Exact Splitting for Rossby Waves in a Shallow-water Model

[摘要]  The time-tendency operator for a shallow-water model is split into ‘advection’ and ‘adaption’ operators. Rossby eigen-modes and a gravity-wave subspace are defined for perturbations on any state where, over the whole domain, either the divergence is uniform, or else the absolute vorticity has a uniform sign. It is then shown that  a) the adaption operator yields zero tendency for Rossby modes,  b) advection does not transform gravity-wave modes into Rossby modes,  c) that (a) and (b) allow an ‘exact splitting for Rossby modes’  This splitting allows selective approximation of gravity wave modes without introducing error in the Rossby-modes, so that economical long timesteps can be used without degrading the accuracy of the part of the solution which is significant for weather prediction.  A particular computational method using this splitting is constructed and tested experimentally. This has less time-differencing error for Rossby-modes than the ‘leapfrog’ scheme, and has no computational mode. This particular scheme strongly attenuates high-frequency gravity wave modes.

[学科分类] 大气科学