Dynamo action associated with random inertial waves in a rotating conducting fluid

Abstract

It is shown that a random superposition of inertial waves in a rotating conducting fluid can act as a dynamo, i.e. can systematically transfer energy to a magnetic field which has no source other than electric currents within the fluid. Dynamo action occurs provided the statistical properties of the velocity field lack reflexional symmetry, and this occurs when conditions are such that there is a net energy flux (positive or negative) in the direction of the rotation vector Ω.

If the magnetic field grows from an infinitesimal level, then the mode of maximum growth rate dominates before the back-reaction associated with the Lorentz force becomes significant. This mode is first determined, and then the back-reaction associated with it alone is analysed. It is shown that the magnetic energy grows exponentially during the stage when the Lorentz forces are negligible, then reaches a maximum depending on the values of the parameters \[ R_m = u_0 l/\lambda,\quad Q = \Omega l^2/\lambda, \] (u₀ = initial r.m.s. velocity, l = length scale characteristic of the velocity field, λ = magnetic diffusivity) and ultimately decays as t⁻¹ (equation (5.15)). This decay is coupled with a decay of the velocity field due to ohmic dissipation, and it occurs because there is no external source of energy for the fluid motion.