Measurement of the Initiation and Growth of Surface Water Waves under the Action of a Laminar Air Flow

Abstract

Miles (1997) recently presented a short review of the progress in theoretical modelling of wave generation by wind during the period since his own pioneering work and that of Benjamin in the late fifties. With minor analytical elaborations and the major advances in computational capabilities, the original Miles-Benjamin model is still widely applied in linear instability analysis of this important practical phenomenon with very useful results. It appears likely, however, that further significant advances in predictive modelling will require improved understanding of the highly complex physics of the interaction process between the turbulent wind flow at the interface and the deforming water surface. At present, this knowledge can only come from direct numerical simulation and advanced physical experimentation, paralleling similar studies of solid wall layer turbulence. On the other hand, a laminar flow is a simple and fixed model. The classic experiment of Schubauer and Skramstad and the later numerical calculation of Kaplan have proved that, on a solid plate, the initial growth rate of some selected frequencies of artificial two-dimensional air waves inside the laminar boundary layer can be explained by linear instability theory. It is, therefore, interesting to know, for the coupled flow at an air-water interface, if the physical processes of the initial formation of water waves under the action of laminar air flow will be dominated by linear instability theory. Following this reasoning, the present wind tunnel study has been designed to provide information on the basic mechanics and physics of initial formation and growth of waves on a flat water surface under the action of laminar air flow. Primary objectives of the study therefore include measurement of the wave growth rate and phase velocity as a function of wave frequency and space under the fundamentally driving laminar flow conditions. A numerical calculation to solve the coupled Orr-Sommerfeld equations in the space-amplified growth rate was also developed for comparison with observed results.