Turbulent Mixing in Stably-Stratified Fluids Subjected to Zero-Mean Shear

Abstract

The interaction of a sharp density interface with oscillating grid induced shear-free turbulence was experimentally investigated. A linear photodiode array was used in conjunction with laser-induced fluorescence to measure the concentration of a tracer that was initially located in the less dense layer. A laser-Doppler velocimeter was used to measure the vertical component and a horizontal component of velocity near the interface, and also at a point where tracer concentration was measured. Potential refractive index fluctuation problems were avoided using solutes that provided a homogeneous optical environment. The study consists of two major parts. In the first part of the investigation, energy spectra, velocity correlations, and kinetic energy fluxes were measured. Amplification of the horizontal turbulent velocity fluctuations, coupled with a sharp reduction in the vertical velocity fluctuation level, was observed near the density interface. Moreover, the experiments indicate that the density interface acts in a manner qualitatively similar to a rigid flat plate inserted in the flow. These findings are in agreement with previous results pertaining to shear-free turbulence near rigid walls (Hunt and Graham 1978). In the second part of the investigation, internal wave spectra, wave amplitudes and velocities, and the interfacial mixing layer thickness were measured. The results indicate that mixing occurs in intermittent bursts and that the local gradient Richardson number J remains constant for a certain range of the overall Richardson number Rj. The spectra of the internal waves decay as f-3 at frequencies below the maximum Brunt-Vaisala frequency. These findings give support to a model of oceanic turbulence proposed by Phillips (1977) in which the internal waves are limited in their spectral density by sporadic local instabilities and breakdown to turbulence. The results also indicate that, for a certain Rj range, the thickness of the interfacial layer (normalized by the integral lengths scale of the turbulence)is a decreasing function of Rj. At sufficiently high Rj the interfacial thickness becomes limited by diffusive effects. A simple model for entrainment at a density interface in the presence of shear-free turbulence is presented and compared with the observations.