Abstract
A perfectly conducting, nonviscous fluid is assumed to be permeated by an inhomogeneous, time-independent external magnetic field. Propagation of small-amplitude hydromagnetic waves with the velocity vector satisfying div v = 0 is investigated in a curvilinear coordinate system in which the lines of the external magnetic field are chosen as coordinate lines. It is shown that, if the lines have no torsion and if the external magnetic field has a certain symmetry, such that the field intensity is independent of one of the curvilinear coordinates, there exist rigorous solutions of the linearized hydromagnetic equations describing waves which travel along the lines of the external magnetic field, with the velocity of the fluid motion directed everywhere along the binormal to the local magnetic line of force. The examples of magnetic fields of plane and axial symmetry are discussed.
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