On mixing and transport at a sheared density interface

Abstract

Mixing and transport of a stratifying scalar are investigated at a density interface imbedded in a turbulent shear flow. Steady-state interfacial shear flows are generated in a laboratory water channel for layer Richardson numbers, Ri, between about 1 and 10. The flow field is made optically homogeneous, enabling the use of laser-induced fluorescence with photodiode array imaging to measure the concentration field at high resolution. False-colour images of the concentration field provide valuable insight into interfacial dynamics: when the local mean shear Richardson number, Ris, is less than about 0.40–0.45, interfacial mixing appears to be dominated by Kelvin–Helmholtz (K–H) instabilities; when Ris is somewhat larger than this, interfacial mixing appears to be dominated by shear-driven wave breaking. In both cases, vertical transport of mixed fluid from the interfacial region into adjacent turbulent layers is accomplished by large-scale turbulent eddies which impinge on the interface and scour fluid from its outer edges.Motivated by the experimental findings, a model for interfacial mixing and entrainment is developed. A local equilibrium is assumed in which the rate of loss of interfacial fluid by eddy scouring is balanced by the rate of production (local mixing) by interfacial instabilities and molecular diffusion. When a single layer is turbulent and entraining, the model results are as follows: in the molecular-diffusion-dominated regime, δ/h ∼ Pe−1/2 and E ∼ Ri−1Pe−1/2; in the wave-breaking-dominated regime, δ/h ∼ Ri−1/2 and E ∼ Ri−3/2; and in the K–H-dominated regime, δ/h ∼ Ri−1 and E ∼ Ri−2, where δ is the interface thickness, h is the boundary-layer thickness, Pe is the Péclet number, and E is the normalized entrainment velocity. In all three regimes, the maximum concentration anomaly, [gcy ]m ∼ Ri−1. When both layers are turbulent and entraining, E and δ depend on combinations of parameters from both layers.