Periodic water waves through a heterogeneous coastal forest of arbitrary shape

Abstract

Small-amplitude water waves propagating through a heterogeneous coastal forest of arbitrary shape is studied. Following the theoretical approach introduced by [10], the forest is modeled by an array of rigid and vertical cylinders. Assuming that the wavelength is much larger than the cylinder diameter and the cylinder spacing, a multi-scale perturbation theory of homogenization ([15]) is applied to separate the micro-scale flow problem within a unit cell, containing one or more cylinders, from the macro-scale wave dynamics. The complex coefficients in the derived macro-scale governing equations are computed from the solutions of micro-scale problem, in which the macro-scale pressure gradients are the driven force. The boundary integral equation method is employed to solve the macro-scale wave dynamic problem where the forest has an arbitrary shape and is composed of multiple forest patches. Each forest patch can be divided into subzones according to different forest properties, such as the porosity and cylinder diameter. Each subzone is considered as a homogeneous forest region with a constant bulk eddy viscosity, which is determined by invoking the balance of the time-averaged dissipation rate and the rate of work done by wave forces. A computing program has been developed based on the present approach. The numerical model is checked with existing theoretical works and laboratory experiments. The numerical solutions compare almost perfectly with the semi-analytical solutions for a single circular forest reported in [10]. The numerical model is then applied to cases where the forest region is made of multiple circular patches. Experimental data for these cases ([12,14]) is used to validate the numerical results. The comparison between model predictions and the experimental data is in reasonable agreement. The effectiveness of these two special forest configurations on wave attenuation is also discussed.