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SUMMARYLooking forward towards mesh adaptivity for simulating turbulent atmospheric=oceanic ows, we are pursuing advanced algorithms for evaluating vector di erential operators cast in time-dependent curvilinear co-ordinates. In this paper, we review our e ort to date with the development of a deformableco-ordinates multi-scale anelastic model designed from the bottom-up relying on strengths of non-oscillatory transport methods. We have shown in earlier works that e ective multi-scale adaptive numerical models for high-Reynolds-number meteorological ows can be designed that dispense with rigorous evaluation of the more cumbersome of the vector di erential 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, we discuss selected extensions of the generic explicitly inviscid approach.

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