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Flow and solute transport through a periodic array of vertical cylinders in shallow water

Published online by Cambridge University Press:  05 September 2014

Xiaoyu Guo ,
Benlong Wang  and
Chiang C. Mei
Xiaoyu Guo
Affiliation:
Ministry of Education Key Laboratory of Hydrodynamics, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai, PR China
Benlong Wang
Affiliation:
Ministry of Education Key Laboratory of Hydrodynamics, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai, PR China
Chiang C. Mei*
Affiliation:
Ministry of Education Key Laboratory of Hydrodynamics, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai, PR China Department of Civil & Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA
*
†Email address for correspondence: ccmei@mit.edu
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Abstract

A micro-mechanical theory is proposed for the prediction of macro-scale properties of flow and dispersion in a current through a periodic array of vertical cylinders standing on a horizontal bed. A two-scale analysis reduces the numerical task to the solution of two canonical boundary value problems in a unit cell. Using measured data on the drag coefficient measured for an array in open channels, the eddy viscosity in the interstitial flow on the micro-scale is calculated for a wide range of Reynolds numbers. The macro-scale relation between the mean velocity and the surface gradient is found in the form of a nonlinear Darcy’s law. The interstitial velocity is then used to derive the macro-scale convection diffusion equation for the solute concentration, also by a two-scale analysis. The Taylor dispersivity and the total effective diffusivity are computed for a wide range of flow rates and solid fractions. Features specific to the periodic geometry are pointed out.

JFM classification

Geophysical and Geological Flows: Coastal engineering Geophysical and Geological Flows: Shallow water flows Turbulent Flows: Turbulence modelling
Type
Papers
Information
Journal of Fluid Mechanics , Volume 756 , 10 October 2014 , pp. 903 - 934
Copyright
© 2014 Cambridge University Press 

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