Turbulent mixing at a shear-free density interface

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 dye that was initially only in the less dense layer. A laser-Doppler velocimeter was used to measure the vertical velocity in and above the density interface at a point where the dye concentration was also measured. Potential refractive-index-fluctuation problems were avoided using solutes that provided a homogeneous optical environment across the density interface. Internal wave spectra, amplitudes and velocities, as well as the vertical mass flux were measured. The results indicate that mixing occurs in intermittent bursts and that the gradient (local) Richardson number remains constant for a certain range of the overall Richardson number Rj, defined in terms of an integral lengthscale, buoyancy jump and turbulence intensity. The spectra of the internal waves decay as f−3 at frequencies below the maximum Brunt-Väisälä frequency. These findings give support to a model for oceanic mixing 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 lengthscale of the turbulence) is a decreasing function of Rj. At sufficiently high Rj the interfacial thickness becomes limited by diffusive effects. Finally, we discuss a simple model for entrainment at a density interface in the presence of shear-free turbulence.