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

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Abstract
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 (= ΔbD3*/K2, where Δb 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 Ri½. The present results, together with the results of the earlier work of Fernando & Long, show a good agreement with a theory of Long (1978b) for behaviour at high values of Ri. The closure assumptions of that theory were also verified by our measurements.
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