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.

We present the kinematic model of the ship wake in the presence of horizontal subsurface current linearly varying with the depth of water. An extension of the Whitham–Lighthill theory for calm water is developed. It has been established that the structure of ship waves under the action of a shear flow can radically differ from the classical Kelvin ship wake model. Co propagating ship and shear current lead to increasing the total wedge angle up to full one ${180}^{°}$ and decreases for the counter shear current. At relatively large unidirectional values of the shear current, cusp waves in the vicinity of the wedge boundary are represented by transverse waves and, conversely, by diverging waves directed almost perpendicular to the ship track for the opposite shear current. The presence of a shear flow crossing the direction of the ship’s movement gives a strong asymmetry of the wake. An increase in the perpendicular shear flow leads to an increase in the difference between the angles of the wake arms. The limiting value of the shear current corresponds to one or both arms angles equal to ${90}^{°}$. Transverse and divergent edge waves for this limiting case coincide.

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.

Experiments are conducted to measure the motion properties of water particle for the progressive water wave propagation in the presence of following and adverse uniform currents. The experimental data are used to validate the fifth-order Lagrangian solution from Chen and Chen. The experimental results show that the measured data of the particle motion properties such as the b line (denoted as the line connecting the positions of consecutive particles of the same b label), the particle velocity, the particle transport velocity (drift velocity), the particle trajectory, the particle motion period, and the Lagrangian mean level are in close agreement with those of the fifth-order Lagrangian solution. The study also shows that the particle label could adopt the position coordinates of the particle as if it were in still water. The motion of the b line oscillates like wave motion: its wavelength is equal to the progressive wavelength and its wave velocity obeys the Doppler effect so the sum of the velocities of the progressive wave and current, the particle motion period, the Lagrangian mean level, and the particle transport velocity less current velocity are the same as for the case of pure progressive waves. For following currents, the shape of particle trajectory depends on the horizontal particle velocity at the trajectory trough. For adverse currents, the shape of particle trajectory depends on the horizontal particle velocity at the trajectory crest. For a description of the flow motion, the Lagrangian solution could be more effective and precise than the Eulerian solution.

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.