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Wave analysis of different splitting methods in the linearised shallow water equations

The shallow water equations describe motions in a shallow, incompressible and nonviscous fluid layer on the rotating Earth. Due to their relative simplicity, they are widely used for testing and analysing new numerical methods developed for weather prediction models. In this paper, we apply different operator splittings, based on directional decomposition, to the linearised form of the shallow water equations obtained by the method of small perturbations. This system has three types of harmonic wave solutions with known dispersion relations and phase velocities. We investigate how the application of operator splitting modifies these important characteristics, and compare the performance of different splitting methods from this point of view.