Nonlinear dynamics of magnetohydrodynamic flows of heavy fluid over an arbitrary surface in shallow water approximation

Abstract

The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of constant inclination. All self-similar discontinuous and continuous solutions are found. The exact explicit solutions of initial discontinuity decay problem over a flat plane and a slope are found. It is shown that the initial discontinuity decay solution is represented by one of five possible wave configurations. For each configuration the necessary and sufficient conditions for its realization are found. The change of dependent and independent variables transforming the initial equations over a slope to those over a flat plane is found.

43 pages, submitted to Theoretical and Computational Fluid Dynamics

References in corpus (4)

• Spread of Matter over a Neutron-Star Surface During Disk Accretion: Deceleration of Rapid Rotation
• Magnetohydrodynamic Shallow Water Waves: Linear Analysis
• Polar confinement of the Sun's interior magnetic field by laminar magnetostrophic flow
• Nonlinear dynamics of magnetohydrodynamic flows of heavy fluid over an arbitrary surface in shallow water approximation

Cited by in corpus (3)

• Nonlinear dynamics of magnetohydrodynamic flows of heavy fluid over an arbitrary surface in shallow water approximation
• Symmetries and conservation laws of the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates
• Nonlinear theory of magnetohydrodynamic flows of stratified rotating plasma in two-layer shallow water approximation. Rossby waves and their three-wave interactions