Wind Wave Growth

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.

Characteristics of air flow driven by the free surface of the open channel

Spillway tunnels are a key structure in large-scale water conservancies. The high-head water inlet makes the water surface-velocity extremely high, and the air is driven by the free surface of the water to move downstream. This paper studies the air velocity distribution above the water surface through the model tests, under the assumption that the airflow is a turbulent boundary layer with a rough interface, and the influence of the water depth and the water velocity on the air velocity distribution is analyzed. It is shown that the air velocity is in an exponential distribution. As the measured position moves upward, the air velocity gradually decreases, and the gradient decreases. When the water depth increases, the air velocity increases but with the same distribution form. With the increase of the water surface-velocity, the air velocity at the same measuring point increases, the variation range near the water surface is large, the air boundary layer height increases slightly, and the index coefficient of the air velocity distribution function decreases. Through numerical fitting, the calculation formula of the air boundary layer thickness at different water surface velocities is obtained, along with the numerical value of the index coefficient.