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On physical realizability and uncertainty of numerical solutions

Numerical experiments of the stratified flow past a bell‐shaped mountain with a shallow shear layer aloft are performed. Two different approximations of the entropy equation (explicit vs implicit numerical treatment of gravity waves) lead to a substantial discrepancy of the numerical results. As the flow is metastable, it turns out that both solutions are physically realizable and the quality of the solution changes in response to small variations in the accuracy of the numerical approximation. Copyright © 2005 Royal Meteorological Society