Modeling transient long waves propagating through a heterogeneous coastal forest of arbitrary shape

Abstract

A model is proposed to study transient long waves propagating through coastal vegetation. The coastal forest is modeled by an array of rigid and vertically surface-piercing cylinders. The homogenization method, i.e. multi-scale perturbation theory, is applied to separate two contrasting physical length scales: the scale characterizing transient waves and the scale representing the diameter of and the spacing among cylinders. Fourier transform is employed so that the free surface elevation and velocity field are solved in the frequency domain. For each harmonic, the flow motion within a unit cell, consisting of one or more cylinders, is obtained by solving the micro-scale boundary-value problem, which is driven by the macro-scale (wavelength scale) pressure gradients. The cell-averaged equations governing the macro-scale wave amplitude spectrum are derived with the consideration of the effects of the cell problem solution. Similar to [1], the macro-scale wave amplitude spectrum is solved numerically with the boundary integral equation method, where a vegetated area is composed of multiple patches of arbitrary shape. Each forest patch can be divided into subzones according to different properties, such as planting pattern and vegetation size. Each subzone is considered as a homogeneous forest region with a constant bulk eddy viscosity determined by the empirical formula suggested in [13]. Once the solutions for wave amplitude spectrum are obtained, the free surface elevation can then be computed from the inverse Fourier transform. A computing program is developed based on the present numerical model. To check the present approach, we investigate several different forest configurations. However, we focus on incident waves with a soliton-like shape. We first re-examine the forest belt case. The numerical model is then checked by available theoretical results along with experimental measurements for two special forest configurations. For a single circular forest, the numerical results compare almost perfectly with the analytical solutions. The comparison with experimental data also shows very good agreements. The effects of different wave parameters on damping rate are discussed. The numerical model is further compared with the experiments for a forest region consisting of multiple circular patches. Good agreements are also observed between the simulated free surface elevations and the experimental measurements. The effectiveness of these two forest configurations on wave attenuation is discussed.