DYNAMICS OF INTERFACES AND LAYERS IN A STRATIFIED TURBULENT FLUID

This paper formulates a model of mixing in a stratified and turbulent fluid. The model uses the horizontally averaged vertical buoyancy grad ient and the density of turbulent kinetic energy as variables. Heurist ic 'mixing-length' arguments lead to a coupled set of parabolic differ ential equations. A particular form of mechanical forcing is proposed; for certain parameter values the relationship between the buoyancy fl ux and the buoyancy gradient is non-monotonic and this leads to an ins tability of equilibria with linear stratification. The instability res ults in the formation of steps and interfaces in the buoyancy profile. In contrast to previous ones, the model is mathematically well posed and the interfaces have an equilibrium thickness that is much larger t han that expected from molecular diffusion. The turbulent mixing proce ss can take one of three forms depending on the strength of the initia l stratification. When the stratification is weak, instability is not present and mixing smoothly homogenizes the buoyancy. At intermediate strengths of stratification, layers and interfaces form rapidly over a substantial interior region bounded by edge layers associated with th e fluxless condition of the boundaries. The interior pattern subsequen tly develops more slowly as interfaces drift together and merge; simul taneously, the edge layers advance inexorably into the interior. Event ually the edge layers meet in the middle and the interior pattern of l ayers is erased. Any remaining structure subsequently decays smoothly to the homogeneous state. Both the weak and intermediate stratified ca ses are in agreement with experimental phenomenology. The model predic ts a third case, with strong stratification, not yet found experimenta lly, where the central region is linearly stable and no steps form the re. However, the edge layers are unstable; mixing fronts form and then erode into the interior.