 Viscous regularization of the Taylor constraint

With small viscosity, the azimuthal cylindrical balance permits Lorentz force torque to be cancelled by viscous stress. For ordinary no-slip rotating boundaries an Ekman layer gives stress of order $\rho \Omega LU\sqrt{E}$, larger than the order-$E$ bulk viscous correction at fixed velocity. Thus bounded small-$E$ flows approach a magnetostrophic Taylor state but need not satisfy its constraint exactly at finite viscosity. An order-one uncompensated magnetic torque would require a divergent flow as $E\to 0$, invalidating the assumed small-inertia balance. Stress-free boundaries remove the leading no-slip friction and require their own torque/regularity conditions.