A model of turbulent mixing across a density interface including the effect of rotation

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Abstract
A new theoretical approach is presented, which determines the entrainment laws with and without background rotation in a two-layer stratified fluid with one layer stirred by turbulent motions. The model gives the entrainment coefficient E as a function of the local turbulent Richardson number Ri = g′l/u2, the Rossby number Ro = u/fl and the Péelet number Pe = ul/κ. The following entrainment laws are obtained: (i) without rotation and for a high Péclet number: (iii) with rotation and for a high Péclet number: E ∝ RoRi−l. These entrainment laws are consistent with experiments for the three different cases. The model relies to a great extent on the spectral distribution of interface oscillations measured in experiments. Comparison is made with experiments and with earlier models of entrainment.