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Interaction between double diffusion and differential diffusion in a stratified turbulent flow

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Abstract

Salt fingers, which can occur in a fluid with stable temperature stratification and unstable salinity stratification, have larger fluxes when the ratio of the contributions of temperature and salinity to the density gradient (i.e., the density ratio) is close to one. This study investigated whether differential diffusion—or the preferential transport of temperature in a weakly turbulent, strongly stratified flow—can decrease an initially large density ratio enough to strengthen salt fingers. Laboratory experiments were conducted in which a stratification favorable for salt fingers was stirred with oscillating arrays of vertical rods. The density ratio decreased slightly when its initial value was large, as expected in differential diffusion, and it increased when its initial value was small, as expected for salt fingers. The mixing efficiency was less than 4%, and in two of the runs with low initial density ratio, it started negative. A one-dimensional eddy diffusion model in which the overall eddy diffusivities simply sum the contributions of salt fingers and mechanically generated turbulence described the evolution well and predicted an equilibrium state once the two eddy diffusivities became equal.

Article highlights

  • The evolution of the density ratio illustrated the importance of salt fingers and differential diffusion.

  • The mixing efficiency was less than 4%, and it showed features of differential diffusion and fingering.

  • A model that adds the mixing from mechanical turbulence and fingering predicts equilibrium.

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Funding

This material is based upon work supported by the National Science Foundation under Grant No. 1034221. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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  1. Department of Civil, Construction, and Environmental Engineering, Iowa State University, Ames, IA, USA

    Ian P. Willard & Chris R. Rehmann

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  1. Ian P. Willard
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Correspondence to Chris R. Rehmann.

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Willard, I.P., Rehmann, C.R. Interaction between double diffusion and differential diffusion in a stratified turbulent flow. Environ Fluid Mech 23, 1099–1113 (2023). https://doi.org/10.1007/s10652-022-09900-2

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