On the nature of the entrainment interface of a two-layer fluid subjected to zero-mean-shear turbulence

An experimental study was performed to further understanding of turbulent mixing in a two-layer fluid subjected to shear-free turbulence. At low Richardson numbers Ri (= Δ bD 3 * / K 2 , where Δ b is the buoyancy jump, D * is the depth of a mixed layer and K is ‘action’) the entrainment seems to occur through the eroding effect of large eddies, whereas at high Ri the large eddies flatten at the density interface and the quasi-isotropic eddies near the interface are responsible for the entrainment. The buoyancy transfer can be well described by a gradient-transport model when the eddy diffusivity is properly defined. At or just above the entrainment interface, the buoyancy flux is of the same order as the dissipation, and the diffusive-flux Richardson number tends to a constant. The thickness h of the interfacial layer was measured in three different ways and was found to grow linearly with D * in agreement with preliminary findings of an earlier investigation of Fernando & Long (1983). The buoyancy gradient in the interfacial layer was found to be constant, and the resulting buoyancy conservation law was experimentally verified. The frequency of the interfacial-layer waves appears to vary as Ri ½ . The present results, together with the results of the earlier work of Fernando & Long, show a good agreement with a theory of Long (1978 b ) for behaviour at high values of Ri . The closure assumptions of that theory were also verified by our measurements.