V. V. Ostapenko, A. V. Speshilova, A. A. Cherevko, A. P. Chupakhin, “Numerical simulation of wave motions on a rotating attracting spherical zone”, Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 3,Pages <nobr>469

Numerical simulation of wave motions on a rotating attracting spherical zone

V. V. Ostapenko^ab, A. V. Speshilova^a, A. A. Cherevko^ab, A. P. Chupakhin^ab

^a Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent'eva 15, Novosibirsk, 630090, Russia
^b Novosibirsk State University, Universitetskii pr. 2, Novosibirsk, 630090, Russia

Abstract: The Riemann problem for the shallow water model on a rotating attracting spherical zone numerically is solved. A shock-capturing difference scheme is constructed that approximates the system of conservation laws describing discontinuous solutions of the given model. The Riemann problem is formulated as one of developing a wave process from initial data representing a spherical zone covered by various equilibria and zonal flows. Two Riemann problems are numerically simulated: the breakdown of water “ridges” of various shapes at equilibrium and propagation of contact discontinuity perturbations between an equilibrium and a zonal flow. The general properties of such solutions independent of the geometric configuration of the domains occupied by elementary solutions in the initial data are demonstrated.

Key words: conservation laws for shallow water equations on a rotating attracting spherical zone, Riemann problem, equilibrium, zonal flows, shock-capturing difference scheme, decay of ridges in the form of chevrons and elliptic annuli.

UDC: 519.634

MSC: Primary 65M06; Secondary 86A10

Received: 24.09.2013
Revised: 09.10.2014

DOI: 10.7868/S0044466915030138