans and undulating seif dunes — conclusions that have been recently borne out by computer modelling.

The general problem that Bagnold faced — to account for spontaneous pattern formation — was addressed more famously in D'Arcy Wentworth Thompson's seminal 1917 book On Growth and Form. But Bagnold seemed unaware of that. Thompson's epic revised edition, published in 1942, surprisingly neglects not only Bagnold's efforts but the entire issue of ripple and dune formation. A connection to more general patterning processes ultimately emerged from Alan Turing's work on biochemical morphogenesis, described in a 1952 paper. When, in the 1970s, mathematical biologists Hans Meinhardt and Alfred Gierer identified the fundamental ingredients of Turing's stationary chemical patterns — the presence of a locally acting autocatalytic 'activator' and an inhibitor that suppresses pattern elements over longer ranges — it became apparent why sand ripples resembling in plan form the striped markings of zebras probably result from a Turing-like mechanism. The formation of a ripple is self-enhancing because it captures more sand the bigger it gets. Meanwhile, this process depletes the air of sand grains, suppressing another ripple for some distance downwind.

The fact that granular flow might serve as a universal analogy for other physical phenomena had been suspected in the late nineteenth century by Osborne Reynolds, a pioneer of fluid dynamics. In order to flow, a collection of grains must expand a little, and Reynolds decided that this 'dilatancy' of powders could explain all the mechanical behaviours in nature if space were filled with submicroscopic grains. A portrait from 1904 shows Reynolds holding a basin of ball bearings, and two years earlier he revealed what he had in mind: “I have in my hand the first experimental model Universe, a soft India rubber bag filled with small shot.” William Blake's world in a grain of sand is invoked to the point of cliché in granular research, but here it was claimed as a reality.

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  1. Philip Ball is a consultant editor for Nature. His forthcoming book series is Nature's Patterns: A Tapestry in Three Parts.

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