Numerical Simuulation of Geophysical Turbulence

Piotr Smolarkiewicz

Looking forward towards mesh adaptivity for simulating turbulent atmospheric/oceanic flows, we are pursuing advanced algorithms for evaluating vector differential operators cast in time-dependent curvilinear coordinates. In this lecture, I review our effort to date with the development of a deformable-coordinates multi-scale anelastic model designed from the bottom up relying on strengths of nonoscillatory transport methods. We have shown in earlier works that effective multi-scale adaptive numerical models for high-Reynolds-number meteorological flows can be designed that dispense with rigorous evaluation of the more cumbersome of the vector differential operators, such as the curl or the strain rate. These operators are nonetheless important for budget analyses of the model results, estimating physical uncertainties, driving the mesh adaptivity itself, and extending the model's applicability beyond standard meteorological situations. Here, I discuss selected extensions of the generic explicitly-inviscid approach.

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