Experimental and Theoretical Investigations of Hydrodynamic Loads on Cultivated Seaweeds and Their Structural Responses

The recent emergence of seaweed cultivation in the Blue Bioeconomy has attracted significant attention. This thesis addresses several challenges associated with the hydrodynamic modelling of cultivated seaweeds across multiple scales by employing analytical, experimental, and numerical approaches.

In this study, we first present a fully explicit coupled wave-vegetation interaction model capable of efficiently solving the coupled wave dynamics and flexible vegetation motion with large deflections. The flow model is formulated using the continuity equation and linearized momentum equations for an incompressible fluid, incorporating additional terms within the canopy region to account for vegetation presence. This linearized flow solver is unconditionally stable and second-order accurate. A truss-spring model is proposed to capture vegetation motion with substantial deflections, and is proven to be mathematically consistent with the governing equation for the flexible vegetation motion. This model facilitates explicit time integration with large time steps enabling the efficient simulation of highly compliant vegetation. The model, combining the linearized flow solver and the truss-spring model, is validated against experimental data and verified with numerical results at both the blade scale and a two-dimensional seaweed farm scale, demonstrating high efficiency.

Furthermore, we investigate the hydrodynamic drag on side-by-side flexible blades in both steady and unsteady flows, a fundamental physical problem underlying the responses and loads on the longlines supporting seaweed cultivation, using experimental and theoretical approaches. In both scenarios, flutter, also known as a dynamic instability, occurs at high flow speeds. Key non-dimensional parameters are analyzed to assess their impact on bulk drag coefficients and flutter dynamics. An effective Cauchy number correlates the bulk drag coefficient between steady and unsteady flows, allowing the application of analytical steady-flow models to predict drag loads prior to the onset of flutter. Additionally, the numerical model developed in this study is employed to examine each term of the reactive force model, identifying their effects on system stability and drag reduction. The results show that it is necessary to include all terms in the reactive force model for highly compliant blades in cross flows.

An analytical framework is developed at the seaweed farm scale to describe the attenuation of regular and irregular waves propagating over cultivated seaweeds. Kelp blades suspended on longlines are approximated as rigid bars rotating around their upper ends. The hydrodynamic problem involving regular waves propagating over suspended seaweed canopies is formulated using the continuity equation and linearized momentum equations, incorporating additional source terms within the vegetation region after linearizing the quadratic drag load. Unlike traditional energy conservation-based models, which assume velocity profiles consistent with linear wave theory, the analytical model predicts reduced velocities within the canopy. The analytical solutions are validated against existing experimental data and verified against the numerical model developed in this study. The model effectively captures wave attenuation, as well as velocity profiles and phase lag. Drag and inertial forces are found to have cancellation effects on wave decay, and both affect phase lag.

The theories, datasets, and tools developed in this thesis are instrumental for analyzing the hydrodynamic loads and structural responses of cultivated seaweeds in both scientific research and engineering applications.