Phenomenology of decaying turbulence beneath surface waves

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 Physica D . 98 , 415–441), wherein the curl of the Stokes drift, ${\boldsymbol{\nabla}} \times {\boldsymbol{u^{S}}}$ , takes on the role of the background vorticity (for example, $(f_0 + \beta y) {\boldsymbol{\hat{z}}}$ on the beta plane). We pursue this thread further by showing that a two-equation model proposed by Bardina et al. (1985 J. Fluid Mech. 154, 321–336) for rotating turbulence reproduces the simulated evolution of volume-integrated kinetic energy. This success of the two-equation model – which explicitly parametrises wave-driven suppression of kinetic energy dissipation – carries implications for modelling 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.