Magneto-Hydrodynamic waves in incompressible and compressible fluids*

Abstract

This is the second of two papers dealing with a systematic study of the linearized problems in magneto-hydrodynamics of incompressible and compressible fluids. The first paper (Banos 1955) deals mainly with the general theory of plane homogeneous waves and of time harmonic cylindrical waves propagating in a homogeneous and isotropic conducting fluid of infinite extent embedded in a uniform field of magnetic induction. The medium is assumed to consist of an ideal fluid devoid of viscosity and expansive friction, which is characterized (in rationalized mks units) by the rigorously constant macroscopic parameters p, e and o, where pe = c-2 and o is the (ohmic) conductivity. The present paper deals with the application of the general theory to the determination of the modes of propagation and to the computation of the corresponding propagation constants. It is shown that an incompressible fluid sustains two types of modes: one type devoid of pressure fluctuations (velocity modes), and the other accompanied by pressure oscillations (pressure modes). In the case of cylindrical waves in an incompressible fluid there are two distinct pressure modes, one of which, however, is highly attenuated and therefore of little physical interest. It is found that a compressible fluid also sustains the same class of velocity modes (devoid of pressure fluctuations and hence independent of the velocity of sound in the medium) as an incompressible fluid. In addition, a compressible fluid is shown to propagate two distinct pressure modes which, under appropriate limiting conditions peculiar to each type, behave respectively as a modified sound wave and as a modified magneto-hydrodynamic wave. And, for every mode discussed here, there are presented the limiting forms of the propagation constant in three cases of physical interest: infinite conductivity, slightly attenuated modes, and weak magneto-hydrodynamic coupling which arises when the externally applied field is vanishingly small.