- The seminal model for the effect of winds on surface ocean currents was proposed by Ekman more than a century ago. It demonstrated the non-trivial effect of the Earth's rotation on surface ocean currents driven by constant wind. Here we show that this model is ill-defined when forced by a more realistic stochastic wind – the component of the stochastic wind that resonates with the Coriolis frequency leads to the divergence (singularity) of the surface and depth-integrated currents. The addition of a linear friction term to the model suppresses this unphysical singularity. We present explicit solutions for the surface and depth-integrated currents for wind stress with exponentially decaying and oscillating temporal correlations and show that the wind's temporal correlations and the friction drastically affect, and can even diminish, the resonance. Winds and currents from the Gulf of Elat are compared with the model's predictions.