On the entrainment rate across a density interface

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Abstract
Mixed-layer deepening due to grid-generated turbulence is studied experimentally with the aim of explaining the contradictory results of previous studies. Entrainment rates are calculated at fixed distances from the grid in order to avoid the necessity of using an empirical expression for the decay of the turbulent velocity scale. It is shown that an incorrect form of this decay law can cause large errors in the predicted Richardson number dependence of the entrainment rate. For this study this dependence can be expressed as a power law of the form E = KRi−1,2. The spread of the results imply that an error of at least ± 10% is realistic in the determination of the exponent.The turbulent velocity decay law is also deduced from the data, and it is found that the decay cannot be represented by a simple power law. Indeed two distinct flow regions, with differing decay rates, are present.