The LANS-α and Leray turbulence parameterizations in primitive equation ocean modeling

Ocean modeling presents several unique technical challenges: there is a tremendous range of spatial scales; the kinetic energy forcing scale occurs at the Rossby radius of deformation (20–100 km), which is often at or below the grid resolution; and mixing is strongly anisotropic, occurring primarily along nearly horizontal isopycnal surfaces. We present analysis and numerical results to show that the Lagrangian-averaged Navier–Stokes alpha (LANS-α) turbulence parameterization and, to a lesser extent, the Leray parameterization are well suited to ocean modeling. LANS-α and Leray are fundamentally different from purely dissipative turbulence models in that both LANS-α and Leray are more energetic and produce more eddy structure near the gridscale. This is consistent with expectation from linear stability analysis, where it has been shown that these models resolve the process of baroclinic instability on coarser meshes than standard Navier–Stokes. Formulations of LANS-α and Leray models for the primitive equations are presented. In an idealized ocean channel domain, LANS-α produces turbulence statistics in kinetic energy, eddy kinetic energy and temperature distributions that resemble a doubled-resolution simulation without LANS-α. Leray produces qualitatively similar results, but to a lesser degree than LANS-α. Finally, the Leray model is tested in a North Atlantic domain with realistic topography and forcing, and produces higher kinetic and eddy kinetic energy than the non-Leray model.

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