7 research outputs found
Nonlinear dynamics of magnetohydrodynamic flows of heavy fluid over an arbitrary surface in shallow water approximation
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.Comment: 43 pages, submitted to Theoretical and Computational Fluid Dynamic