 Geostrophic wind with linear drag

A steady horizontal parcel with drag acceleration $-r\mathbf{u}$ obeys $0=-{\nabla }_{h}p/\rho -f\hat{\mathbf{z}}\times \mathbf{u}-r\mathbf{u}$. Inverting the horizontal rotation-plus-drag matrix gives the title. For $r>0$, the velocity has a component toward lower pressure and a component along atmospheric isobars. For $p_x=0$, $f>0$, $p_y>0$, both $u,v$ are negative. The cross-isobar angle is $\arctan (r/f)$, and the speed is smaller than the corresponding frictionless wind. A vertically resolved turbulent stress is not generally equivalent to one constant $r$.