Effects of wave–current interaction on the current profile

Wave–current laboratory experiments have shown that the logarithmic current profile observed in pure current flows is modified due to the presence of waves. When waves propagate opposite the current, an increase in the current intensity is achieved near the mean water level, while a reduction is obtained for following waves and currents. With the aim of analyzing these nonlinear effects along the whole water column, an Eulerian wave–current model is presented. In contrast to previously presented wave–current models, the present is able to include the variation of the free surface elevation due to the wave motion and the effect of a non hydrostatic pressure field. Therefore it does not restrict its application to waves in shallow waters. Moreover, the model is able to simulate all the possible angles between waves and currents.     

Quadtree grid numerical model of nearshore wave–current interaction

This paper describes an adaptive quadtree-based 2DH wave–current interaction model for evaluating nearly horizontal wave-induced currents in the surf-zone. The model accounts for wave breaking, shoaling, refraction, diffraction, wave–current interaction, set-up and set-down, mixing processes (turbulent diffusion), bottom frictional effects, and movement of the land–water interface at the shoreline. The wave period- and depth-averaged governing equations, which conserve mass, momentum, energy and wave action, are discretised explicitly by means of an Adams–Bashforth second-order finite difference technique on adaptive hierarchical staggered quadtree grids. Grid adaptation is achieved through seeding points distributed according to flow criteria (e.g. local current gradients). The model is verified for nearshore circulation at a sinusoidal beach and nearshore currents at a multi-cusped beach. Reasonable agreement is obtained with experimental data from da Silva Lima [da Silva Lima, S.S.L., 1981. Wave-induced Nearshore Currents. PhD Thesis, Department of Civil Engineering, University of Liverpool] and Borthwick et al. [Borthwick, A.G.L., Foote, Y.L.M., Ridehalgh, A., 1997. Nearshore measurements at a cusped beach in the UK Coastal Research Facility, Coastal Dynamics '97, Plymouth, 953–962]. The modelling approach presented herein should be useful in simulating nearshore processes in complicated natural coastal domains. Of particular value is the local grid enrichment capability, which permits refined modelling of important localised flow behaviour such as rip currents and surf-zone circulation systems.     

Numerical simulations of wave–current flow in an ocean basin

Wave–current flow is a phenomenon that is present in many practical engineering situations. Over the past several decades, this type of flow has been increasingly investigated under controlled laboratory conditions. This paper presents a numerical study of wave–current flow in the ocean basin of the LabOceano (COPPE/UFRJ). A homogeneous multiphase model based on the RANS equations and the k–ɛ turbulence model implemented in ANSYS-CFX code were used. A cross section of the ocean basin was represented. A regular wave with a height of 0.08 m and a period of 1.80 s (i.e., a wave steepness of H/L = 0.016), propagating on favourable currents, was simulated. The behaviour of the free surface elevation over time and the streamlines along the basin for wave and wave–current flows were presented. The numerical results were compared to the non-viscous theory given by the Rayleigh equation applied to the problem of wave–current interaction. Good agreement was found between the wave length estimated by the numerical results and the analytical solutions, with a deviation of less than 2%.     

A model of the formation and development of ocean shear wave

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Evaluation of the simulation capability of the Wavewatch Ⅲ model for Pacific Ocean wave

