Wave damping by large-scale offshore kelp farms - A numerical modelling framework using a porous medium approach

Abstract

Large-scale cultivation of seaweed presents opportunities for multiple global challenges currently at play. Cultivated seaweed can provide a sustainable source of protein for humans and cattle without competing for land, freshwater supply or the use of fertilisers. Kelp forests are known to be a solid basis for an elaborate biome that supports biodiversity in areas that have been damaged by over-fishing or rising sea temperatures. Additionally, kelp forests can lock-in large amounts of Blue Carbon, expanding the oceans’ buffering capacity to mitigate anthropogenic emissions. Furthermore, with their densely seeded lines, offshore kelp farms are found to attenuate wave amplitude, thus providing coastal protection and benefits like increased workability for offshore operations. Both academic publications and industry reviews underline the potential of this sector and significant growth in cultivation is expected in the near future.

Methods currently used for quantification of the damping effects of large-scale offshore kelp farms are diverse and entail varying degrees of accuracy and computational cost. Experimental observations that support the outcomes of these methods are limited to scaled experiments in wave flumes, with various methods used to mimic vegetation. No convergence is found in the most suitable methods for application to large-scale offshore kelp farms.
This research presents a novel modelling framework based upon the Finite Element method, implemented using Julia Programming Language. The effects of the vegetation on the wave climate are represented with a Darcy-Forchheimer term borrowed from porous medium flow theory, including a linear and a quadratic resistance term. The framework comprises a numerical wave tank, using the incompressible Navier Stokes equations. The single-phase model captures the free surface using the coupling of dynamic pressure with a virtual elevation variable through a linearized transpiration boundary condition. Wave energy dissipation is shown to increase significantly by moving the farm structure close to the water surface. Similarly, a decrease in relative water depth - compared to the vegetated height - increases damping potential. Wave period is found to be of strong influence on dissipation, where short waves are attenuated more. Scaling vegetation length with wave length, however, diminishes the reduction in damping of longer waves. Conversely, wave amplitude is shown to be of less influence on the transmission of amplitude through a vegetated patch.
The framework presents a method that is easily scalable, flexible in application on a wide range of flows and vegetation characteristics, and at reasonable computational cost. Introduction of both the linear and quadratic terms extends applicability compared to traditional methods. The approach is verified using convergence studies, application of the model is validated by comparison to existing experimental data. It is shown that experimental set-ups can be reproduced effectively, and simulation results coincide with experimental findings. Validation of outcomes on scales larger than common wave tanks was found unfeasible due to a lack of measurement data. A theoretical case study was performed to predict wave damping of a full-scale kelp farm, demonstrating promising potential with up to 40% wave energy reduction at the local peak wave period.

Further research into the establishment of the Darcy- and Forchheimer-coefficients is recommended. A preliminary range of values has been found, based upon calibration on existing experiments that represent realistic ranges of vegetation characteristics. Furthermore, the main conditions of the flow and vegetation that dictate damping potential are identified. On this basis, research into a physics-based determination of the coefficients is recommended. Additionally, full-scale measurements are advised to validate application on future kelp farm designs.
Through this novel approach, the range of application is increased compared to existing methods, while straightforward setup and usage are governed, and limited computational costs allow for simulation without the need for a dedicated computer setup. The framework is shown to be robust by generating consistent simulation results. In summary, the established framework shows to be a good alternative to existing approaches to investigate the wave damping potential of large-scale offshore kelp farms.