Numerical simulation of wave phenomena using FreeFEM

In this research free surface motion governed by the shallow water equations is considered. A numerical scheme based on the finite element method, which is incorporated in the open source FreeFEM, was used to simulate several wave phenomena. By carefully setting the corresponding initial condition as well as boundary conditions, several numerical computations were conducted. Numerical simulations presented here are standing wave in a closed basin, progressive wave over a flat bottom, as well as wave shoaling over a decreasing depth and wave refraction. In all cases above, the existing analytical formula are used to validate the numerical results. These computations suggest that explicit-implicit scheme is appropriate for varying water wave simulations.

Numerical Simulation of Propagation and Run-Up of Long Waves in U-Shaped Bays

Wave propagation and run-up in U-shaped channel bays are studied here in the framework of the quasi-1D Saint-Venant equations. Our approach is numerical, using the momentum conserving staggered-grid (MCS) scheme, as a consistent approximation of the Saint-Venant equations. We carried out simulations regarding wave focusing and run-ups in U-shaped bays. We obtained good agreement with the existing analytical results on several aspects: the moving shoreline, wave shoaling, and run-up heights. Our findings also confirm that the run-up height is significantly higher in the parabolic bay than on a plane beach. This assessment shows the merit of the MCS scheme in describing wave focusing and run-up in U-shaped bays. Moreover, the MCS scheme is also efficient because it is based on the quasi-1D Saint-Venant equations.

Internal wave shoaling in nearly linear stratifications

<div> <div> <div> <p>In the theory of internal waves in the coastal ocean, linear stratification plays an exceptional role. This is because the nonlinearity coefficient in KdV theory vanishes, and in the case of large amplitude waves, the DJL theory linearizes and fails to give solitary wave solutions. We consider small, physically consistent perturbations of a linearly stratified fluid that would result from a localized mixing near a particular depth. We demonstrate that the DJL equation does yield exact internal solitary waves in this case. These waves are long due to the weak nonlinearity, and we explore how this weak nonlinearity manifests during shoaling.</p> </div> </div> </div>

Vulnerability assessment of nearshore clam habitat subject to storm waves and surge

Present work studied the lesion mechanism of coastal clam and its vulnerability assessment subject to the hydrodynamic disturbance of extreme storm events. A clam habitat at the northeast coast of China was chosen for the demonstration study. Relocation failure after passive transport due to excessive substrate erosion or suffocation in anoxic burial under overburdening sedimentation was identified the major cause of negative biomass responses during the storm. Based on the biological propensity and physiological sensitivity of the clam, a tunable loss probability function correlating the mortality with the shell length and the seabed change was proposed. A hydrodynamic model was then adopted to compute the sediment transport and net changes in the seafloor in response to the comprehensive process of storm waves and surge. The spatial distribution of the damage states was evaluated based on the numerical results incorporating the loss probability function. The estimated damage was mainly concentrated along the wave shoaling and breaking belts parallel to the shoreline. High surge levels pushed the “damage belt” shoreward, in which case large waves were able to propagate close to the shoreline before breaking. The scientific findings are helpful to better understand the vulnerability of the clam habitat to the storm disturbance. The study result as well provides a practical methodology of the storm risk assessment for benthic communities in broader ecological and geophysical scopes. The methodology are expected to be further validated and improved by more widespread sampling on coastal ecosystem or mariculture that will withstand future storms.

Characteristics of Transforming Waves Breaking Over a Fringing Reef

Direct numerical simulation (DNS), based on solution of the Navier Stokes equations, is used to study the characteristics of the transformation of monochromatic waves over a simplified fringing reef, including wave shoaling, and wave breaking that occurs under certain circumstances. The reef geometry involves a sloped plane beach extended with a simple submerged horizontal reef flat. The characteristics are studied for several case studies involving a selection of submergence depths on the reef flat and for a range of incident wave conditions, corresponding to nonbreaking, a spilling breaker and a plunging breaker, are considered. The results are compared with those of laboratory experiments (Kouvaras and Dhanak, 2018). Consistent with other studies, generation of harmonics of the fundamental wave frequency is found to accompany the wave transformation over the reef and the process of transfer of energy through wave breaking. The energy flux decreases dramatically in the onshore direction when the waves break. The more severe the wave breaking process, the greater the decrease in energy flux, particularly in the wave shoaling process. Most of the wave energy is carried by the first harmonic throughout its passage over the fringing reef. In nonbreaking waves, the energy gradually transfers from the first harmonic to the second harmonic due to bottom effects in terms of flat wave troughs and secondary waves. The further the distance away from the fore edge of the reef, the larger the percentage of the transmission, resulting in a single dominant harmonic frequency at the end of the wave surfing zone. For breaking waves, the energy carried by the first harmonic gradually decreases in the onshore direction. Energy transmission between harmonics is not as efficient as nonbreaking waves, while wave dissipation is significant in the wave breaking process.