Wave-averaged properties in a submerged canopy: Energy density, energy flux, radiation stresses and Stokes drift

This work analyses basic wave properties originating from the interaction between waves and submerged rigid vegetation. First of all, an analytical framework is presented that describes the propagation and dissipation of waves over a rigid and submerged canopy, where the flow resistance is linearised. A nonlinear closure term is introduced to ensure that the work done by the linearised flow resistance equals that of the nonlinear flow resistance. The anisotropic flow resistance is found to have an impact on both the distribution of velocities and pressure inside the canopy and it partly explains the small decrease in flow velocities inside the canopy, which was previously observed experimentally. The following second order wave properties are derived: the wave energy density, the wave energy flux, the vegetated group velocity of the wave energy density, the radiation stress components parallel and perpendicular to the direction of wave propagation, the Eulerian and Lagrangian Stokes velocities and fluxes. The additional Stokes drift due to the discontinuity in the velocity field at the top of the vegetation is derived; the inclusion of this mass flux in the Lagrangian formulation of the Stokes drift is important for the ratio between the Lagrangian and Eulerian Stokes drifts. The relation between the wave energy density and the wave energy flux, i.e. the vegetated group velocity of the wave energy density, is of practical importance for large scale wave modelling. The modification to the vegetated group velocity relative to that derived from linear wave theory on non-dissipative waves is described. It is seen that the corrections to linear wave theory are of Hγ, where γ is in the interval 1.5–2.0. •The wave energy flux in a canopy of submerged rigid vegetation is derived.•The advection velocity of the wave energy density differs from the group velocity.•The Eulerian and Lagrangian Stokes drifts are identical under dissipative conditions.•Only minor errors are introduced, when transferring a measured pressure in a submerged canopy to a surface elevation signal by applying linear wave theory.