Electromagnetic and Viscous Damping of Core Oscillations

Abstract

Summary A detailed investigation of the interaction of core oscillations with the main magnetic field is made. Selection rules and interaction coefficients are obtained. Although the strengths of the interactions vary over nearly three orders of magnitude, all are extremely weak. Ohmic and viscous dissipation are considered in parallel calculations. It is found that core oscillations are almost unaffected by either damping mechanism. Most of the Ohmic dissipation takes place within a few skin depths of the boundary. Viscous dissipation is estimated only for the body of the liquid core. Even though it is expected to be much larger near the boundaries, it would seem unlikely to be sufficiently large to be of any significance. Our conclusion is that core oscillations are virtually free of damping. In a subadiabatic core, gravitational oscillations might be persistent enough to sustain an oscillatory geodynamo. 1. Introduction In any discussion of the dynamics of the Earth’s liquid outer core, it is important to know the rate at which energy dissipation takes place. There are two possible dissipative mechanisms in the liquid core, Ohmic and viscous. In this paper we consider their relative importance in the damping of small harmonic oscillations. The full geometries of both the main magnetic field and the oscillatory displacements are taken into account. Electromagnetic damping of elastic waves in the core appears to have been first suggested by Cagniard (1952) and an estimate of the strength of such damping was made by Knopoff (1955). Both Knopoff (1955) and Baiios (1955, 1956) developed theories of the modes of propagation of disturbances in the presence of a uniform magnetic field. Using accepted values of the physical parameters involved, they showed that at seismic frequencies the attenuation would be very weak. A similar result was obtained by Kraut (1965) for the damping of radial oscillations of a fluid sphere immersed in a uniform field. Lilley (1967) was the first to point out that as well as the damping that arises in a uniform magnetic field due to the distortion of the medium, there is an additional electromagnetic dissipation which occurs in non-uniform magnetic fields due to translation of the medium into regions of differing flux density. He confirmed the effect both theoretically and experimentally for elastic waves travelling in magnetic field gradients (Lilley & Smylie 1968; Lilley & Carmichael 1968, 1970). The relevance of the non-uniform field effect to the Earth’s core was only briefly considered by Lilley (1967). He concluded that a Q of about lo9 might characterize