Wind Wave Growth

Abstract

A recent formula for the lift force on a low speed wing of circular arc cross-section [1] is adapted to the upward pressure force on the crests of a surface gravity wave propagating in the wind. In both cases, the main feature is the utilization of the air’s compressibility. At and near a wave crest, it is predicted that the air density is increased over the ambient value and that the air density decreases inversely as the square of the upward distance from the radius of curvature of the crest. As a consequence, the air pressure also decreases upward inversely as the square of the same distance. Therefore, an upward pressure force on each crest occurs which presumably will make the crests grow. Growth rates are largest for small wavelengths and large mean slopes of the wave surface. Contrary winds should produce wave growth (not damping) as well as no wind at all.