While the details of the Ekman velocity profile are difficult to verify, there is a robust relationship between the wind stress and the depth integral of the Ekman velocities given by $ U_{ek} \equiv \underbrace{\int_{-D}^{0} u_{ek} \, dz}_{\substack{\text{Ekman volume flux per unit length} \\ \text{(D as Ekman layer depth)}}} = \frac{\underbrace{\tau_y^s}_{\text{northward wind stress}}}{\underbrace{\rho}_{\text{density}} \, \underbrace{f}_{\text{Coriolis parameter}}} , \quad V_{ek} \equiv \underbrace{\int_{-D}^{0} v_{ek} \, dz}_{\substack{\text{Ekman volume flux per unit length} \\ \text{(D as Ekman layer depth)}}} = - \frac{\underbrace{\tau_x^s}_{\text{eastward wind stress}}}{\underbrace{\rho}_{\text{density}} \, \underbrace{f}_{\text{Coriolis parameter}}} $