Two-dimensional surface waves in magnetohydrodynamics

The Zero Surface Tension Limit of Two-Dimensional Water Waves

We consider two-dimensional water waves of infinite depth, periodic in the horizontal direction. It has been proven by Wu (in the slightly different nonperiodic setting) that solutions to this initial value problem exist in the absence of surface tension. Recently Ambrose has proven that solutions exist when surface tension is taken into account. In this paper, we provide a shorter, more elemen...

Propagating magnetohydrodynamics waves in coronal loops.

High cadence Transition Region and Coronal Explorer (TRACE) observations show that outward propagating intensity disturbances are a common feature in large, quiescent coronal loops, close to active regions. An overview is given of measured parameters of such longitudinal oscillations in coronal loops. The observed oscillations are interpreted as propagating slow magnetoacoustic waves and are un...

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...

Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics

Monolithic Multigrid Methods for Two-Dimensional Resistive Magnetohydrodynamics

Magnetohydrodynamic (MHD) representations are used to model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. The resulting linear systems that arise from discretization and linearization of the nonlinear problem are generally difficult to s...