 Geostrophic flow preserving the Taylor constraint

For an instantaneous magnetostrophic Taylor state, the momentum equation leaves a geostrophic null component $u_g=s\omega (s)\hat{\varphi }$. Decompose the velocity into this component and a particular ageostrophic flow, substitute the induction equation into the displayed derivative constraint, and solve the resulting linear equation for $\omega$ with magnetic boundary conditions imposed. When magnetic surface torque vanishes, the geostrophic part is ${\mu }_0^{-1}{\partial }_s[s^3{\int }_{C_s}{B}_s^{2}d\varphi dz{\omega }^{\prime }]$. Boundary terms generally cannot be discarded for an insulating exterior; the primary analysis is Hardy and collaborators' boundary-compatible geostrophic-flow construction. Regularity and an angular-momentum normalization fix remaining homogeneous freedoms when the magnetic coupling is nondegenerate.