Experiments on mixing in wakes in shallow water

Cafiero, Gioacchino and Woods, Andrew W. (2016) Experiments on mixing in wakes in shallow water. Journal of Fluid Mechanics, 804. pp. 351-369. ISSN 0022-1120, ESSN: 1469-7645 DOI https://doi.org/10.1017/jfm.2016.505

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Abstract

We report on a series of laboratory experiments in which we investigate the mixing in a wake produced downstream of an obstacle in a uniform flow. The fluid is confined within a channel of finite width, and the water depth is small compared with the channel width. The mixing appears to be dominated by dispersion caused by the circulation of the eddies that are shed alternately from each side of the obstacle. However, due to bottom friction, these eddies gradually dissipate downstream. In turn, the intensity of the cross-stream mixing of the tracer decays in the downstream direction, limiting the cross-stream extent of the tracer. We present a time-averaged picture of the experiments which illustrates the deviation of the time-averaged flow in the wake relative to the uniform flow upstream. We then develop a time-averaged model for the flow, using mixing length theory to account for the cross-channel momentum transfer as an eddy viscosity λ1ud , where 2ud is the cross-channel integral of the perturbation in the along-channel speed associated with the wake. We also include a frictional stress to account for the bottom friction. The model predicts a similar pattern of variation of the along-channel velocity in both the along- and cross-channel directions to our experimental data. By matching the cross-channel data with the model, we find that the constant λ1 has value 0.2. We also analyse our experimental data to develop a time-dependent picture of the mixing of a stream of dye released into the wake. Using the model for the evolution of the flow, we develop a model for the time-averaged mixing, again based on mixing length theory. The model predicts a similar spatial distribution for the tracer in both the cross-stream and along-stream directions to that seen in our experimental data. By quantitative comparison of the model with the data, we find that the best fit of the empirical eddy diffusivity, λ2ud , with the data occurs with λ2=0.22 . We discuss implications of our results for modelling cross-stream mixing in shallow turbulent flow.

Item Type:	Article
Uncontrolled Keywords:	2016AREP; IA71
Subjects:	05 - Petrology - Igneous, Metamorphic and Volcanic Studies
Divisions:	05 - Petrology - Igneous, Metamorphic and Volcanic Studies 99 - Other
Journal or Publication Title:	Journal of Fluid Mechanics
Volume:	804
Page Range:	pp. 351-369
Identification Number:	https://doi.org/10.1017/jfm.2016.505
Depositing User:	Sarah Humbert
Date Deposited:	09 Jun 2017 14:07
Last Modified:	09 Jun 2017 14:07
URI:	http://eprints.esc.cam.ac.uk/id/eprint/3983

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