A cell by cell anisotropic adaptive mesh ALE scheme for the numerical solution of the Euler equations

In this paper a cell by cell anisotropic adaptive mesh technique is added to an existing staggered mesh Lagrange plus remap finite element ALE code for the solution of the Euler equations. The quadrilateral finite elements may be subdivided isotropically or anisotropically and a hierarchical data structure is employed. An efficient computational method is proposed, which only solves on the finest level of resolution that exists for each part of the domain with disjoint or hanging nodes being used at resolution transitions. The Lagrangian, equipotential mesh relaxation and advection (solution remapping) steps are generalised so that they may be applied on the dynamic mesh. It is shown that for a radial Sod problem and a two-dimensional Riemann problem the anisotropic adaptive mesh method runs over eight times faster.

Langmuir turbulence and deeply penetrating jets in an unstratified mixed layer

The influence of surface waves and an applied wind stress is studied in an ensemble of large eddy simulations to investigate the nature of deeply penetrating jets into an unstratified mixed layer. The influence of a steady monochromatic surface wave propagating parallel to the wind direction is parameterized using the wave-filtered Craik-Leibovich equations. Tracer trajectories and instantaneous downwelling velocities reveal classic counterrotating Langmuir rolls. The associated downwelling jets penetrate to depths in excess of the wave's Stokes depth scale, δs. Qualitative evidence suggests the depth of the jets is controlled by the Ekman depth scale. Analysis of turbulent kinetic energy (tke) budgets reveals a dynamical distinction between Langmuir turbulence and shear-driven turbulence. In the former, tke production is dominated by Stokes shear and a vertical flux term transports tke to a depth where it is dissipated. In the latter, tke production is from the mean shear and is locally balanced by dissipation. We define the turbulent Langmuir number Lat = (v*/Us)0.5 (v* is the ocean's friction velocity and Us is the surface Stokes drift velocity) and a turbulent anisotropy coefficient Rt = /( + ). The transition between shear-driven and Langmuir turbulence is investigated by varying external wave parameters δs and Lat and by diagnosing Rt and the Eulerian mean and Stokes shears. When either Lat or δs are sufficiently small the Stokes shear dominates the mean shear and the flow is preconditioned to Langmuir turbulence and the associated deeply penetrating jets.