A Theory Of Mixing In A Stably Stratified Fluid

A theory is developed for turbulence in a stably stratified fluid. A growing mixed layer of thickness D 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) of thickness h. When there is stratification, the fluid motion is unaffected by buoyancy forces in the mixed layer. If the upper fluid is of uniform buoyancy, D delta b = v squared may be shown to be constant if we accept the experimental observation that h is proportional to D. In general v may be taken to be a fundamental parameter expressing the stability. The quantity Ri = (v d/k) squared is the most fundamental of the several Richardson numbers that have been introduced in this problem because, with its use, constants of proportionality do not depend on the molecular coefficients of viscosity or diffusion (for high Reynolds number turbulence) or on the geometry of the grid.