Linear and nonlinear frequency-domain modelling of oscillatory flow over submerged canopies

An analytical and experimental study of flow velocities within submerged canopies of rigid cylinders under oscillatory flows is presented, providing insights into the momentum transfer mechanisms between the different flow harmonics. The experimental dataset covers an unprecedented wide range of flow amplitudes with in-canopy velocity reductions ranging between 0.2 and 0.8 of the free stream velocity (from inertia- to drag-dominated in-canopy flow). Results from the analytical model with nonlinear drag compare favourably to the experimental data. Having application of theories for free surface waves over canopies in mind, the effects of linearization of the drag are analysed by comparing sinusoidal and nonlinear model predictions. Finally, a unified prediction formula for in-canopy velocities for sinusoidal, velocity-skewed, and velocity-asymmetric free stream velocities is presented. The formula depends on two non-dimensional parameters related to inertia and drag forces, and the unified formula allows for easy assessment of the maximum in-canopy velocity.