Wave analysis for different splittings of the shallow water equations on the β-plane

The effects of operator splitting on the wave Solutions of the linearized shallow water equations have been investigated in [A. Havasi, Dispersion analysis of operator splittings in the linearized shallow water equations, in: I. Lirkov, S. Margenov, J. Wasniewski (Eds.), Large-Scale Scientific Computing: 5th International Conference, LSSC 2005, Sozopol, Bulgaria, June 6-10, 2005, in: Lecture Notes in Computer Science, vol. 3743, Springer, 2006] by directional decomposition of the sub-operators and by the constant Coriolis parameter f. This - so-called f-plane - approximation does not allow the formation of Rossby waves, which play a major role in the evolution of midlatitude weather systems. In this paper we apply beta-plane approximation in the shallow water equations and examine how the resulting Rossby-gravity waves are influenced by the separation of different physical effects in some concrete splitting schemes. (C) 2007 Elsevier Ltd. All rights reserved.