Plane-parallel magnetohydrodynamic flow with imposed shear
= Plane-parallel magnetohydrodynamic flow with imposed shear
A useful <ideal magnetohydrodynamics> reduction has $\mathbf u=\mathbf v(z,t)+ax\mathbf e_y$, $\mathbf B=\mathbf B(z,t)$ and $\rho=\rho(z,t)$. The constant background <shear flow> supplies $av_x$ in the axial momentum equation and $aB_x$ in axial magnetic induction. The solenoidal constraint and <MHD induction equation> together make $B_z$ constant.