Numerical study of solitary wave propagating through vegetation

Abstract

In this study, the effects of vegetation on the tsunami wave propagation are investigated through the study of solitary wave propagating past vegetation. The overall objective is to understand the physics of wave height reduction and wave energy dissipation in the presence of non-submerged rigid vegetation with different vegetation conditions. A combined theoretical, experimental and numerical approach is adopted. Theoretically, a temporal-volume double averaging method is employed to average the original 3D Navier-Stokes equations to introduce the vegetation effect into the fluid governing equations. This approach avoids the problem of a simple addition of the drag-related body force in the momentum equation which does not represent the energy budget correctly. After the double averaging, a system of modified momentum equations and energy budget equation is obtained by parameterizing the vegetation-related terms. The new system of equations has been successfully applied to the general 3D fluid-vegetation problems, along with vegetation-related parameters that have been systematically derived, calibrated and validated. In the above modified equations, drag and inertial force coefficients are among the most significant parameters to be quantified. A series of experiments of wave propagating within the vegetation are conducted to investigate the variation of drag and inertial force coefficients with wave conditions. Based on the experimental data, an empirical formula to calculate the vegetation drag force coefficient has been derived as a function of not only the Renolds number Re and porosity, which are largely used in vegetation-open channel flow problem, but also KC number that can feature the wave characteristic. The formula can be used in the numerical modeling of vegetation effect on wave propagation. Incorporating the above work, a new three-dimensional wave/flow model has been developed to study the fluid-vegetation interaction problem. The numerical model solves the newly derived system of equations for the two phase flow. The rigid vegetation is represented by the distribution of porosity which provides the convenient treatment of non-homogeneous distributed vegetation. A two-step projection method has been employed in the numerical solution, accompanied by a Bi-CGSTAB technique to solve the Pressure Poisson Equation (PPE) for the averaged pressure field. Volume-of-Fluid (VOF) method that is of second-order accuracy in interface reconstruction is used to track the free surface evolution. The drag and inertial force coefficients from current experiments are imbedded in the model. The numerical model has been successfully validated against available analytical wave solutions and experiments without vegetation in terms of accuracies of free surface and velocity field. The model has also been used to study several cases of solitary wave propagating through vegetation. The results show that porosity and the coverage length of the vegetative region are two of the dominant factors on reducing wave height and current velocities. The effect of increasing the coverage length of vegetation can be equally achieved by reducing the porosity. The force coefficients seem to be insignificant in the wave height dissipation at least in the condition of large porosity. The gap in vegetation region can amplify the current velocities and form a water jet which can cause more severe damages on the assets or human beings on its way. For the general porosity of mangrove (85%-95%), the coverage length of 10-20m can reduce half of the incident wave height. However, special attention should be paid to the region having a vegetation gap. Coastal structures such as breakwaters are required to protect the assets along the gap. In general, the numerical model has been approved to be a robust model for the study of wave-vegetation problem and can be used in the future coastal engineering studies.