HYDROMAGNETIC SCALE ANALYSIS AT EARTHS CORE-MANTLE BOUNDARY

Scale analysis of the MHD equations appropriate to the surface layers of the Earth's outer core is used to understand why the peak amplitude of the geomagnetic field on the core-mantle boundary (CMB), B0, is some 8 gauss, corresponding to an Alfven speed of at least 200 km/yr in the core; and why the horizontal fluid motion just beneath the CMB reaches a typical speed, v0, of only about 30 km/yr. The scale analysis reveals that B0 is similar to (rho0OMEGA/sigma0)1/2 and v0 is similar to (OMEGA/mu0(2)sigma0(2)c)1/3 where rho0, mu0, sigma0,OMEGA and c, are respectively, the density of the core at its surface, its magnetic permeability, electrical conductivity, angular velocity, and radius. Customary estimates of these five geophysical parameters yield B0 is similar to 12 gauss, v0 is similar to 12 km/yr. The expression for B0 coincides with that adopted by Malkus and Proctor (1975), but that for v0 conflicts with their choice of v0 is similar to 1/mu0sigma0c, whose numerical value is about 1.4 m/yr, i.e. three orders of magnitude too slow. This scale analysis also predicts that the gradient of excess pressure scales as rho0(mu0(2)sigma0(2)cOMEGA-4)-1/3, amounting to a few times 10(-4) Pa m-1; that horizontal magnetic fields grow vertically near the top of the core on the same length scale, l0, as the horizontal flow varies horizontally; and that l0 is similar to (mu0sigma0OMEGAc-1)-1/3 is similar to 4.2 km. This is consistent with the existence of order 200 gauss horizontal fields within about 100 km beneath the core-mantle boundary corresponding to a typical horizontal current density of order 0.2 amp/m2 near the top of the core. We also find that the evolution time for the vertical field, t0, is (mu0(2)sigma0(2)c4OMEGA-1)1/3, about 295 years for the Earth.