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Coastal forests, a part of natural coastal ecosystem, have long been considered as an effective means on protecting shore regions against wind waves, storm surges and tsunamis. To study the capability of coastal forest on dissipating wave energy, we employ the multi-scale perturbation theory of homogenization and develop a model to investigate the interactions of incident waves with vegetated area.
Due to strong contrast between the incident wavelength and tree spacing, the multi-scale perturbation method is applied to separate the micro- and macro-scale. The flow motion in a micro-scale cell, with one or more cylinders inside, can be obtained by solving the boundary-value problem numerically. The macro-scale equations governing the wave dynamics are derived with complex coefficients computed from the cell problem solutions.
Figure 1: Sketch of a typical coastal forest configuration
Figure 2: Typical micro-scale cell arrangement
Figure 3: Snapshots of dimensionless free surface elevation over two special types of forest
A numerical model based on the boundary integral equation method is established for a heterogeneous vegetated area, which can be composed of multiple patches of arbitrary shape, as is commonly observed in the field. A forest patch can be further divided into several subzones based on different forest properties, such as vegetation type, planting pattern and porosity. Using the boundary integral equation method, the boundary of each subzone is discretized into elements such that the macro-scale wave dynamics can be solved numerically.
Figure 4: Comparison of dimensionless wave amplitude (periodic waves) between numerical results (solid and dashed lines) with experimental data (squares and circles).
- Left panel: circular forest.
- Right panel: Multiple patches
Figure 5: Comparison of solitary wave height between model predictions (solid lines) and experimental data (dashed lines).
- Left panel: circular forest.
- Right panel: Multiple patches
Two different types of incident waves are investigated. Small-amplitude periodic waves are first used to model wind waves and their interactions with coastal forest. A transient long wave with a soliton-like shape is then tested. For both conditions, model validation has been carried out by several special forest configurations with existing experimental data. For example, a circular forest with constant porosity are studied with the semi-analytical solutions also being derived. Multiple circular forest patches are used to further check the numerical model. In the data-model comparison, the wave attenuation and diffraction are both evident. Good agreement between the model results and the experimental measurements are also observed.
We are currently extending the model to weakly nonlinear cases and investigating the possible influences on the predicted wave attenuation.
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