Formation of thermoclines in zero‐mean‐shear turbulence

Heating q at the surface of a turbulent and initially unstratified ocean may form a thermocline if strong enough. It is proposed here that the heating is strong enough if turbulence occurs infrequently enough past some depth not to transport heat downward. Turbulence is taken not to occur if the gradient Richardson number Ri = N2/(uz2 + Vz2) rises above a critical value of 0.25. The probability that this occurs becomes very small when and where the population Richardson number is greater than about 1.33. This traps the heat above that layer, increasing and forming a thermocline. Let stirring action K be generated at a depth D below heating, and scale the heating as B = gαq/ρcp. Then the population Richardson number criterion translates: if H = BD4/K3 < Hc ≈ 1.6, a thermocline will form above the stirring (“tidal friction”). If H < Hc, no thermocline will form above the stirring, but after a time 0.9(K/B)1/2, the thermocline will form at a depth 0.6D+2.2(K3/B)1/4 below the stirring (“wave breaking”). These theoretical results match experimental results of Hopfinger and Linden (1982).