The Wavy Ekman Layer: Langmuir Circulations, Breaking Waves, and Reynolds Stress

Abstract

Large-eddy simulations are made for the canonical Ekman layer problem of a steady wind above a uniformly rotating, constant-density ocean. The focus is on the influence of surface gravity waves: namely, the wave-averaged Stokes-Coriolis and Stokes-vortex forces and parameterized wave breaking for momentum and energy injection. The wave effects are substantial: the boundary layer is deeper, the turbulence is stronger, and eddy momentum flux is dominated by breakers and Langmuir circulations with a vertical structure inconsistent with both the conventional logarithmic layer and eddy viscosity relations. The surface particle mean drift is dominated by Stokes velocity with Langmuir circulations playing a minor role. Implications are assessed for parameterization of the mean velocity profile in the Ekman layer with wave effects by exploring several parameterization ideas. The authors find that the K-profile parameterization (KPP) eddy viscosity is skillful for the interior of the Ekman layer with wave-enhanced magnitude and depth scales. Furthermore, this parameterization form is also apt in the breaker and Stokes layers near the surface when it is expressed as a Lagrangian eddy viscosity (i.e., turbulent Reynolds stress proportional to vertical shear of the Lagrangian mean flow, inclusive of Stokes drift) with a derived eddy-viscosity shape and with a diagnosed vertical profile of a misalignment angle between Reynolds stress and Lagrangian mean shear.

Observations of the Transfer of Energy and Momentum to the Oceanic Surface Boundary Layer beneath Breaking Waves

“…The results from the TKE balance presented above are consistent with numerical simulations that include a stochastic parameterization for wave breaking (Sullivan et al 2007;McWilliams et al 2012). In these studies the effects of breaking surface waves are modeled by imposing randomly distributed horizontal accelerations near the ocean surface.…”

“…These accelerations are imposed as an external force in the model, which generates an additional term in the TKE equation that is referred to as ''breaker work. '' McWilliams et al (2012) document that the production of TKE by the sum of the total TKE transport and breaker work is balanced by dissipation at first order. The sum of the breaker work and the total TKE transport term is more showing strong drops in pressure and negative skewness.…”

“…In the water column, the ADV data are used to estimate the dominant terms in the TKE budget, which for a horizontally homogeneous flow at steady state in the Boussinesq approximation can be written as (e.g., McWilliams et al 1997):…”

Wave-induced mixing and transport of buoyant particles: application to the Statfjord A oil spill

“…An interesting topic for future work would be to study particle drift in models with a more elaborate representation of Langmuir turbulence, especially for cases with more stratification and/or neutrally buoyant particles. In this study we have considered a twoequation model; however, it should be noted that a firstorder model that includes both the effect of wave breaking and Langmuir turbulence has been proposed by McWilliams et al (2012).…”

“…Unfortunately we lack long time series of co-located meteorological, wave, current, and hydrographic measurements at these high latitudes. Such measurements would allow us to study the importance of surface waves for the upper ocean mixing in the high north and in particular the usefulness of recently suggested parametrizations for Langmuir turbulence in more detail (e.g., Kantha and Clayson, 2004;Carniel et al, 2005;McWilliams et al, 2012;Harcourt, 2013).…”