Remote sensing of surf zone waves using stereo imaging

The measurement of water wave characteristics, such as wavelength and wave height, in the surf zone is important for monitoring, prediction of erosion, and numerical model calibration. Traditional methods of measuring wave heights have either been limited to a small number of points or have required contact with the water. An experimental study of the remote sensing of water wave elevations, through the application of stereo photogrammetry, is presented. This method uses two spatially offset cameras, with overlapping fields of view, to determine water surface elevation. This remote sensing approach provides data with excellent spatial coverage and spatial and temporal resolution. Additionally, the hardware needs are minimal and the system is quickly deployed, calibrated, and operational.     

Laboratory observation of boundary layer flow under spilling breakers in surf zone using particle image velocimetry

A boundary layer flow under spilling breakers in a laboratory surf zone with a smooth bottom is investigated using a high resolution particle image velocimetry (PIV) technique. By cross-correlating the images, oscillatory velocity profiles within a viscous boundary layer of O(1) mm in thickness are resolved over ten points. Using PIV measurements taken for an earlier study and the present study, flow properties in the wave bottom boundary layer (WBBL) over the laboratory surf zone are obtained, including the mean velocities, turbulence intensity, Reynolds stresses, and intermittency of coherent events. The data are then used to estimate the boundary layer thickness, phase variation, and bottom shear stress. It is found that while the time averaged mass transport inside the WBBL is onshore in the outer surf zone, it changes to offshore in the inner surf zone. The zero Eulerian mass transport occurs at h/h_b ≈ 0.92 in the outer surf zone. The maximum overshoot of the streamwise velocity and boundary layer thickness are not constant across the surf zone. The bottom shear stress is mainly contributed by the viscous stress through mean velocity gradient while the Reynolds stress is small and negligible. The turbulence level is higher in the inner surf zone than that in the outer surf zone, although only a slight increase of turbulent intensity is observed inside the WBBL from the outer surf zone to the inner surf zone. The variation of phase inside and outside the WBBL was examined through the spatial velocity distribution. It is found the phase lead is not constant and its value is significantly smaller than previous thought. By analyzing instantaneous velocity and vorticity fields, a remarkable number of intermittent turbulent eddies are observed to penetrate into the WBBL in the inner surf zone. The size of the observed large eddies is about 0.11 to 0.16 times the local water depth. Its energy spectra follow the − 5/3 slope in the inertial subrange and decay exponentially in the dissipation subrange.     

Numerical modeling of long waves in shallow water using Incremental Differential Quadrature Method

Incremental Differential Quadrature Method (IDQM) as a rapid and accurate method for numerical simulation of Nonlinear Shallow Water (NLSW) waves is employed. To the best of authors’ knowledge, this is the first endeavor to exploit DQM in coastal hydraulics. The one-dimensional NLSW equations and related boundary conditions are discretized in space and temporal directions by DQM rules and the resulting system of equations are used to compute the state variables in the entire computational domain. It was found that the splitting of total simulation time into a number of smaller time increments, could significantly enhance the performance of the proposed method. Furthermore, results of this study show two main advantages for IDQM compared with other conventional methods, namely; unconditional stability and minimal computational effort. Indeed, using IDQM, one can use a few grid points (in spatial or time direction) without imposing any stability condition on the time step to obtain an accurate convergent solution.     

Simulating nonlinear waves on the free surface in surf zones with two-dimensional sloping beach

Unsteady nonlinear wave motions on the free surface in shallow water and over slopes of various geometries are numerically simulated using a finite difference method in rectangular grid system. Two-dimensional Navier–Stokes equations and the continuity equation are used for the computations. Irregular leg lengths and stars are employed near the boundaries of body and free surface to satisfy the boundary conditions. Also, the free surface which consists of markers or segments is determined every time step with the satisfaction of kinematic and dynamic free surface conditions. Moreover, marker-density method is also adopted to allow plunging jets impinging on the free surface. Either linear or Stokes wave theory is employed for the generation of waves on the inflow boundary. For the simulation of wave breaking phenomena, the computations are carried out with various wave periods and sea bottom slopes in surf zone. The results are compared with other existing computational and experimental results. Agreement between the experimental data and the computation results is good.     

