An estimate of the radial gradient of the toroidal magnetic field at the top of the Earth's core

Abstract

In an αω-type geodynamo, the toroidal magnetic field generated from the poloidal field through differential rotation can be sufficiently strong to make the Lorentz force comparable in strength with the Coriolis force. Thus the fluid flow at the top of the core should contain some information about the toroidal magnetic field. The magnetostrophic approximation is used in the momentum equation for fluid motion to relate the fluctuating part of the axisymmetric poloidal motion of the fluid with the radial gradient, ∂B/∂r, of the steady part of the axisymmetric toroidal field at the core-mantle boundary (CMB). The former can be determined from a geomagnetic secular variation model using Braginsky's (Sov. Phys. JETP, 20: 1462-1471, 1965a) theory of the hydromagnetic dynamo. A geomagnetic secular acceleration model is then used to estimate ∂B/∂r at the CMB. The truncation level N for the geomagnetic field model is varied from three to six and consistent values of ∂B/∂r are only obtained for a range of colatitudes θ between 135° and 180° . It is seen that |∂B/∂r| increases from zero at θ = 180° and attains a maxi near θ ≈ 145° for N = 3 and N = 4, and ∂B/∂r is negative throughout this range of θ in all cases. The average value of ∂B/∂r over this range of θ is found to be around -4 × 10^-6 T m^-1.