Wave Attenuation by Cultivated Seaweeds: a Linearized Analytical Solution

An analytical framework is presented to describe the attenuation of regular and irregular waves propagating over floating seaweed farms. Kelp blades suspending on the longlines are modeled, 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 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 within the vegetation region. Analytical solutions are obtained for the regular waves with their heights decaying exponentially as they propagate over the canopy. These analytical solutions are utilized as the basis to predict the wave attenuation of irregular waves while stochastic linearization of the quadratic drag loads is employed. The wave power spectral density is also seen to decay exponentially over the canopy. The present solutions can also be extended to include the elastic deformation of the vegetation blades.