Wave attenuation by cultivated seaweed: a linearized analytical solution

An analytical framework is presented to describe the attenuation of regular and irregular waves propagating over a floating seaweed farm. The high flexibility of the seaweed blades renders gravity the primary restoring force, rather than the bending stiffness. Motivated by observations from our recent model tests, the blades suspended on the longlines may be modeled, as a first approximation, by rigid bars rotating around their upper ends, provided that the involved Keulegan-Carpenter numbers are lower than ~10. Assuming small-amplitude blade motions under low to moderate sea conditions, the frequency transfer function of the rotations can be obtained, with important 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 for flow regions above and within the canopy. The hydrodynamic loads on the seaweed blades are approximated by Morison’s equation, while their coupling to the flow field is achieved through source terms in the linearized momentum equations. To this end, analytical solutions are obtained for the regular waves with their heights decaying exponentially as they propagate over the canopy.

Given that irregular waves can be approximated by a superposition of linear waves, the analytical solution developed for regular waves can be utilized to predict the attenuation of irregular waves propagating over a floating seaweed farm. For irregular waves, stochastic linearization, a standard procedure in offshore engineering to handle quadratic drag loads, has been employed. The wave power spectral density is also seen to decay exponentially over the canopy.

The present model considers the disturbance of the local flow field by the blades, which is not accounted for in any other energy-conservation-based models where the local flow velocity profile is assumed to follow a linear wave theory. For cases where the damping due to blades is low, the present theory predicts slightly lower but very close results, in terms of wave-decay coefficient at the leading edge of the canopy, to those by the energy-based theories. Considering some typical spans of floating seaweed farms, our study indicates that the existing energy-based theories may overestimate the wave attenuation in comparison to the present solutions, in particular at the ending edge of the canopy. Future work should focus on experimental validation, numerical calibration, and extension of this simple analytical model to include flexible modes. The limitation of the model should also be investigated by comparing it to model-test or full-scale measurements.