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Diapycnal mixing in stratified plane Couette flows

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If you have a question about this talk, please contact Akshath Sharma.

Stratified shear flows are common in natural and engineering systems. It is important to understand the ‘mixing efficiency’ at which kinetic energy is converted to potential energy via irreversible diapycnal mixing occurring in these systems. A specific task is to determine how the flux Richardson number R f varies with characteristic flow parameters, such as the gradient Richardson number Rig and the buoyancy Reynolds (Gibson) number Reb . In this talk, I will review experimental and numerical results in the literature and present new data obtained by direct numerical simulations of stratified plane Couette flows. Particular attention in the latter is paid to the effects of varying Prandtl number Pr from 0.7, 7 and 70 motivated by the wide range of Pr that is encountered in geophysical flows. The fluid between the oppositely moving walls is either continuous stratified or initialized with a two-layer density profile, which enables us to investigate various mixing scenarios. In the continuously stratified set-up, we characterise the mixing properties in the framework of Monin-Obukhov similarity theory and bridge the gap between Rig – and Reb -based parameterizations of R f . In the layered set-up, we investigate possible self-maintaining mechanism of sharp density interfaces motivated by Phillips’ proposal (Deep-Sea Res., vol. 19, 1972) on how layers and interfaces can spontaneously form due to vertical variation of diapycnal flux. I will present a ‘self-sharpening’ mechanism which is due to the combined effects of the ‘scouring’ induced by the turbulence external to the interface and comparatively weak molecular diffusion across the core region of the interface. The effective diapycnal diffusivity and irreversible buoyancy flux are quantified in the tracer-based reference coordinate proposed by Winters and D’Asaro (J. Fluid Mech., vol. 317, 1996) and Nakamura (J. Atmos. Sci., vol. 53, 1996), which enables a detailed investigation of the self-sharpening process by analysing the local budget of buoyancy gradient in the reference coordinate. Some theoretical development in refining Phillips’ work will also be discussed.

This talk is part of the Fluid Mechanics (CUED) series.

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