Hall current effects on waves in an electrically conducting rotating fluid

Abstract

The waves generated by an obstacle moving with constant velocity U along the axis of an inviscid, incompressible, infinitely conducting fluid with Hall current effects, rotating with an angular velocity Ω are studied by Lighthill's technique. Three cases arise according as U>A ₁, U=A ₁ or U<A ₁, where A ₁ is the modified Alfven velocity due to Hall current term. In the cases U> and <A ₁ the wave-number surface consists of two distinct spheres and four coincident planes. The waves corresponding to the points on the outer sphere trail behind and those on the inner sphere travel ahead of the disturbance if U>A ₁ and vice-versa if U<A ₁. When U=A ₁ the wave-number surface consists of two coincident spheres and four coincident planes and the spherical waves are found both ahead and behind. By drawing appropriate normals to the four planes, it is seen that the formation of the Taylor column ahead of the disturbance is possible in all the cases.