Search

The time evolution of translationally symmetric hydromagnetic waves in a nonideal magnetohydrodynamic (MHD) plasma is investigated. Exact time-dependent wave solutions of the nonlinear resistive and dissipative MHD equations for the plasma within a cylindrical annulus are presented. It is shown that the magnetic field and the velocity have different damping time and that in the asymptotic limit t→∞ the plasma relaxes toward the equilibrium state involving uniform rotation and no magnetic field.

The propagation of nonlinear hydromagnetic waves in a highly conducting, self‐gravitating fluid in a spherical geometry, subject to the convective forces produced by a radial temperature gradient, is treated in a Boussinesq approximation. Exact wave solutions of the nonlinear magnetohydrodynamic equations (in the Boussinesq approximation) in the presence of convective forces are obtained for the toroidal velocity and magnetic fields. The solution represents waves propagating along the mean magnetic field with the velocity depending on the mean magnetic (or velocity) field strength and the strength of stratification, under the influence of the azimuthal magnetic and velocity fields and convective forces. The solutions may be applicable to the hydromagnetic waves in the Earth’s core and the solar convection zone.

The propagation of nonlinear hydromagnetic waves in a highly conducting, self‐gravitating fluid in a cylindrical geometry, subject to the convective forces produced by a radial temperature gradient, is treated in a Boussinesq approximation. Exact wave solutions of the nonlinear magnetohydrodynamic equations (in the Boussinesq approximation) in the presence of convective forces are obtained for the case when the physical quantities are helically symmetric in cylindrical coordinates. The solutions represent waves propagating helically on the cylindrical surfaces, under the influence of the helical magnetic and velocity fields and the convective forces. The solutions may be applicable to the hydromagnetic waves in the Earth’s fluid core and the solar convection zone with suitable modifications to account for spherical geometry.

Exact wave solutions of the nonlinear magnetohydrodynamic equations for a highly conducting incompressible fluid within an axisymmetric container are obtained for the case when the physical quantities are independent of the axial coordinate or the azimuthal angle in the cylindrical coordinates. The solutions represent waves propagating in the azimuthal or axial direction under the influence of helical magnetic and velocity fields whose strength varies with radius. The solutions are applicable to astrophysical and laboratory plasmas as well as the Earth’s core.

Exact wave solutions of the nonlinear magnetohydrodynamic equations for a highly conducting incompressible fluid within an axisymmetric container are obtained for the case when the physical quantities are helically symmetric in cylindrical coordinates. The solutions represent the waves propagating helically on the cylindrical surfaces, under the influence of helical magnetic and velocity fields whose strength varies with radius. The solutions are applicable to astrophysical and laboratory plasmas as well as the Earth’s core.

An exact axisymmetric wave solution of the nonlinear magnetohydrodynamic equations for a highly conducting incompressible fluid within a perfectly conducting cylindrical wave guide is obtained. The solution represents a cylindrical wave guide mode propagating in the axial direction with constant velocity under the influence of the helical magnetic field.

An exact helically symmetric wave solution of the nonlinear magnetohydrodynamic equations for a highly conducting incompressible fluid within a perfectly conducting cylindrical waveguide is obtained. The solution represents a cylindrical waveguide mode propagating along the helical magnetic field with the velocity proportional to the Alfven velocity.

Exact solutions of the nonlinear magnetohydrodynamic equations for a highly conducting fluid within an axisymmetric container are obtained. Attention is focused on fluids in which the unperturbed velocity and magnetic field are axially symmetric and purely zonal. It is shown that there are exact solutions with large amplitude but restricted form, indicating that an arbitrary disturbing force produces other motions as well as Alfven waves propagating along an azimuthal magnetic field whose strength varies with radius.