Single-parameter Model of Vegetated Aquatic Flows

Thursday, 18 December 2014
Ilenia Battiato, San Diego State University, Mechanical Engineering Dept., San Diego, CA, United States and Simonetta Rubol, University of Trento, Department of Civil, Environmental and Mechanical Engineering, Trento, Italy
Coupled flows through and over permeable layers occur in a variety of natural phenomena including turbulent flows over submerged vegetation. In this work, we employ a two-domain approach to model flow through and over submerged canopies. The model, amenable of a closed-form solution, couples the log-law and the Darcy-Brinkman equation, and is characterized by a novel representation of the drag force that does not rely on a parametrization through an unknown drag coefficient. This approach limits to one, i.e., the obstruction permeability, the number of free parameters. Analytical expressions for the average velocity profile through and above the canopies, volumetric flow rate, penetration length, and canopy shear layer parameter are obtained in terms of the canopy layer effective permeability. The model suggests that appropriately rescaled velocities in the canopy and surface layers follow two different scaling laws. The analytical predictions match with the experimental data collected by Ghisalberti and Nepf (2004) and Nepf et al. (2007).