Abstract
AbstractFive families of exact axisymmetric solutions of the nonlinear shallow‐water equations in spherical geometry have recently been proposed as an aid to the development and testing of global numerical models. Sufficient conditions for the stability of these solutions are here derived to guide the choice of values for the family parameters. Thus it can be ensured that any significant time evolution occurring in a numerical model initialised with one of these exact solutions is of numerical origin, and does not reflect an inherent physical instability. With the caveat that only sufficient conditions for stability are examined, it appears that planetary rotation stabilises the solutions (as would be so if the flow were governed by barotropic vorticity dynamics), and that low Rossby and Froude numbers favour their stability. © Crown Copyright 2008. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd
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