Weak discontinuities in shallow-liquid magnetohydrodynamics

Evolution of weak discontinuities in shallow water equations

In this paper, we determine the critical time, when a weak discontinuity in the shallow water equations culminates into a bore. Invariance group properties of the governing system of partial differential equations (PDEs), admitting Lie group of point transformations with commuting infinitesimal operators, are presented. Some appropriate canonical variables are characterized that transform equat...

Rossby waves in ” shallow water ” magnetohydrodynamics

Aims. The influence of a toroidal magnetic field on the dynamics of Rossby waves in a thin layer of ideal conductive fluid on a rotating sphere is studied in the " shallow water " magnetohydrodynamic approximation for the first time. Methods. Dispersion relations for magnetic Rossby waves are derived analytically in Cartesian and spherical coordinates. Results. It is shown that the magnetic fie...

Liquid Oxygen Magnetohydrodynamics

Remarks on rotating shallow-water magnetohydrodynamics

We show how the rotating shallow-water MHD model, which was proposed in the solar tachocline context, may be systematically derived by vertical averaging of the full MHD equations for the rotating magneto fluid under the influence of gravity. The procedure highlights the main approximations and the domain of validity of the model, and allows for multi-layer generalizations and, hence, inclusion...

Hyperbolic theory of the ‘‘shallow water’’ magnetohydrodynamics equations

Recently the shallow water magnetohydrodynamic ~SMHD! equations have been proposed for describing the dynamics of nearly incompressible conducting fluids for which the evolution is nearly two-dimensional ~2D! with magnetohydrostatic equilibrium in the third direction. In the present paper the properties of the SMHD equations as a nonlinear system of hyperbolic conservation laws are described. C...