Liu, Z., 1993: Thermocline forced by varying Ekman pumping. Part I: Spinup and Spindown. Journal of Physical Oceanography, 23(12) 2505-2522.

Abstract: A two-layer planetary geostrophic model is used to investigate the thermocline variability under a suddenly changing Ekman pumping. The effect of ventilation and the associated advection is particularly emphasized in the ventilated zone. The governing equation is a quasi-linear equation, which is solved analytically by the method of characteristics.
It is found that the dynamics differs substantially between a shadow zone and a ventilated zone. In the shadow zone, the Rossby wave is the dominant mechanism to balance the Ekman pumping. After a sudden change in the wind field, the Ekman pumping changes rapidly, but the baroclinic Rossby wave evolves at a much slower time scale (years to decades). This mismatch of response time scale produces an imbalance in forcings and in turn results in a strong thermocline variability. However, in the ventilated zone, the cold advection replaces the Rossby wave to become the major opposing mechanism to the Ekman pumping. After a sudden wind change, both the Ekman pumping and the cold advection vary rapidly at the time scale of barotropic Rossby waves (about one week) to achieve a new steady balance, leaving little thermocline variability.
The evolution of thermocline structure and circulation differs dramatically between a spinup and a spindown. For instance, with a change in the Ekman pumping field, the lower-layer fluid in the shadow zone is no longer motionless. After a spinup, the lower-layer water moves southward because of the compression on planetary vortex tubes by the downward anomalous Ekman pumping. The associated circulation is an anticyclonic gyre. In contrast, during a spindown, the water moves northward because of the stretching of planetary vortex tubes by the upward anomalous Ekman pumping. The lower-layer circulation now consists of two counterrotating gyres: an anticyclonic gyre to the north and cyclonic gyre to the south.