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

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

Journal

Lobachevskii Journal of Mathematics
ISSN: 1995-0802 , E-ISSN: 1818-9962

Output data

Year: 2025, Volume: 46, Number: 9, Pages: 4343-4355 Pages count : 13 DOI: 10.1134/S1995080225611609

Tags

shallow water on a sphere, stationary solutions, Gaussian and mean curvature

Authors

Chupakhin A.P. ^1,2 , Stetsyak E.S. ^1,2

Affiliations

1	Lavrentyev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090 Russia
2	Novosibirsk State University, Novosibirsk, 630090 Russia

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.

Chupakhin A.P. , Stetsyak E.S.
The Geometric Properties of Shallow Water Equation Solutions on a Rotating Sphere
Lobachevskii Journal of Mathematics. 2025. Т.46. №9. С.4343-4355. DOI: 10.1134/S1995080225611609

Submitted:	Apr 8, 2025
Accepted:	Jul 31, 2025

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