A theory of mixing in a stably stratified fluid

A theory is developed for turbulence in a stably stratified fluid in which there is no shear and the turbulence is induced by a source of energy near the lower boundary of the fluid. A growing mixed layer appears in the lower portion of the fluid, separated from the non-turbulent fluid above, in which the mean buoyancy gradient is given, by an interfacial layer (IL). The lower mixed layer has a very weak buoyancy gradient but a large buoyancy difference exists across IL. If u is the rms horizontal velocity and l is the integral length scale, ul = K is a constant in a layer of homogeneous fluid agitated by a grid and at some distance from the grid. When there is stratification, the fluid motion is unaffected by buoyancy forces in the mixed layer so that ul should also be constant in the lower portions of the mixed layer.