In the following pictures, which show contours computed by way of the two-fluid turbulence model:
The first picture shows the volume fraction of lower (saline) fluid. Note the initial delay; then mixing; then unmixing.
This picture shows how the temperature of the saline fluid first rises; it falls later, as heat is transferred to the fresh-water fluid.
This picture shows how the fresh-water temperature rises, gaining its heat from the saline fluid.
Here is shown the density of the saline fluid. It first diminishes, because of the temperature rise, eventually becoming lighter than the fresh water. As it cools, it becomes heavier again.
Here is shown the density of the fresh-water fluid. This also diminishes, as heat is transferred from the saline solution; but it also increases later because some salt diffuses into it.
This picture shows how the vertical velocity of the saline fluid becomes positive, once its density falls below that of the fresh water.
Here are the corresponding vertical-velocity contours of the fresh water
Later, cooling causes it to become negative again. Reminder: the horizontal dimension is time, increasing to the right.
The salt content of the lower fluid does diminish somewhat in the course of time.
The salt content of the upper fluid correspondingly increases.
No Kolmogorov-type model is capable of simulating the process even qualitatively.