Finite volume scheme for the solution of 2D extended Boussinesq equations in the surf zone

In this paper, a hybrid finite volume-finite difference scheme is applied to study surf zone dynamics. The numerical model solves the 2DH extended Boussinesq equations proposed by Madsen and Sørensen (1992) where nonlinear and dispersive effects are both relevant whereas it solves NSWE equations where nonlinearity prevails. The shock-capturing features of the finite volume method allow an intrinsic representation of wave breaking and runup; therefore no empirical (calibration) parameters are necessary. Comparison with laboratory measurements demonstrates that the proposed model can accurately predict wave height decay and mean water level setup, for both regular and solitary wave breaking on a sloping beach. The model is also applied to reproduce two-dimensional wave transformation and breaking over a submerged circular shoal, showing good agreement with experimental data.     

Measurements of the vertical correlation in turbulence under broken waves

Turbulence measurements have been carried out in the surf zone of a wave flume. The purpose of the measurements is to determine the length scale of the turbulence generated by the wave breaking. The length scale of the turbulence is estimated on basis of the correlation between simultaneous measurements of the vertical turbulent fluctuations, taken at different levels above the bed.     

Temporal and spatial variability of fecal indicator bacteria in the surf zone off Huntington Beach, CA

Fecal indicator bacteria concentrations measured in the surf zone off Huntington Beach, CA from July 1998-December 2001 were analyzed with respect to their spatial patterns along 23 km of beach, and temporal variability on time scales from hourly to fortnightly. The majority of samples had bacterial concentrations less than, or equal to, the minimum detection limit, but a small percentage exceeded the California recreational water standards. Areas where coliform bacteria exceeded standards were more prevalent north of the Santa Ana River, whereas enterococci exceedances covered a broad area both north and south of the river. Higher concentrations of bacteria were associated with spring tides. No temporal correspondence was found between these bacterial events and either the timing of cold water pulses near shore due to internal tides, or the presence of southerly swell in the surface wave field. All three fecal indicator bacteria exhibited a diel cycle, but enterococci rebounded to high nighttime values almost as soon as the sun went down, whereas coliform levels were highest near the nighttime low tide, which was also the lower low tide.     

2DOF numerical investigation of a planing vessel in head sea waves in deep and shallow water conditions

Analysis of a craft with two degrees of freedom (2DOF) consumes time more than simulation of a craft with a fixed trim condition; therefore in most of the previous researches fixed trim condition is taken into account to analyze the flow field around a craft in shallow water and head sea wave conditions. In this paper numerical simulation of Reynolds Average Naiver Stokes (RANS) equations are used to analyze the motion of DTMB 62 model 4667-1 planing vessel in calm water and head sea waves in both deep and shallow water with two degrees of freedom (heave and pitch). For this purpose, a finite volume ANSYS-FLUENT code is used to solve the Navier-Stokes equations for the simulation of the flow field around the vessel. In addition, an explicit VOF scheme and SST k-ω model is used with dynamic mesh scheme to capture the interface of a two-phase flow and to model the turbulence respectively in the 2DOF model.Regarding the results, reducing the wavelength and also the depth of the water can increase the drag force. Also comparing the results of a fixed trim vessel with the results of a free to sink and trim one in calm water shows a difference of approximately 50% in the drag force in shallow water.     

Propagation of shallow water waves in an open parabolic channel using the WKB perturbation technique

A singular perturbation analysis based on the WKB technique to study the hydrodynamic performance of periodic ocean waves that are incident on an open parabolic channel of constant depth is proposed. We derive a linear model to predict the propagation of the long ocean waves into the channel. In this manner, the spatial distribution for the surface elevation of the ocean waves inside the channel as a function of two dimensionless parameters, namely, a kinematical parameter, κ and a geometrical parameter ε, is governed by a second-order ordinary differential equation. The kinematical parameter κ denotes the ratio of the potential head, due to gravity, to the kinetic head of the ocean waves along the longitudinal axis of the parabolic channel. Meanwhile, ε is a dimensionless geometrical parameter that represents a characteristic ratio of the parabolic channel. Using matching conditions, simple expressions for the reflection and transmission coefficients are obtained.     

