Steady-state solutions of the vertical heat-balance equation have been obtained for various assumed vertical profiles of the vertical component of velocity and eddy conductivity. Relationships have been found for the depth and the thickness of the thermocline in terms of parameters that characterize the vertical velocity and eddy conductivity. Two of the solutions agree with observations in regions having respectively divergent and convergent Ekman mass transport.
Overstreet, Roy, and Maurice Rattray. 1969. "On the roles of vertical velocity and eddy conductivity in maintaining a thermocline." Journal of Marine Research 27, (2). https://elischolar.library.yale.edu/journal_of_marine_research/1151