Phenomenology of decaying turbulence beneath surface waves

Abstract: This paper explores decaying turbulence beneath surface waves that is initially isotropic and shear-free. We start by presenting phenomenology revealed by wave-averaged numerical simulations: an accumulation of angular momentum in coherent vortices perpendicular to the direction of wave propagation, suppression of kinetic energy dissipation, and the development of depth-alternating jets. We interpret these features through an analogy with rotating turbulence (Holm 1996), wherein the curl of the Stokes drift, $\boldsymbol{\nabla}\times\boldsymbol{u}^S$, takes on the role of the background vorticity (for example, $(f_0 + \beta y) \hat{\boldsymbol{z}}$ on the beta plane). We pursue this thread further by showing that a two-equation model proposed by Bardina et al. (1985) for rotating turbulence reproduces the simulated evolution of volume-integrated kinetic energy. This success of the two-equation model -- which explicitly parametrizes wave-driven suppression of kinetic energy dissipation -- carries implications for modeling turbulent mixing in the ocean surface boundary layer. We conclude with a discussion about a wave-averaged analogue of the Rossby number appearing in the two-equation model, which we term the "pseudovorticity number" after the pseudovorticity $\boldsymbol{\nabla}\times\boldsymbol{u}^S$. The pseudovorticity number is related to the Langmuir number in an integral sense.