Magnetostrophic Turbulence and the Geodynamo

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The flow generated by a random buoyancy field in a rotating medium permeated by a dynamo-generated magnetic field is considered, under the assumptions that the Rossby number and the magnetic Reynolds number (based on the scale of the buoyancy fluctuations) are both small. This permits linearisation of the governing evolution equations. Provided ‘up-down’ symmetry is broken, a mean helicity and an associated α-effect are generated. These are calculated in terms of the spectrum function of the buoyancy field. Expressions are also obtained for the buoyancy flux and the Reynolds stresses (kinetic and magnetic), and an outline dynamo scenario is proposed. The nature of this type of magnetostrophic turbulence is briefly discussed.