Evolution of forced magnetohydrodynamic waves in a stratified fluid

The evolution of a buoyancy disturbance in a stratified incompressible fluid permeated by a uniform vertical magnetic field is investigated. Two regimes are considered in the absence of background rotation - that of strong stratification, where the internal gravity wave frequency omega(A) is much higher in magnitude than the magnetic (Alfven) wave frequency omega(M), and that of strong magnetic field, where omega(M) is dominant. For small but finite magnetic diffusion, perturbations that initially lie in the strong-field regime are shown to cross over to the regime of strong stratification, so that small-scale motions may exist as damped internal gravity waves at large times. The induced magnetic field propagates as damped Alfven waves for a much longer time than the velocity before undergoing the above transition. With strong rotation, the unstably stratified system that satisfies the inequality vertical bar omega(C)vertical bar > vertical bar omega(M)vertical bar >> vertical bar omega(A)vertical bar >> vertical bar omega(eta)vertical bar, where omega(C) is the inertial wave frequency and omega(eta) is the diffusion frequency, is of relevance to convection-driven dynamos. Here, a parameter space with vertical bar omega(M)/omega(C)vertical bar similar to 0.1 is found wherein the flow intensity of the slow magnetic-Archimedean-Coriolis (MAC) waves is of the same order of magnitude as that of the fast MAC waves. Slow wave motions at horizontal length scales much smaller than the width of the fluid layer can therefore generate substantial helicity in rapidly rotating dynamos. The excitation of slow MAC waves at scales of similar to 10 km in the Earth's core may play a crucial role in the generation of the axial dipole field.