Shallow water equations on a rotating attracting sphere 2. Simple stationary waves and sound characteristics

Abstract

This paper studies a model of shallow water on a rotating attracting sphere that describes large-scale motions of the planetary atmospheric gases and World ocean water. The propagation of sound perturbations on an equilibrium state is studied. The system of equations for bicharacteristics is integrated in elliptic functions. A description of simple stationary waves is given. It is proved that there exist two types of solutions (supercritical and subcritical ) describing gas motion in a spherical zone, so that one of the boundary parallels is a source and the other is a sink. The obtained solutions are interpreted as large-scale circulating cells in the atmosphere.

Nonlinear-dispersive shallow water equations on a rotating sphere and conservation laws

“…It should be noted that for NLD models in spherical geometry, there are almost no results similar to those obtained for nondispersive shallow water models on a sphere [6,7]. Thus, there is a gap between the active application of the NLD equations in calculations of the propagation of ocean waves and validation of the models used.…”

Dispersive shallow water wave modelling. Part III: Model derivation on a globally spherical geometry

“…The right hand sides of the last two NSW equations contain the Coriolis effect, additional terms due to rotating coordinate system and hydrostatic pressure gradient. Recently a new set of NSW equations on a sphere was derived [12,13] including also the centrifugal force due to the Earth rotation. The applicability range of this model was discussed [12] and some stationary solutions are provided [13].…”

“…Recently a new set of NSW equations on a sphere was derived [12,13] including also the centrifugal force due to the Earth rotation. The applicability range of this model was discussed [12] and some stationary solutions are provided [13]. NSWE on a sphere are reported in [59] in a non-conservative form and including the bottom friction effects.…”