<p>The work examines the Ekman current &#160;response to a steady<br>wind within the Stokes-Ekman paradigm. Under constant wind<br>in the classical Ekman model there is a single attractor<br>corresponding to the Ekman (1905)steady solution. It is<br>known that the account of wind waves &#160;strongly affects the<br>Ekman current dynamics via the Stokes drift, which is<br>described by the Stokes-Ekman &#160;model. Waves continue to<br>evolve even under constant wind, which makes &#160;steady<br>solutions of the Stokes-Ekman equation impossible. Since<br>the dynamics of the Ekman response in the presence of<br>evolving wave field have not been considered, &#160;the basic<br>questions on how &#160;the Ekman current evolves and,<br>especially, whether it grows or decays at large times,<br>remain open.</p><p>Here by employing the known self-similar laws of wave<br>field evolution and &#160;solving analytically the<br>the Stokes-Ekman equation we&#160; find and analyse<br>evolution of the Ekman current. We show that the system has<br>a single time dependent attractor which can be described<br>asymptotically. The large time asymptotics of the Ekman<br>current is found to be determined by the regime of wave<br>field evolution: &#160;for the regimes typical of young waves<br>&#160;the Ekman current grows with time to infinity, in contrast, for<br>`old waves' &#160;the Ekman current asymptotically decays.</p><p>&#160;</p>
Large time behavior of solutions to a class of doubly nonlinear parabolic equations
