A Scalable Nonhydrostatic Model Featuring Variably Stepped Topography Part 1: Formulation and Evaluation of Performance on Simple Obstacle Flow Problems
نویسنده
چکیده
This paper describes the formulation and performance of a nonhydrostatic model featuring a unique variable stepped topography representation capable of capturing steep topographical slopes, while at the same time accurately representing subtle topography variations. The proposed enstrophy conserving formulation and the quasi-compressible closure cast on a multiply nested rotated spherical grid are presented. The numerical differencing scheme and methodologies to treat the variably stepped lower boundary and satisfying integral constraints are described. The adherence to integral constraints throughout the prescription of the stepped boundary formulation maintains the dynamical integrity of the solution. Model simulations of classical fluid dynamics problems involving flow relative to an obstacle that has known analytical or laboratory-simulated solutions are presented to evaluate the stepped topography system. In certain situations, such as when the topography becomes excessively severe, conventional terrain-following coordinate systems used in many atmospheric models contain large errors making a stable integration possible only if the topography is smoothed. In other cases, conventional stepped coordinate models, because of limitations resulting from the discrete terrain stepping algorithms, also encounter difficulties reproducing the known solution in regions of slowly varying topography. Overall, the evaluation results presented show the variable stepped UW-NMS overcomes the major limitations of both conventional approaches making this proposed formulation ideally suited for a scalable model that must accurately represent both subtle and strong terrain features.
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