Direct numerical simulations of surface wave-induced forces

Abstract

A gradient force, together with the Coriolis-Stokes and vortex force are residual surface-wave driven forces showing up in the equations of motion averaged over the wave cycle under certain assumptions. They are part of the so-called Craik-Leibovich equations, which are often used to understand surface wave-driven (Langmuir) turbulence, and to simulate the wave effects on the ocean’s mixed layer in numerical models. The surface wave effects can be implemented in those models by the wave-driven forces without directly resolving the waves, which is otherwise numerically challenging. Since observational or modelling evidence for the surface-wave driven forces is only partly available, we diagnose here the Reynolds stress divergences of a two-phase model of air and water directly simulating surface waves, to compare with all corresponding forces in the Craik-Leibovich equations in a systematic manner, the first time to our knowledge. We also explore the limits of the assumptions of the Craik-Leibovich equations by using mean flow of different magnitude and shear. It turns out that the Coriolis-Stokes and vortex force are very good approximations within the limits of the assumptions, and that they remain useful even beyond those limits. The comparison with the gradient force, however, is complicated by the lack of a precise definition of the mean pressure in several studies. The latter finding has consequences for the treatment of wave-driven turbulence in mixed layer closures.