Spatially varying mixing of a passive scalar in a buoyancy-driven turbulent flow

van Sommeren, Daan D. J. A. and Caulfield, C. P. and Woods, Andrew W. (2014) Spatially varying mixing of a passive scalar in a buoyancy-driven turbulent flow. Journal of Fluid Mechanics, 742. pp. 701-719. ISSN 0022-1120, ESSN: 1469-7645 DOI 10.1017/jfm.2014.25

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Official URL: http://dx.doi.org/10.1017/jfm.2014.25

Abstract

We perform experiments to study the mixing of passive scalar by a buoyancy-induced turbulent flow in a long narrow vertical tank. The turbulent flow is associated with the downward mixing of a small flux of dense aqueous saline solution into a relatively large upward flux of fresh water. In steady state, the mixing region is of finite extent, and the intensity of the buoyancy-driven mixing is described by a spatially varying turbulent diffusion coefficient κv(z) which decreases linearly with distance z from the top of the tank. We release a pulse of passive scalar into either the fresh water at the base of the tank, or the saline solution at the top of the tank, and we measure the subsequent mixing of the passive scalar by the flow using image analysis. In both cases, the mixing of the passive scalar (the dye) is well-described by an advection–diffusion equation, using the same turbulent diffusion coefficient κv(z) associated with the buoyancy-driven mixing of the dynamic scalar. Using this advection–diffusion equation with spatially varying turbulent diffusion coefficient κv(z), we calculate the residence time distribution (RTD) of a unit mass of passive scalar released as a pulse at the bottom of the tank. The variance in this RTD is equivalent to that produced by a uniform eddy diffusion coefficient with value κe=0.88⟨κv⟩, where ⟨κv⟩ is the vertically averaged eddy diffusivity. The structure of the RTD is also qualitatively different from that produced by a flow with uniform eddy diffusion coefficient. The RTD using κv has a larger peak value and smaller values at early times, associated with the reduced diffusivity at the bottom of the tank, and manifested mathematically by a skewness γ1≈1.60 and an excess kurtosis γ2≈4.19 compared to the skewness and excess kurtosis of γ1≈1.46, γ2≈3.50 of the RTD produced by a constant eddy diffusion coefficient with the same variance.

Item Type: Article
Uncontrolled Keywords: 2014AREP; IA67; BPI;
Subjects: 05 - Petrology - Igneous, Metamorphic and Volcanic Studies
99 - Other
Divisions: 99 - Other
05 - Petrology - Igneous, Metamorphic and Volcanic Studies
Journal or Publication Title: Journal of Fluid Mechanics
Volume: 742
Page Range: pp. 701-719
Identification Number: 10.1017/jfm.2014.25
Depositing User: Sarah Humbert
Date Deposited: 29 May 2014 17:02
Last Modified: 09 Jun 2017 16:18
URI: http://eprints.esc.cam.ac.uk/id/eprint/3060

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