On mixing across an interface in stably stratified fluid

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Abstract
Mixed-layer deepening in stratified fluid has been studied experimentally in mean-shear-free turbulence generated by an oscillating grid. Conditions were varied over a wide range and both two-layered and constant-gradient fluid systems were considered. It is shown that the mixed-layer deepening rate is represented well by power laws, and when local scaling is used all the data can be collapsed on an entrainment relation E = K Ri−n with n = 1.50±0.05 when Ri [gsim ] 7. This power law suggests that the turbulent kinetic energy is made available for mixing on a buoyancy timescale characteristic of eddy recoil or internal-wave breaking rather than a turbulent-eddy overturning timescale. In the constant-gradient situation internal waves are generated which radiate energy away from the interface. An evaluation of the radiated energy indicates, however, that generally energy radiation does not affect the entrainment rate. The coefficient K therefore has the same value (K ≈ 3.8) in linearly stratified fluid as in the two-layer situation. The interface thickness is found to be a function of stability, but reaches an asymptotic value of h/D = 0.055 when Ri is very large. There is some indication that the interface thickness is also a weak function of Reynolds number.