A new multi-layer irrotational Boussinesq-type model is proposed for both linear and nonlinear surface water waves over mildly sloping seabeds. The model is formulated in terms of computational horizontal and vertical velocity components within each layer and satisfies exact kinematic and dynamic free-surface conditions as well as kinematic seabed conditions. Using a Stokes-type expansion, a theoretical analysis of the new multi-layer model is carried out to examine both linear and nonlinear properties, including wave celerity, velocity profiles, shoaling amplitude, second- and third-order transfer functions and amplitude dispersion. The dispersive coefficients in the governing equations are determined by optimizing the linear celerity or linear velocity profiles. For example, the four-layer model shows extremely high accuracy and is applicable up to $kh=667$ –800 (where $k$ is the wavenumber and $h$ is a typical water depth) with a 1 % error in wave phase celerity, and up to $kh=352$ –423 with a 1 % error in the linear velocity components. The super- and subharmonic transfer functions are extremely accurate up to $kh=300$ (1 % error), the third-order harmonics and amplitude dispersion are accurate up to $kh=477$ (1 % error), and the shoaling property is optimized to cover the range of $0<kh<300$ , which presents a 0.06 % tolerance error in shoaling amplitude. The high-accuracy nature of the model increases its suitability for simulating random wave propagation from extremely deep to shallow waters over mildly sloping topographies. The model is implemented numerically on a non-staggered grid via a composite fourth-order Adams–Bashforth–Moulton time integration. The numerical results show good agreement with both the analytical solutions and experimental data.

The permeable submerged breakwater has gained popularity in recent days due to its merits of reducing incident wave energy without negatively impacting the aesthetics of the ocean view and allowing for water exchange. However, the effect of porosity on wave nonlinearity and turbulence motion close to the water/structure interface is not well resolved in the literature. This paper presents an experimental and numerical study of regular wave propagation over a permeable submerged breakwater with a wide top width. The laboratory experiments were conducted in a wave flume and included 45 test cases. The numerical simulations were performed utilizing validated olaFoam. The results show that the nonlinearity of the waves on the permeable submerged breakwater is weak, which can effectively suppress and reduce the second harmonic waves. A large amount of turbulent kinetic energy exists at the interface between the permeable submerged breakwater and the water body, which helps to dissipate wave energy. For the wider permeable submerged breakwater in this paper, the wave dissipation capacity is greatest when the porosity is between 0.2 and 0.3, and as the length of the breakwater increases, the energy transmission coefficient decreases, and the energy dissipation coefficient increases. Better wave attenuation is achieved when the permeable submerged breakwater has a certain porosity and a large width.

Rip currents are the strong narrow seaward current produced by waves breaking on the coast. Of the many types of rip currents, the present study investigates, experimentally and numerically, the rip current system produced by the wave reflection on a finite-length shore-normal structure (corresponding to groin, jetty and headland in a real-word environment) with strong wave reflection strength. The incident wave condition of an obliquely propagating monochromatic surface gravity wave is considered for the bottom topographies of planar and barred beaches without or with a rip channel. The corresponding laboratory experiment was conducted and used to validate the numerical model. A set of higher order Boussinesq equations is used to reproduce the experimental observation and produce the results for the related prototype cases, with the latter considering more factors which may influence the formation and evolution of rip current flow patterns. The resulting rip current system contains two parts: the node rips formed due to the presence of the longshore standing wave in the wave reflection field and the deflection rip formed due to the interaction between the incoming longshore current and the reflection wave field mentioned above. A new formation mechanism of the deflection rip has been proposed, i.e., the deflection rip is formed by the meeting and then deflection of the longshore current and lateral flow. The effects of different wave reflection strengths of the structure, wave incident angles and bathymetric conditions on the pattern and flow volume of the deflection rip are also studied.

This paper presents a depth-integrated, non-hydrostatic model for coastal water waves. The shock-capturing ability of this model is its most attractive aspect and is essential for computation of energetic breaking waves and wet–dry fronts. The model is solved in a fraction step manner, where the total pressure is decomposed into hydrostatic and non-hydrostatic parts. The hydrostatic pressure component is integrated explicitly in the framework of the finite volume method, whereas most of the existing models use the finite difference method. The fluxes across the cell faces are computed in a Godunov-based manner through an efficient multi-stage scheme. The flow variables are reconstructed at each cell face to obtain second-order spatial accuracy. Wave breaking is treated as a shock by locally switching off the non-hydrostatic pressure in the wave front. A moving shoreline boundary is also incorporated. The robustness and accuracy of the developed model are demonstrated through numerical tests.