What happens with the Ekman current under constant wind?

The work examines the Ekman current  response to a steady
wind within the Stokes-Ekman paradigm. Under constant wind
in the classical Ekman model there is a single attractor
corresponding to the Ekman (1905)steady solution. It is
known that the account of wind waves  strongly affects the
Ekman current dynamics via the Stokes drift, which is
described by the Stokes-Ekman  model. Waves continue to
evolve even under constant wind, which makes  steady
solutions of the Stokes-Ekman equation impossible. Since
the dynamics of the Ekman response in the presence of
evolving wave field have not been considered,  the basic
questions on how  the Ekman current evolves and,
especially, whether it grows or decays at large times,
remain open.

Here by employing the known self-similar laws of wave
field evolution and  solving analytically the
the Stokes-Ekman equation we  find and analyse
evolution of the Ekman current. We show that the system has
a single time dependent attractor which can be described
asymptotically. The large time asymptotics of the Ekman
current is found to be determined by the regime of wave
field evolution:  for the regimes typical of young waves
 the Ekman current grows with time to infinity, in contrast, for
`old waves'  the Ekman current asymptotically decays.