A hybrid spectral/finite-difference large-eddy simulator of turbulent processes in the upper ocean

A three-dimensional numerical model for large-eddy simulation (LES) of oceanic turbulent processes is described. The numerical formulation comprises a spectral discretization in the horizontal directions and a high-order compact finite-difference discretization in the vertical direction. Time-stepping is accomplished via a second-order accurate fractional-step scheme. LES subgrid-scale (SGS) closure is given by a traditional Smagorinsky eddy-viscosity parametrization for which the model coefficient is derived following similarity theory in the near-surface region. Alternatively, LES closure is given by the dynamic Smagorinsky parametrization for which the model coefficient is computed dynamically as a function of the flow. Validation studies are presented demonstrating the temporal and spatial accuracy of the formulation for laminar flows with analytical solutions. Further validation studies are described involving direct numerical simulation (DNS) and LES of turbulent channel flow and LES of decaying isotropic turbulence. Sample flow problems include surface Ekman layers and wind-driven shallow water flows both with and without Langmuir circulation (LC), generated by wave effects parameterized via the well-known Craik–Leibovich (C–L) vortex force. In the case of the surface Ekman layers, the inner layer (where viscous effects are important) is not resolved and instead is parameterized with the Smagorinsky models previously described. The validity of the dynamic Smagorinsky model (DSM) for parameterizing the surface inner layer is assessed and a modification to the surface stress boundary condition based on log-layer behavior is introduced improving the performance of the DSM. Furthermore, in Ekman layers with wave effects, the implicit LES grid filter leads to LC subgrid-scales requiring ad hoc modeling via an explicit spatial filtering of the C–L force in place of a suitable SGS parameterization.