The Effect of a Vertical Magnetic Field on the Propagation of Gravity Waves Along the Plane Surface of a Semi-Infinite Viscous, Electrically Conducting Fluid.

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view Abstract Citations (9) References (5) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Effect of a Vertical Magnetic Field on the Propagation of Gravity Waves Along the Plane Surface of a Semi-Infinite Viscous, Electrically Conducting Fluid. Roberts, P. H. ; Boardman, A. D. Abstract The basic equations and boundary conditions governing the effect of vertical magnetic and gravitational fields on small-amplitude perturbations of the free equilibrium surface of a viscous, electrically conducting fluid are presented Normal modes are examined. A dispersion relationship is derived which relates the complex "frequency" n of the normal mode to the Allven velocity, V, the viscosity, , the magnetic diffusivity, X, and the horizontal wave number, k. This dispersion relationship is solved in nine extreme cases In six of these, the magnetic field is too weak to modify substantially the familiar gravity- wave solution holding in the absence of a magnetic field. The influence of the field is so strong in the remaining three cases that they have no parallel in the zero-field case One of these holds for any k if the magnetic field is sufficiently strong In this case n = gV-l(X/ l/2 i e, the effect of the magnetic field is so great that the disturbance is attenuated aperiodically as the Aliven waves radiate energy away from the free surface. Another interesting feature demonstrated is the existence (if V is sufficiently large) of a band of wave numbers k for which no normal-mode solution exists It is nevertheless demonstrated that the associated initial-value problem can be solved for such values of k. In addition to the nine extreme cases mentioned above, three special cases are solved for all k for particular values of V, namely, p = p = 0, and X = 0. Publication: The Astrophysical Journal Pub Date: March 1962 DOI: 10.1086/147291 Bibcode: 1962ApJ...135..552R full text sources ADS |