Foaming to a rough sea.

Wind, water, and waves. These three ingredients combine to create a rich panoply of seascapes, from glassy ripples roused by a gentle breeze and scattered whitecaps churned up by a stiff wind to gigantic swells lashed into a drenching foam by the fury of a full-blown hurricane. Each of these responses of water to wind represents a transfer of energy and momentum from the wind to surface water waves. But the physical mechanisms by which this transfer occurs remain only partially understood.

Now Alan C. Newell and Vladimir E. Zakharov of the Arizona Center for Mathematical Sciences at the University of Arizona in Tucson have developed a simple theoretical model that focuses on what happens in rough seas whipped by high winds. In this case, the amount of energy imparted by the wind is too great for a smoothly undulating surface to absorb, and the water surface has to increase its surface area by breaking up and spraying droplets into the air, According to the researchers, this process creates a layer of foam consisting of water droplets suspended in air, and this new phase becomes the principal means by which the wind's energy is dissipated into the water.

Using their theory, the researchers calculated how foam depth and droplet size would depend on the energy flow from wind to water and on the liquid's surface tension. These predictions can be checked in the laboratory, they suggest. At sea, a fully developed foam would probably arise only under hurricane-like conditions, the researchers say. They attribute the spottiness of whitecaps usually observed in rough seas to local energy-flow intensification associated with the passage of long, large water waves. When energy flow gets focused in a spot just ahead of a wave crest, the water surface breaks into spray, But once the wave has passed by, energy drains out of the foam left behind, and the foam disappears.

Newell and Zakharov admit that their simple theory leaves out a number of factors that may also play a role in energy dissipation and momentum transfer. During wave breaking, for example, water not only explodes into droplets but also captures air to form a cloud of air bubbles. Indeed, it's possible that a surface-hugging blanket of foam could include a top layer of water droplets in air, a middle layer of thoroughly mixed air and water, and a bottom layer of air bubbles in water. In addition, a more sophisticated model would take into consideration such factors as turbulence in the water itself.

The researchers' report their results in the Aug. 24 PHYSICAL REVIEW LETTERS, describing them as "a step in the right direction" toward gaining a more complete picture of energy dissipation in Wind-water interactions.