Single-parameter model of vegetated aquatic flows

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 which 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). Key Points Analytical model characterized by one fitting parameter Velocities in the canopy and surface layers follow two different scaling laws Good agreement between model predictions and experimental data