Numerical Modeling of the Wave-Plate-Current Interaction by the Boundary Element Method

The aim of this work is to propose a numerical study of the interaction of a wave-horizontal plate fixed and completely immersed in a flat-bottomed tank with a uniform current flowing in the same direction as the incident wave. We investigate in particular the effect of the plate at minimizing the impact of the wave on the coast of beaches by studying the free surface elevation and the reflection coefficient, as well as the influence of the various geometrical parameters on the latter, taking into account the presence of the current. The numerical method used in this study is the boundary element method (BEM), and the results obtained will be confronted with experimental and analytical data existing in the literature.

Relation between orbital velocities, pressure and surface elevation in non-linear nearshore water waves

The inability of the linear wave dispersion relation to characterize the dispersive properties of non-linear shoaling and breaking waves in the nearshore has long been recognised. Yet, it remains widely used with linear wave theory to convert between sub-surface pressure, wave orbital velocities and the free surface elevation associated with non-linear nearshore waves. Here, we present a non-linear fully dispersive method for reconstructing the free surface elevation from sub-surface hydrodynamic measurements. This reconstruction requires knowledge of the dispersive properties of the wave field through the dominant wavenumbers magnitude κ, representative in an energy-averaged sense of a mixed sea-state composed of both free and forced components. The present approach is effective starting from intermediate water depths - where non-linear interactions between triads intensify - up to the surf zone, where most wave components are forced and travel approximately at the speed of non-dispersive shallow-water waves. In laboratory conditions, where measurements of κ are available, the non-linear fully dispersive method successfully reconstructs sea-surface energy levels at high frequencies in diverse non-linear and dispersive conditions. In the field, we investigate the potential of a reconstruction that uses a Boussinesq approximation of κ, since such measurements are generally lacking. Overall, the proposed approach offers great potential for collecting more accurate measurements under storm conditions, both in terms of sea-surface energy levels at high frequencies and wave-by-wave statistics (e.g. wave extrema). Through its control on the efficiency of non-linear energy transfers between triads, the spectral bandwidth is shown to greatly influence non-linear effects in the transfer functions between sub-surface hydrodynamics and the sea-surface elevation.

Experimental Data of Bottom Pressure and Free Surface Elevation including Wave and Current Interactions

Force plates are commonly used in tank testing to measure loads acting on the foundation of a structure. These targeted measurements are overlaid by the hydrostatic and dynamic pressure acting on the force plate induced by the waves and currents. This paper presents a dataset of bottom force measurement with a six degree-of-freedom force plate (AMTI OR6-7 1000, surface area 0.464 m × 0.508 m) combined with synchronised measurements of surface elevation and current velocity. The data cover wave frequencies between 0.2 to 0.7 Hz and wave directions between 0∘ and 180∘. These variations are provided for current speeds of 0 and 0.2 m/s and a variation of the current in the absence of waves covering 0 to 0.45 m/s. The dataset can be utilised as a validation dataset for models predicting bottom pressure based on free surface elevation. Additionally, the dataset provides the wave- and current-induced load acting on the specific load cell at a fixed water depth of 2 m, which can subsequently be removed to obtain the often-desired measurement of structural loads.

Similarity and Froude Number Similitude in Kinematic and Hydrodynamic Features of Solitary Waves over Horizontal Bed

This study presents, experimentally, similarity and Froude number similitude (FNS) in the dimensionless features of two solitary waves propagating over a horizontal bed, using two wave gauges and a high-speed particle image velocimetry (HSPIV). The two waves have distinct wave heights H0 (2.9 and 5.8 cm) and still water depths h0 (8.0 and 16.0 cm) but identical H0/h0 (0.363). Together with the geometric features of free surface elevation and wavelength, the kinematic characteristics of horizontal and vertical velocities, as well as wave celerity, are elucidated. Illustration of the hydrodynamic features of local and convective accelerations are also made in this study. Both similarity and FNS hold true for the dimensionless free surface elevation (FSE), wavelength and celerity, horizontal and vertical velocities, and local and convective accelerations in the horizontal and vertical directions. The similarities and FNSs indicate that gravity dominates and governs the wave kinematics and hydrodynamics.

Focused Plunging Breaking Waves Impact on Cylinder Group in Deep Water

The correct estimation of wave loading on a cylinder in a cylinder group under different impact scenarios is essential to determine the structural safety of coastal and offshore structures. This scenario differs from the interaction of waves with a single cylinder but not a lot of studies focus on cylinder groups under different arrangements. In this study, the interaction between plunging breaking waves and cylinder groups in deep water is investigated using the two-phase flow model in REEF3D, an open-source computational fluid dynamics program. The Reynolds-averaged Navier-Stokes equation with the two equation k–Ω turbulence model is adopted to resolve the numerical wave tank, with free surface calculated using the level set method. In this study, focused waves in deep water were modeled with a fixed wave steepness method. Wave breaking occurs when the steepness of the wave crest front satisfies the breaking criteria. The model is validated by comparing the numerical wave forces and free surface elevation with measurements from experiments. The computational results show fairly good agreement with experimental data for both free surface elevation and wave forces. Four cases are simulated to investigate the interaction of breaking waves with a cylinder group with different relative distance, number of cylinders and arrangement. Results show that breaking wave forces on the upstream cylinder are smaller than on a single cylinder with a relative distance of one cylinder diameter. The wave forces on cylinders in the pile group are effected by the relative distance between cylinders. The staggered arrangement has a significant influence on the wave forces on the first and second cylinder. The interaction inside a cylinder group mostly happens between the neighbouring cylinders. These interactions are also effected by the relative distance and the numbers of the neighbouring cylinders.

