Turbulent universality and the drift velocity at the interface between two homogeneous fluids

Abstract

The drift velocity U0 at the interface between two homogeneous turbulent fluids of arbitrary relative densities in differential mean motion is considered. It is shown that an analytical expression for U0 follows from the classical scaling for these flows when the scaling is supplemented by standard turbulent universality and symmetry assumptions. This predicted U0 is the weighted mean of the free-stream velocities in each fluid, where the weighting factors are the square roots of the densities of the two fluids, normalized by their sum. For fluids of nearly equal densities, this weighted mean reduces to the simple mean of the free-stream velocities. For fluids of two widely differing densities, such as air overlying water, the result gives U0 ≈ αV∞, where α ≪ 1 is the square root of the ratio of the fluid densities, V∞ is the free-stream velocity of the overlying fluid, and the denser fluid is assumed nearly stationary. Comparisons with two classical laboratory experiments for fluids in these two limits and with previous numerical simulations of flow near a gas–liquid interface provide specific illustrations of the result. Solutions of a classical analytical model formulated to reproduce the air–water laboratory flow reveal compensating departures from the universality prediction, of order 15% in α, including a correction that is logarithmic in the ratio of dimensionless air and water roughness lengths. Solutions reproducing the numerical simulations illustrate that the logarithmic correction can arise from asymmetry in the dimensionless laminar viscous sublayers.