 Laminar Ekman boundary stress

For $f>0$, a stationary lower no-slip boundary condition below uniform exterior geostrophic flow $W_g$ produces $W_E=-W_g{e}^{-(1+i)z/{\delta }_E}$. The upward shear component at the bottom is $T_b=\rho \nu W_E^{\prime }(0)=\rho \sqrt{f\nu /2}(1+i)W_g$; the bottom traction on the fluid is $-T_b$. This law cannot be assigned to an arbitrary prescribed surface wind stress without an additional boundary condition.