URANS Simulations of a Cruise Ship in Crabbing Motion

In ship manoeuvrability, the crabbing test is critical to evaluate the hydrodynamic quantities for the guidance of an efficient and safe berthing or unberthing manoeuvres. In the present study, the crabbing performance of a cruise ship is investigated by an unsteady Reynolds-averaged Navier-Stokes (URANS) method considering the instantaneous relative motion between the ship and the quay. In the numerical simulations, the cruise ship is approaching the quay wall at a constant lateral speed. The crabbing motion with five degrees of freedom is modeled by the dynamic overset mesh technique, while the free surface elevation is simulated by the Volume of Fluid method. For reliable predictions of the crabbing performances, the timestep dependency study is conducted and a suitable time step is determined. From the computations, the hydrodynamic performances of the cruise ship, including forces and moments, as well as the surge, sinkage, roll, trim and yaw motions are predicted. The numerical results indicate variations of the hydrodynamic quantities under the impacts of ship speed and blockage effects by the quay wall. The present results can be used to evaluate the crabbing ability of the cruise ship and to provide guidance for estimating and designing the crabbing model test in further investigations.

Numerical Investigation of Sloshing Under Roll Excitation at Shallow Liquid Depths and the Effect of Baffles

Sloshing is relevant in several applications like ship tanks, space and automotive industry and seiching in harbours. Due to the relationship between ship and sloshing motions and possibility of structural damage, it is important to represent this phenomenon accurately. This paper investigates sloshing at shallow liquid depths in a rectangular container using experiments and RANS simulations. Free and forced sloshing, with and without baffles, are studied at frequencies chosen specifically in proximity to the first mode natural frequency. The numerically calculated free surface elevation is in close agreement with observations from experiments. The upper limit of the resonance zone, sloshing under different filling depths and roll amplitudes and sloshing with one, two and four baffles are also investigated. The results show that the extent of the resonance zone is reduced for higher filling depth and roll amplitude. It is also found that the inclusion of baffles moves the frequency at which the maximum free surface elevation occurs, away from the fundamental frequency. Finally, a submerged baffle is found to dissipate more energy compared to a surface piercing baffle and that the effect of several submerged baffles is similar to that of a single submerged baffle.

Anomalous wave statistics following sudden depth transitions: application of an alternative Boussinesq-type formulation

Recent studies of water waves propagating over sloping seabeds have shown that sudden transitions from deeper to shallower depths can produce significant increases in the skewness and kurtosis of the free surface elevation and hence in the probability of rogue wave occurrence. Gramstad et al. (Phys. Fluids 25 (12): 122103, 2013) have shown that the key physics underlying these increases can be captured by a weakly dispersive and weakly nonlinear Boussinesq-type model. In the present paper, a numerical model based on an alternative Boussinesq-type formulation is used to repeat these earlier simulations. Although qualitative agreement is achieved, the present model is found to be unable to reproduce accurately the findings of the earlier study. Model parameter tests are then used to demonstrate that the present Boussinesq-type formulation is not well-suited to modelling the propagation of waves over sudden depth transitions. The present study nonetheless provides useful insight into the complexity encountered when modelling this type of problem and outlines a number of promising avenues for further research.

TSUNAMI RUNUP AMPLIFICATION OF BREAKING AND NON-BREAKING ERROR-FUNCTION WAVES OVER A SLOPING BEACH IN SHADOW ZONE BY A SMALL ISLAND

The time series of free surface elevation measured in and outside the shadow zone were compared and analyzed in the time-frequency domain by employing the continuous wavelet transform. Regardless of the conditions of the ERF wave in the shadow zone, an increase in magnitude of energy is noticeable not only in the peak frequency within a range of approximately 0.8 to 1 Hz but also in the low-frequency range of around 0.1 Hz corresponding to second up to third crest of the leading wave. To determine the effective frequency of ERF waves and evaluate their runup characteristics, we applied a new method of describing the ERF wave, which consists of linear superposition of two solitary waves. As a result, the ERF waves show the same trend in runup characteristics as for solitary waves.

OpenFOAM Based Approach for the Prediction of the Dam Break with an Obstacle

The phenomenon of the flow impact on a vertical wall resulting from a dam problem is simulated by using OpenFOAM. In this simulation, a dam break was also simulated with the addition of obstacles with various dimensions. The aim of this study is to assess the accuracy of the solver for problems in the impact wave category from the experimental results of previous researchers and other numerical solution techniques compared with the results of this solver. Different aspects of flow such as free surface elevation before and after the initial impact have been observed in depth. The method used in this research is numerical computation simulation with the OpenFOAM approach which has the advantage of being more accurate and fast simulation time. The variations in the dimensions of the obstacle in this study were b / h = 0.25, b / h = 0.5 and b / h = 1.0. From the simulation data, it is found that the numerical approach has been validated through quantitative comparisons with experimental measurements. The computational positions of the leading edge of the collapsed water column match the experimental data. The difference between the experiment and this numerical solution is below 2%.