Turbulent mixing in a stratified fluid

The strength of diapycnal mixing by small-scale motions in a stratified fluid is investigated through changes to the mean buoyancy profile. We study the mixing in laboratory experiments in which an initially linearly stratified fluid is stirred with a rake of vertical bars. The flow evolution Ž . depends on the Richardson number Ri , defined as the ratio of buoyancy forces to inertial forces. At low Ri, the buoyancy flux is a function of the local buoyancy gradient only, and may be modelled as gradient diffusion with a Ri-dependent eddy diffusivity. At high Ri, vertical vorticity shed in the wakes of the bars interacts with the stratification and produces well-mixed layers separated by interfaces. This process leads to layers with a thickness proportional to the ratio of Ž . grid velocity to buoyancy frequency for a wide range of Reynolds numbers Re and grid solidities. In this regime, the buoyancy flux is not a function of the local gradient alone, but also depends on the local structure of the buoyancy profile. Consequently, the layers are not formed by the PhillipsrPosmentier mechanism, and we show that they result from vortical mixing previously thought to occur only at low Re. The initial mixing efficiency shows a maximum at a critical Ri which separates the two classes of behaviour. The mixing efficiency falls as the fluid mixes and as the layered structure intensifies and, therefore, the mixing efficiency depends not only on the overall Ri, but also on the dynamics of the structure in the buoyancy field. We discuss some implications of these results to the atmosphere and oceans. q 1999 Elsevier Science B.V. All rights reserved.