Effect of shallow and narrow water on added mass of cylinders with various cross-sectional shapes

The sway, heave and roll added masses of three uniform cylinders with semi-circular, rectangular and triangular cross-sectional shapes in shallow and narrow water are numerically analysed. The method is based on simulation of the potential flow induced by the cylinder's mode of motion. The effects of shallow and narrow water on added mass are analysed and presented. It is concluded that the shallow and narrow water effects on added mass depend on the different cross-section shapes of the cylinders. In particular, the water depth effect on sway added mass is stronger than that on heave added mass while the narrow water effect on sway is weaker than that on heave. The shallow water effect on added mass tends to weaken the narrow water effect. Lastly the effect of shallow and narrow water on added mass on a rectangular cylinder is the strongest while that on a triangular cylinder is the weakest.     

Validation of the three-wave quasi-kinetic approximation for the spectral evolution in shallow water

This paper aims at validating the three-wave quasi-kinetic approximation for the spectral evolution of weakly nonlinear gravity waves in shallow water. The problem is investigated using a one-dimensional numerical wave propagation model, formulated in the spectral representation. This model includes both a nonlinear triad interactions term and a wave breaking dissipation term. Some numerical tests were carried out in order to show the importance of using the triad nonlinear term in wave propagation spectral models, particularly to describe both behavior of the spectral integral parameters and of the spectral shape evolution in shallow water depth. Furthermore; a comparison against different set of experimental observations was carried out. Comparing the numerical results with the experimental observations made it possible to show the modeling efficiency of the three-wave quasi-kinetic approximation.     

浅水非线性波作用下沙质底床孔隙水压力响应数值分析

近岸水深较浅,波浪具有较强的非线性,海床破坏与波浪作用下孔隙水压力的分布有着密切的关系。波浪场控制方程采用雷诺时均方程和k-ε紊流模型,入射波采用椭圆余弦波,采用PLIC-VOF法追踪自由表面;海床域以Biot动力固结理论为基础,建立了非线性波浪与海床相互作用的弱耦合数学模型,获得椭圆余弦波作用下沙质海床中孔隙水压力响应规律。计算结果表明,与线性波浪相比,浅水非线性波作用下沙质海床中孔隙水压力幅值增大非常显著。     

A numerical method for the two layer shallow water equations with dry states

A numerical method is proposed for solving the two layer shallow water equations with variable bathymetry in one dimension based on high-resolution f-wave-propagation finite volume methods. The method splits the jump in the fluxes and source terms into waves propagating away from each grid cell interface. It addresses the required determination of the system’s eigenstructure and a scheme for evaluating the flux and source terms. It also handles dry states in the system where the bottom layer depth becomes zero, utilizing existing methods for the single layer solution and handling single layer dry states that can exist independently. Sample results are shown illustrating the method and its handling of dry states including an idealized ocean setting.     

Directional spreading of waves in the nearshore zone

The directionality of waves inside a groin field near the German coastal zone of the island of Norderney is studied in the frequency domain. The maximum entropy method is adopted to estimate the directional spreading function. The various characteristics of the directional distribution of waves have been presented for the locations both inside and outside the groin field. The variation of directional spreading with depth and the importance of study of directional waves in coastal regions are discussed.     

浅水不规则波浪中油轮运动研究

本文对一般油轮在浅水不规则波浪中六自由度运动进行了试验分析,并对其碰底情况做了研究。试验时对有流情况下不同波高、不同装载的条件进行了分析比较。模型的六自由度运动是用非接触式六自由度运动测量与分析方法求得。该方法应用位置测量仪（ＰＳＤ）对安置在模型上的红外线发光源（ＬＥＤ）进行测量,然后所编制的软件计算出模型的六个自由度运动情况。     

Calculation of the added mass of elliptical cylinders with vertical fins in shallow water

In order to carry out any studies of ship motions, concerning either seakeeping or manoeuvring, it is usually necessary to have knowledge of the added mass of the hull section shapes. In deep water, the added mass can be found using conformal mapping techniques combined with residue calculus, or by means of surface singularity distributions. In shallow water, the need to utilise an infinite number of mirror images, to represent the effects of the seabed and the free surface, precludes the use of the deep-water methods in this case. In previous papers, the author presented methods to evaluate the added mass of semi-circular and elliptical body sections. Now, using a similar Schwarz–Christoffel method, the added mass of elliptical body sections with vertical fins in shallow water is evaluated.     

Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations

A one-dimensional high-resolution finite volume model capable of simulating storm waves propagating in the coastal surf zone and overtopping a sea wall is presented. The model (AMAZON) is based on solving the non-linear shallow water (NLSW) equations. A modern upwind scheme of the Godunov-type using an HLL approximate Riemann solver is described which captures bore waves in both transcritical and supercritical flows. By employing a finite volume formulation, the method can be implemented on an irregular, structured, boundary-fitted computational mesh. The use of the NLSW equations to model wave overtopping is computationally efficient and practically flexible, though the detailed structure of wave breaking is of course ignored. It is shown that wave overtopping at a vertical wall may also be approximately modelled by representing the wall as a steep bed slope. The AMAZON model solutions have been compared with analytical solutions and laboratory data for wave overtopping at sloping and vertical seawalls and good agreement has been found. The model requires more verification tests for irregular waves before its application as a generic design tool.     

Observation and measurement of the bottom boundary layer flow in the prebreaking zone of shoaling waves

In this paper, the characteristics of the bottom boundary layer flow induced by nonlinear, asymmetric shoaling waves, propagating over a smooth bed of 1/15 uniform slope, is experimentally investigated. Flow visualization technique with thin-layered fluorescent dye was first used to observe the variation of the flow structure, and a laser Doppler velocimeter was then employed to measure the horizontal velocity, U.The bottom boundary layer flow is found to be laminar except within a small region near the breaking point. The vertical distribution of the phase-averaged velocity U at each phase is non-uniform, which is directly affected by the mean velocity, . The magnitude of increases from zero at the bottom to a local positive maximum at about z/δ2.02.5 (where z is the height above the sloping bottom and δ is the Stokes layer thickness), then decreases gradually to zero at z/δ6.07.0 approximately, and finally becomes negative as z/δ increases further. Moreover, as waves propagate towards shallower water, the rate of increase in the maximum onshore oscillating velocity component is greater than that of the offshore counterpart except near the breaking point. The free stream velocities in the profiles of the maximum onshore and offshore oscillating velocity components, and are found to appear at z/δ≥6.0. This implies that, if the Stokes layer thickness is used as a length scale, the non-dimensionalized boundary layer thickness remains constant in the pre-breaking zone. Although is greater than and the asymmetry of the maximum free stream velocities (i.e. ) increases with decrease of water depth, a universal similar profile can be established by plotting z/δ versus ( ) or ( ). The final non-dimensional profile is symmetric and unique for the distributions of the maximum onshore and offshore oscillating velocity components within the bottom boundary layer, which are induced by nonlinear, asymmetric shoaling waves crossing the pre-breaking zone.     

Effect of a submerged plate on the near-bed dynamics underincoming waves in deep water conditions

It is well known that wave induced bottom oscillations become more and more negligible when the water depth exceeds half the wavelength of the surface gravity wave. However, it was experimentally demonstrated for regular waves that the bottom pressure oscillations at both first and second wave harmonic frequencies could be significant even for incoming waves propagating in deep water condition in the presence of a submerged plate [16]. For a water depth h of about the wavelength of the wave, measurements under the plate (depth immersion of top of plate h/6, length h/2) have shown bottom pressure variations at the wave frequency, up to thirty times larger than the pressure expected in the absence of the plate. In this paper, not only regular but also irregular wave are studied together with wave following current conditions. This behavior is numerically verified by use of a classical linear theory of waves. The wave bottom effect is explained through the role of evanescent modes and horizontally oscillating water column under the plate which still exist whatever the water depth. Such a model, which allows the calculation of the velocity fields, has shown that not only the bottom pressure but also the near bed fluid velocity are enhanced. Two maxima are observed on both sides of the location of the plate, at a distance of the plate increasing with the water depth. The possible impact of such near bed dynamics is then discussed for field conditions thanks to a scaling based on a Froude similarity. It is demonstrated that these structures may have a significant impact at the sea bed even in very deep water conditions, possibly enhanced in the presence of current.