Daniel M. Hanes in the department of coastal and oceanographic engineering at the University of Florida, Gainesville, answers:
"The waves you ask about are just one example of so-called bedforms that occur when a fluid flows over loose sedimentary material. They occur all over the world under many different conditions and produce a magnificent variety of shapes and patterns. Some of them remain stationary, such as the diamond-shaped patterns sometimes seen on a dry beach. Others, such as sand dunes in the desert, move in the direction of the prevailing wind or current.
"There are several possible mechanisms leading to the particular bedforms, and this is an area of legitimate scientific controversy. The most accepted explanation is that the flow of the overlying fluid (water or air) interacts with the moving sediment grains in a manner that results in a stable shape, or bedform. The specific shape therefore depends on the density and viscosity of the fluid, its speed above the sand and the nature of the sediment (that is, its characteristic size, shape and density).
"Some of the interesting early observations and explanations of bedform patterns are provided by Ralph A. Bagnold in his book The Physics of Blown Sand and Desert Dunes (Chapman and Hall, 1984 [reprint of 1941 edition])."
Robert S. Anderson, associate professor of earth sciences at the University of California at Santa Cruz, provides a more thorough overview of this deceptively complicated phenomenon:
"Ripples in sand, found on both beaches and dunes, are one of nature's most ubiquitous and spectacular examples of self-organization. They do not result from some predetermined pattern in the wind that is somehow impressed on the surface, but rather from the dynamics of individual grains in motion across the surface. They arise whenever wind blows strongly enough over a sand surface to entrain grains into the wind. The subsequent hopping and leaping of these grains is called saltation. Saltating grains travel elongated, asymmetric trajectories: Rising relatively steeply off the bed, their path is then stretched downwind as they are accelerated by drag forces. They impact the sand surface centimeters to tens of centimeters downwind, typically at a low angle, around 10 degrees. It is this beam of wind-accelerated grains impacting the sand surface at a low angle that is responsible for ripples.
"An artificially flattened sand surface will not remain flat for long. (Try it on the beach or on the upwind side of a dune and see for yourself.) Small irregular mottles in the sand surface, perhaps a couple centimeters in wavelength, rapidly arise and grow once the wind starts to blow hard enough to initiate saltation. They then slowly organize themselves into more regular waves whose low crests are aligned perpendicular to the wind direction and begin to march slowly downwind. Typical ripple spacing is about 10 centimeters, whereas the typical height of the crests above the troughs is a few millimeters. The pattern is never perfect, but instead the ripple crests occasionally split or terminate, generating a pattern that looks remarkably like one's fingerprint. In cross section, the ripples are asymmetric, having low-angle upwind (stoss) faces and steeper downwind (lee) faces. Interestingly, the larger grains tend to accumulate on the crests of the ripples, leaving the troughs enriched in smaller grains.
"How does a low-angle beam of impacting saltating grains result in such downwind-marching waves of sand? This topographic pattern arises from a spatial pattern of deposition and erosion on the sand surface. In order to march downwind, deposition must be occurring on the downwind faces of the ripples, and erosion must be occurring on the upwind faces. Erosion occurs where there are more grains leaving the surface than are arriving, and deposition occurs where more grains are arriving than are leaving. Once saltation is well under way, by far the majority of grains in motion are actually blasted off the sand surface by the impacts of other saltating grains, rather than being carried along directly by fluid forces of the wind. And whereas the grains of sand that hit your ankles or accumulate in your pants cuffs travel long trajectories, most of the grains in motion are traveling in very short hops, only a few millimeters in length. The few grains traveling in long trajectories impact the sand surface with sufficient energy to force a large number of sand grains to hop.