Model z by computation and taylor's condition

Abstract

The spherical geodynamo model of Braginsky (1978) is re-integrated. The original model of Braginsky modified the Taylor's condition to include the influence of viscous core-mantle coupling. Reinstating also the Ø-component of momentum ∂ω_G(s)/∂t [where ω_G(s) is the geostrophic shear] in the expression for the modified Taylor condition makes possible the investigation of solutions for small viscosities. Above a critical dynamo number D _c, the solution enters a viscously-limited branch (“Ekman” or “coupling” branch) and, eventually, as D is further increased, jumps to a strong-field branch. The original numerical solution of Braginsky belongs to the latter branch and is duplicated. But, with weak viscosities, the solution on that branch is proved inviscid. In that inviscid limit, Braginsky's model meets the Taylor's condition. The same code is used to re-investigate another αω dynamo model defined by a simpler choice of α and ω effects [α = Rα cos θ, ω = Rω(r – 1)]