Flow, Mass Transport and Surface Waves in Coastal Water with Vegetation
Mei, Chiang C.
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Mangroves along the sea shores are known to provide partial protection against tsunamis. A theory is given for the effects of emergent coastal forests on the propagation of surface waves of small amplitudes. The forest is idealized by a periodic array of vertical cylinders. Simple models are employed to represent interstitial turbulence generated by flow through the cylinders. Multi-scale (homogenization) analysis is carried out to save computational labor. Analytical and numerical solutions for wave attenuation on the macro-scale for different bathymetries are presented. Numerical results are compared with a laboratory experiment motivated by a proposed measure for coastal protection against tsunamis. Emergent vegetation in lakes and coastal waters affects the flow and transport of nutrients ands pollutants. The multiple-scale theory is extended to the nonlinear flow and dispersion in a current through a periodic array of vertical cylinders standing on a horizontal bed. Using the drag coefficient measured for an array in open channels, eddy viscosity in the interstitial flow on the micro-scale is calculated for a wide range of Reynolds numbers. Nonlinear correction of the classic Darcy's law is deduced on the macroscale. The interstitial velocity is used to derive the macro-scale convection diffusion equation for the solute concentration. Taylor dispersivity and the total effective diffusivity tensors are deduced for a wide range of flow rates and solid fractions.