A numerical model for the onset of stratification in shear-free turbulence

Abstract

Abstract The formation of a thermocline in a water column, where shear-free turbulence is generated from both the surface and the bottom, and a stabilizing buoyancy flux is imposed on the surface, was studied using a numerical model with the aim of understanding the formation of a tidal front in the coastal area. The time evolutions of the distributions of density and turbulent kinetic energy calculated from the model shows that the emergence of a thermocline depends on the conditions determined by the buoyancy flux at the surface Q, the eddy diffusivities maintained at the bottom and at the surface Kb and Ks and the height of the water column H. The criterion for the formation of a thermocline was predicted as Rdelta4 ∼ constant for large δ (δ > 0.5), but the dependence on δ decreases as δ tends to 0, where R = H 4 Q/K 3 b , δ = 1 − D 0/H is the depth of a thermocline in the absence of bottom mixing. The depth of a thermocline was found to decrease as the bottom mixing increases for a given value of D 0....