Air pressures causing wave development, estimate by theory, model tests, and sea observations

Abstract

The wave drag, caused by horizontal components of normal air pressures, had been evaluated by three methods: wind tunnel tests on rigid models, observations of wave growth at sea, and theories of J. W. Miles and T. Brooke Benjamin. It has been found that neither the magnitude nor the functional form of the pressure drag is correctly predicted by the form of the theory specifically developed for application to rigid models. On the other hand, the form of the theory developed for mobile waves gives results in good agreement with wind tunnel model data at corresponding values of wave steepness. Model tests and theory agree in that the pressure drag does not depend on the Reynolds Number. In the absence of experimental data on pressures acting on water waves, the limits, within which the pressure drag must be confined, are defined by considering the observed rate of wave development at sea, and the total and frictional drag of water surface. Model tests, as well as the theory, give pressure drag estimates which lie within the foregoing limits. Miles' form of the pressure drag coefficient,β*, in terms of the friction velocity,u*, leads to a particularly simple expression for the ratio of the pressure drag to total drag. Thus, rational prediction of the wave growth in wind is connected with the ability to predict the total drag of the sea surface.