A theoretical approach for irregular wave attenuation through vegetation and application to spectral wave models

The present work proposes an analytical model for the irregular wave field in submerged and emergent canopies, and the model is based on linear superposition of the solution to the linearized momentum equation. The model naturally resolves the in-canopy velocity reduction due to vegetation, so a spectral dissipation model derived from a (more) accurate in-canopy velocity field can be derived, whereby eliminating the commonly used assumption of validity of linear wave theory within the canopy. The new dissipation model is applied for validation against 137 laboratory studies for emergent, submerged, rigid, and flexible canopies, and it is concluded that an accurate spectral wave transformation can be achieved by utilizing a single and fixed set of force coefficients (hydrodynamic drag and inertia). The model is also applied to the understanding of (i) the common hyperbolic form of closure coefficients in the literature and (ii) the transformation of single- and double-peaked wave spectra through canopies and its importance to the change in spectral wave periods.