Turbulent flow over a boundary is a complex phenomenon for which there is no complete theory. Nevertheless, much experimental data has been collected on flows over solid surfaces, both in the laboratory and in nature, so that from an engineering perspective, the situation is well understood. The force exerted on a surface varies with the roughness of that surface and approximately with the square of the wind speed at a fixed height above it. A wind of 10 meters per second (about 20 knots, or 22 miles per hour) measured at a height of 10 meters will produce a force of some 30 tons per square kilometer on a field of mown grass, or of about 70 tons per square kilometer on a ripe wheat field. On a really smooth surface, such as glass, the force is only about 10 tons per square kilometer.
When wind blows over water, it is more complicated. The roughness of the water is not a given characteristic of the surface but depends on the wind itself. Not only that, the elements that constitute the roughness, the waves, themselves are mostly in the direction of the wind. Recent evidence indicates that a large portion of the momentum transferred from the air into the water goes into waves rather than directly into making water currents; only as the waves break or otherwise lose energy does their momentum become available to generate currents. Waves carry a substantial amount of both energy and momentum (about as much as is carried by the wind in a layer about one wavelength thick), and so the wave-generation process is far from negligible.
A violently wavy surface belies its appearance by acting, as far as the wind is concerned, as though it were very smooth. At a wind of 10 meters per second, the force on a wavy surface is much less than the force would be over mown grass and scarcely more than over glass; in light winds (2 or 3 meters per second) the force on a wavy surface is even less than it would be on glass. The waves’ motion seems to modify the airflow so that air slips over the surface more freely than if it were smooth. This is not the case at higher wind speeds (above about 5 meters per second), but the force remains quite low relative to other surfaces.
Unfortunately, there are no direct observations under conditions when high winds, greater than about 12 meters per second, have had time and fetch (the distance over water) enough to raise substantial waves. A few indirect studies, however, suggest that the water’s apparent roughness may increase under high wind conditions, so that the force on the surface increases more rapidly than the square of the wind speed.
If the force increases at least as the square of the wind speed, high-wind conditions will produce effects far more important than their frequency of occurrence would suggest, as five hours of 60-knot storm winds will put more momentum into the water than a week of 10-knot breezes. If it should be shown that, for high winds, the force on the surface increases even more than the square of the wind speed, then the transfer of momentum to the ocean will turn out to be dominated by the occasional storm rather than by the long-term average winds.