Wave attenuation by cultivated seaweeds: A linearized analytical model

Abstract

An analytical framework is presented to describe the attenuation of regular and irregular waves propagating over floating seaweed farms. Kelp blades suspended on longlines are modelled, as a first approximation, as rigid bars rotating around their upper ends. Assuming small-amplitude blade motions under low to moderate sea conditions, the frequency-dependent transfer function of the rotations can be obtained, with quadratic drag loads linearized. Subsequently, the hydrodynamic problem with regular waves propagating over suspended seaweed canopies is formulated using the continuity equation and linearized momentum equations with additional source terms in the vegetation region. Analytical solutions are obtained for attenuated regular waves with their heights decaying exponentially as they propagate over the canopy. These solutions are utilized as the basis for predicting wave attenuation of irregular waves while stochastic linearization of the quadratic drag loads is employed. In contrast to energy-conservation-based models, which assume the velocity profile follows linear wave theory, the present solution can predict the reduced velocity inside the canopy. The analytical solutions are validated against experimental data and verified against a numerical flow solver. The model is capable of resolving the wave attenuation, along with velocity profiles and phase lag. Drag and inertial force exhibit cancellation effects on wave decay and both affect phase lag.