Yang-Yih Chen

Stokes wave is a classical problem in physics. Various Stokes wave theories in different forms have been developed to help us better understand their characteristics and for engineering applications. Exploring whether these Stokes wave theories can be converted into each other is a mathematical issue. We select three Stokes wave theories with different expansion parameters, all expressed in terms of water depth measured from the mean water level (MWL). Using series reversion to convert between the different expansions, we successfully transform the expressions for the velocity potential, wave profile, and dynamic properties between two of the Stokes wave theories. Through this conversion, we identify an incorrect expression for the water level in one Stokes wave theory.

The run-up of a vortex hydrodynamic bore onto an inclined beach is the subject of this study. To theoretically analyze this problem, we use the Benny equations, which, within the shallow water model, allow us to take into account the distribution of horizontal fluid velocity along the depth of the fluid layer. We show that the presence of a shear flow behind a bore significantly modifies the different regimes of bore motion toward the shoreline depending on its strength. The subsequent collapse of the bore near the shoreline with the release of a high-speed run-up jet onto the dry shore is also significantly modulated by the degree of vorticity of the fluid flow. The maximum flooding length and run-up height increase significantly with increasing vorticity of the fluid flow. We use a theoretical model based on the characteristic Whitham rule for a bore, supplemented by the laws of conservation of mass and the momentum of a liquid crossing a shock wave. It is assumed that the wave run-up that appears after the “collapse” of the bore is determined by gravity. As a result, the maximum value of the wave run-up, its speed, the influence of flow vorticity, and its structure as a whole are estimated. The acceptable agreement of the simulation results with experimental data can serve as a justification for the applicability of our model to the calculation of the bore run-up onto a sloping beach.

Seepage force induced by ocean waves has been related to the liquefaction around submarine structure, and it has been shown to cause significant sediment transport and rapid burial of pipelines and objects (Tsai et al., 2022). This study assesses the impact of momentary soil liquefaction due to pore pressure gradient near seabed generated by waves in the range of oceanic and coastal environment. The nonlinear wave solution of the stream function numerical approximation is applied to cover the wide range of wave condition in ocean and to evaluate the contribution of kinetic term in the energy equilibrium of water waves, which appears at least in third order analytical solution. The dispersion relation for coupled wave-soil interaction is discussed to shed insight on the effect of seabed response on wave dissipation. The present solution demonstrates the momentary liquefaction near mud line, which is triggered by the pore pressure gradient under wave trough and assesses the trigger criterion of wave condition in wave-current environment.

In order to understand the extreme wave acting on the vertical breakwater, a series of experiments were constructed in the wave tank to measure the variations of pressure on the front, rear faces, and below the caisson due to overtopping waves. The front and backward horizontal forces and the uplift forces were estimated by integrating the dynamic wave pressure distributions. The COBRAS numerical model was also used to calculate the wave loads under various overtopping waves. The measured wave pressures and wave forces were compared with the predictions of numerical results and showed good agreement. It was found that the forces acting on the backward side of the vertical structure induced by the wave overtopping should be considered. From the experimental data, new semi-empirical equations for calculating the maximum wave forces are proposed using a least squares approximation.

We present a study of the physical characteristics of traveling waves at shallow and intermediate water depths. The main subject of study is to the influence of nonlinearity on the dispersion properties of waves, their limiting heights and steepness, the shape of solitary waves, etc. A fully nonlinear Serre–Green–Naghdi-type model, a classical weakly nonlinear Boussinesq model and fifth-order Stokes wave solutions were chosen as models for comparison. The analysis showed significant, if not critical, differences in the effect of nonlinearity on the properties of traveling waves for these models. A comparison with experiments was carried out on the basis of the results of a joint Russian–Taiwanese experiment, which was carried out in 2015 at the Tainan Hydraulic Laboratory, and on available experimental data. A comparison with the experimental results confirms the applicability of a completely nonlinear model for calculating traveling waves over the entire range of applicability of the model in contrast to the Boussinesq model, which shows contradictory and unrealistic wave properties for moderate wavelengths.

Flexible plates or membranes located on the sea surface can be effective for attenuation waves approaching the beach. The most efficient structures should be found through comprehensive research using developed experiments and theory. Our experimental work was focused on the wave propagation and attenuation passing through floating elastic structures. The experiments were conducted at the wave flume of Tainan Hydraulics Laboratory, National Cheng Kung University, Taiwan. The experiment mainly analyzes the reflection coefficient, transmission coefficient and energy loss of the regular wave of intermediate water depth after passing through the elastic structure under different wave steepness and other different wave conditions. Our experiments also explore the comparison of energy dissipation effects and the differences in motion characteristics between different elastic plates and different plate fixing methods. Three elastic materials were tested in the experiments: Latex, cool cotton and polyvinyl chloride (PVC). A model of a thin elastic plate covering the sea surface was used to evaluate the effectiveness of the structure of the wave barrier. The results of experiments carried out in the wave flume were compared with theoretical predictions in a wide range of generated waves.

The 3-D Princeton Ocean Model with tidal forcing supplied by a 2-D barotropic model was used to examine the time-depth variability and features of tidal current, turbulence, and power of tidal stream energy in the Taiwan Strait (TS). A number of potential tidal stream sites for the kinetic energy conversion were identified. Numerical simulations showed that semidiurnal tidal currents are predominant in the TS, with along-channel maximum amplitude reaching 1.3 m s^–1. The modeling revealed multicore eddy structures generated by the ebb and flood flows over the Chang-Yuen Rise (CYR). The eddy structures were found to contain filaments with different vorticities, positions, and signs, which depend on the phase of the tide. The maximum of absolute relative vorticity was estimated to reach 100 rad/week. During the flood-ebb cycle, the turbulence exhibited symmetry over the CYR and in the Peng-Hu Channel (PHC), while in the cross-slope direction south from the CYR it was asymmetrical, changing from ebb-dominant to flood-dominant. The maximum values of eddy diffusivity within the bottom boundary layer ranged from ∼10^–3 to 10^–2 m² s^–1. A numerical simulation revealed that, in the PHC, bottom shear turbulence on the flood is suppressed by strong stratification due to the inflow of dense water from the South China Sea. An assessment of power density revealed several potentially attractive sites for the installation of tidal turbines in the vicinity and over the CYR. Tidal currents at these sites are characterized by insignificant flood/ebb asymmetry and the magnitude of power density reached 100 Wm^–2. The most promising site for tidal energy converter installations was identified in the northern extremity of the PHC, where the magnitude of power density reached 300 Wm^–2.