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

  • Xiaoyu Guo (a1), Benlong Wang (a1) and Chiang C. Mei (a1) (a2)


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.


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