Parameterization of Wind Wave Growth Rate, a Direct Numerical Simulation Study

The growth of wind wave is still an open question as current models often diverge in both the mechanism postulated and the growth rate predicted. There have been an increasing number of numerical studies on this subject, with the development of direct numerical simulation (DNS) and growth of computational power. DNS resolves all physically important flow scales, up to the viscous dissipation scale, without any turbulence closure hypothesis. It provides detailed information on velocity and stress fields, which makes it an extremely powerful tool in revealing the whole picture of air-sea interaction, and an important supplementation to currently available laboratory and field measurement. The difficulty in conducting accurate DNS arises from three aspects: the modeling of the turbulent air boundary layer; the response of water to the wind forcing; and the coupling between the two. Separate numerical studies have been done on the first two but are insufficient in revealing the whole picture of wind wave interaction. In this study we use the open source solver Basilisk, which solves a set of two phase incompressible Navier-Stokes equations with adaptive grids. We conduct three dimensional, fully coupled wind wave simulation, with a concentration on submesoscale momentum and energy transformation. A range of parameters that factor into the growth model, including the friction velocity of air, initial wave amplitude, surface tension and viscosity are studied. We further use the DNS results to parameterize wind wave growth rate and other important quantities in atmosphere and ocean modeling (eg. water surface roughness height) in terms of these conditions.