The Geometric Properties of Shallow Water Equation Solutions on a Rotating Sphere

This paper investigates the shallow water model on a rotating attracting sphere, which describes large-scale motions of gas and liquid on the surface of solid planets. We provide a description of the geometric characteristics of simple stationary waves obtained within this model. For two types of stationary wave solutions, an analysis of the curvature of the continuous medium’s profile is performed. Solutions with variable curvature profiles are shown to exist.