Phase mixed rotating magnetoconvection and Taylor's condition II. Travelling pulses

Abstract

Abstract At small Elsasser number, rotating magnetoconvection in a self-gravitating sphere sets in as quasigeostrophic axial rolls. They propagate azimuthally on a short azimuthal wave length and are localised in radial extent close to some cylindrical surface. In part 1, nonlinear equations were derived governing the variation of the complex roll amplitude in the radial direction. They have some similarity with the well studied complex Ginzburg-Landau equation. Our system is complicated by the phase mixing resulting from the wave frequency variation of the propagating rolls in the radial direction. It leads to a linear term with an imaginary coefficient proportional to the radial displacement from the cylindrical surface. The only nonlinearities included stem from the use of the relaxed Taylor's condition appropriate to the Ekman regime. The resulting axisymmetric geostrophic azimuthal flow leads to a cubic term in the amplitude equations but. in contrast to the usual Landau term, involves second radial ...