The explicit form of the governing equation is ∂Br ∂t =− 1 R⊙ sinθ ∂ ∂θ (sinθu θBr) −Ω(θ) ∂Br ∂ϕ + η R2 ⊙ sinθ ∂ ∂θ sinθ ∂Br ∂θ ! + η R2 ⊙ sin2 θ ∂2Br ∂ϕ2 +S

describes the evolution of the radial magnetic field subject to differential rotationΩ(θ), meridional flowu θ(θ), turbulent diffusionη with the induction equation ∂Br ∂t +∇ h ·(u hBr)=η∇ 2 hBr +S,(A · 1990