Why does vertical diffusivity increase with depth in the ocean?
I think you are confusing eddy diffusivity with molecular diffusivity. Whereas the latter increases with temperature, for the former there is no such relationship. Eddy diffusivity describes momentum transport due to eddies. The strength of the eddy diffusivity increases with decreasing buoyancy frequency, which is the case, when moving from the bottom of the mixed layer further downwards in the ocean.