Blade dynamics and wave dissipation in orthogonal wave-current conditions

Introduction

Aquatic vegetation has drawn attention as a promising nature-based solution for coastal protection due to its diverse functions, such as sequestrating carbon and reducing coastal erosion by attenuating incoming waves. Evaluating the effectiveness of and understanding the physics behind nature-based solutions requires knowledge of the dynamics of aquatic vegetation under coastal flows. Wave dissipation over rigid vegetation has long been noted and investigated. Flexible vegetation will reconfigure with flows and behave differently from rigid vegetation, thus leading to different wave-damping models. The motion of flexible vegetation will reduce frontal area and the relative velocity between vegetation and flows, thus leading to the decrease of drag force that acts on flows. Effective blade length, l_e, defined as the length of a rigid blade that experiences the same drag force as a flexible blade of length, has been applied to describe the dynamics of flexible blades in currents and waves (Luhar and Nepf, 2011; Luhar and Nepf, 2016). The ratio between l_e and l was found to scale with the dimensionless parameter Cauchy number (Ca), the ratio of hydrodynamic drag to the restoring force due to blade stiffness, and blade length ratio (L), the ratio of l to wave excursion, A_w. The framework of l_e was then extended to co-directional wave-current studies (Beth Schaefer and Nepf, 2022; Lei and Nepf, 2019; Schaefer, 2024). To date, vegetation dynamics under orthogonal wave-current conditions (i.e., the current is perpendicular to the direction of wave propagation), which usually correspond to wave-induced longshore currents near the coast, have not yet emerged.

Objectives and scopes

The focus of this study is to address the scientific challenge of understanding the behavior of flexible vegetation, considering orthogonal wave-current conditions. Our research enhances the existing body of work through several novel contributions.

• Direct measurement of the drag force of a single flexible blade will be conducted to understand the scaling law of l_e under orthogonal wave-current conditions.
• A numerical model of the dynamics of a single flexible blade will be extended to orthogonal wave-current conditions.
• An analytical model of wave dissipation by vegetation under orthogonal wave-current conditions is developed by incorporating the current-to-wave velocity ratio into the existing model.
• Wave damping over a meadow of vegetation experiments under orthogonal wave-current conditions will be conducted to validate the analytical wave decay model.

Experimental methods

Laboratory experiments will be conducted in a wave basin that can generate orthogonal wave-current flows. the EPDM rubber rods will be used as the representative of flexible vegetation. Two individual vegetation shoots will be attached to two submersible force transducers which are fixed at a customized pyramid in directions that are perpendicular to each other. The drag force at wave propagation and current direction will be measured. The normalized effective length (l_e/l) is determined by comparing the measured drag force with the force measured on a rigid reference shoot of identical geometry to the original length. The relationship between l_e/l and the dimensionless parameters, Ca, L, and u_c/u_w (current-to-wave velocity ratio) will then be analyzed.