Search Results (7)

This paper presents an experimental and numerical investigation of submerged vegetation flow, with a particular focus on vegetation-related terms, especially in the vicinity of the free end. Experimental results indicate that substantial shear stress is observed near the top of vegetation, where the drag coefficient increases significantly due to the disturbance caused by the free end. Furthermore, wake generation is notably suppressed, particularly at heights where wake-generated turbulence dominates, leading to a reduction in turbulent kinetic energy (TKE). A numerical model based on the volume-averaged Reynolds-averaged Navier–Stokes (VARANS) equations was developed, incorporating a vertically varying drag coefficient. The two-scale $⟨k⟩-⟨\epsilon ⟩$ turbulence model is further modified with the inclusion of a new damping function to capture the suppression of wake generation. The model accurately simulates both unidirectional and oscillatory flows, as well as the associated turbulence structures, with good agreement with experimental measurements. The influence of the tips on wave-induced currents, mass transport and TKE distribution is also investigated. It was found that the tip effects play a significant role in strengthening wave-induced currents at the top of loosely arranged, short, and sparse vegetation, with shear kinetic energy (SKE) serving as a critical component of TKE, contributing to the nonuniform distribution. Both Eulerian currents and Stokes drift contribute to streaming in the direction of wave propagation near the vegetation top, which intensifies with increasing solid volume fraction, while tip effects further enhance the onshore mass transport. Within the vegetation, mass transport is more sensitive to wave period and wave height, shifting from onshore to offshore as wavelength increases under constant water depth. Full article

Understanding the stability of the seabed foundation holds paramount significance in guaranteeing the safety and structural soundness of the breakwater alongside additional offshore structures. This study aimed to investigate the stability of a sandy seabed foundation around a semi-circular breakwater under wave loading in nearshore areas. A coupled numerical model of waves, a semi-circular breakwater, and the seabed was developed based on the OpenFOAM platform. The VARANS equations were used to govern the wave behavior. Meanwhile, the Biot’s partially dynamic model was employed to numerically simulate the seabed response considering both consolidation under self-weight and dynamic response under wave loading. The effects of various wave parameters, seabed properties, and the radius of the structure on the dynamic response of the seabed and the depth of liquefaction were investigated. The numerical results indicate that an increase in wave height, period, and permeability coefficient intensifies the dynamic response of the seabed soil. Furthermore, an increase in water depth weakened the soil’s dynamic response. There was a negative correlation between the radius of the semi-circular breakwater and the dynamic response. The influence of Poisson’s ratio on the dynamic response of the seabed was relatively small. Furthermore, a stronger dynamic pore pressure response was observed at the connection between the semi-circular breakwater and the rubble foundation. Full article

This paper presents the results from a numerical simulation study to investigate wave trapping by a series of trapezoidal porous submerged breakwaters near a vertical breakwater, as well as the seabed response around the vertical breakwater. An integrated model, based on the volume-averaged Reynolds-averaged Navier–Stokes (VARANS) equations is developed to simulate the flow field, while the dynamic Biot’s equations are used for simulating the wave-induced seabed response. The reflection of the wave energy over the submerged breakwaters, caused by the vertical breakwater, can be reserved, indicating that the existence of the submerged breakwaters in the front of the vertical breakwater can either provide shelter or worsen the hazards to the vertical breakwater. Numerical examples show two different modes under the Fabry–Pérot (F–P) resonance condition of the wave transformation, namely the wave reflection (Mode 1) and the wave trapping (Mode 2). The distance between the submerged breakwaters and the vertical breakwater, is a key parameter dominating the local hydrodynamic process and the resultant dynamic stresses around the vertical breakwater. The numerical results indicated that more submerged breakwaters and a higher porosity of submerged breakwaters will obviously dissipate more wave energy, and hence induce a smaller wave force on the rear vertical breakwater and liquefaction area around the vertical breakwater. Full article

The purpose of this work is the calibration of a numerical model for simulating the interaction of waves with a composite caisson having an internal rubble mound to dissipate incident sea wave energy. In particular, the analysis focused on the reflection coefficient and the pressure distribution at the caisson vertical walls. The numerical model is based on the Volume-Average Reynolds-Averaged Navier–Stokes (VARANS) equations. Through three closure terms (linear, nonlinear, and transition), such equations take into account some phenomena that cannot be dealt when the volume-average method is used (i.e., frictional forces, pressure force, and added mass). To reproduce properly the real phenomena, a calibration process of such terms is necessary. The reference data used in the calibration process were obtained from an experimental campaign carried out at the Hydraulics Laboratory of the University of Messina. The calibration process allowed the proper prediction of certain phenomena to be expressed as a function of different closing terms. In particular, it was estimated that the reflection coefficient and the wave loading at the frontal wall are better reproduced when all three terms are considered, while the force at the rear wall is better simulated when the effects of such terms are neglected. Full article

Most offshore wind turbines are installed in shallow water and exposed to breaking waves. Previous numerical studies focusing on breaking wave forces generally ignored the seabed permeability. In this paper, a numerical model based on Volume-Averaged Reynolds Averaged Navier–Stokes equations (VARANS) is employed to reveal the process of a solitary wave interacting with a rigid pile over a permeable slope. Through applying the Forchheimer saturated drag equation, effects of seabed permeability on fluid motions are simulated. The reliability of the present model is verified by comparisons between experimentally obtained data and the numerical results. Further, 190 cases are simulated and the effects of different parameters on breaking wave forces on the pile are studied systematically. Results indicate that over a permeable seabed, the maximum breaking wave forces can occur not only when waves break just before the pile, but also when a “secondary wave wall” slams against the pile, after wave breaking. With the initial wave height increasing, breaking wave forces will increase, but the growth can decrease as the slope angle and permeability increase. For inclined piles around the wave breaking point, the maximum breaking wave force usually occurs with an inclination angle of α = −22.5° or 0°. Full article

An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles. Full article

Seabed instability surrounding an immersed tunnel is a vital engineering issue regarding the design and maintenance for submarine tunnel projects. In this study, a numerical model based on the local radial basis function collocation method (LRBFCM) is developed to evaluate the seabed behaviour in a marine environment, in which the seabed is treated as the porous medium and governed by Biot’s “ $u-p$ ” approximation. As for the flow field above the seabed, the VARANS equations are used to simulate the fluid motion and properties. The present model is validated with analytical solutions and experimental data which show a good capacity of the integrated model. Both wave and current loading are considered in this study. Parametric studies are carried out to investigate the effects of wave characteristics and soil properties. Based on the numerical results, the maximum liquefaction depth around the immersed tunnel could be deeper under the wave loading with long wave period (T) and large wave height (H). Moreover, a seabed with lower permeability ( $K_s$ ) and degree of saturation ( $S_r$ ) is more likely to be liquefied. Full article