Wave climate analysis and other applications for the Pacific Ocean require a reliable wave hindcast. Five source and sink term packages in the Wavewatch III model(v3.14 and v4.18) are compared and assessed in this study through comprehensive observations, including altimeter significant wave height, advanced synthetic aperture radar swell, and buoy wave parameters and spectrum. In addition to the evaluation of typically used integral parameters, the spectra partitioning method contributes to the detailed wave system and wave maturity validation. The modified performance evaluation method(PS) effectively reduces attribute numbers and facilitates the overall assessment. To avoid possible misleading results in the root mean square error-based validations, another indicator called HH(indicating the two authors) is also calculated to guarantee the consistency of the results. The widely used Tolman and Chalikov(TC) package is still generally efficient in determining the integral properties of wave spectra but is physically deficient in explaining the dissipation processes. The ST4 package performs well in overall wave parameters and significantly improves the accuracy of wave systems in the open ocean. Meanwhile, the newly published ST6 package is slightly better in determining swell energy variations. The two packages(ACC350 and BJA) obtained from Wavewatch III v3.14 exhibit large scatters at different sea states. The three most ideal packages are further examined in terms of reproducing waveinduced momentum flux from the perspective of transport. Stokes transport analysis indicates that ST4 is the closest to the NDBC-buoy-spectrum-based transport values, and TC and ST6 tend to overestimate and underestimate the transport magnitude, respectively, in swell mixed areas. This difference must be considered,particularly in air–wave–current coupling research and upper ocean analysis. The assessment results provide guidance for the selection of ST4 for use in a background Pacific Ocean hindcast for high wave climate research and China Sea swell type analysis.     

Experimental study of wave–wave nonlinear interactions using the wavelet-based bicoherence

The wavelet-based bicoherence, which is a new and powerful tool in the analysis of nonlinear phase coupling, is used to study the nonlinear wave–wave interactions of breaking and non-breaking gravity waves propagating over a sill. Two cases of mechanically generated random waves based on Jonswap spectra are used for this purpose. Values of relative depth, k_ph (k_p is the wave number of the spectral peak and h is the water depth) for this study range between 0.38 and 1.22. The variations of wavelet-based total bicoherence for the test cases indicate that the degree of quadratic phase coupling increases in the shoaling region consistent with a wave profile that is pitched shoreward, relative to a vertical axis as seen in the experiments, but decreases in the de-shoaling region. For the non-breaking case, the degree of quadratic phase coupling continues to increase until waves reach the top of the sill. Breaking waves, however, achieve their highest level of quadratic phase coupling immediately before incipient breaking and the degree of phase coupling decreases sharply following breaking. In addition the wavelet-based bicoherence spectra provide evidence of the harmonics' growth which is reflected in the energy spectra. The bicoherence spectra also show that quadratic phase coupling between modes within the peak frequency as well as between modes of the peak frequency and its higher harmonics are dominant in the shoaling region, even though there are relatively high levels of quadratic phase coupling occurring between other frequencies. Furthermore, using the temporal resolution property of the wavelet-based bicoherence, we find that the quadratic wave interactions occur more readily during segments of time with large change of wave amplitude, rather than those segments having large wave amplitudes, but small gradients in amplitude.     

Laboratory study on wave dissipation by vegetation in combined current–wave flow

Coastal wetlands such as salt marshes and mangroves provide valuable ecosystem services including coastal protection. Many studies have assessed the influence of plant traits and wave conditions on vegetation-induced wave dissipation, whereas the effect of tidal currents is often ignored. To our knowledge, only two studies investigated wave dissipation by vegetation with the presence of following currents (current velocity is in the same direction as wave propagation) (Li and Yan, 2007; Paul et al., 2012). However, based on independent experiments, they have drawn contradictive conclusions whether steady currents increase or decrease wave attenuation. We show in this paper that this inconsistency may be caused by a difference in ratio of imposed current velocity to amplitude of the horizontal wave orbital velocity. We found that following currents can either increase or decrease wave dissipation depending on the velocity ratio, which explains the seeming inconsistency in the two previous studies. Wave dissipation in plant canopies is closely related to vegetation drag coefficients. We apply a new approach to obtain the drag coefficients. This new method eliminates the potential errors that are often introduced by the commonly used method. More importantly, it is capable of obtaining the vegetation drag coefficient in combined current–wave flows, which is not possible for the commonly used calibration method. Based on laboratory data, we propose an empirical relation between drag coefficient and Reynolds number, which can be useful for numerical modeling. The characteristics of drag coefficient variation and in-canopy velocity dynamics are incorporated into an analytical model to help understand the effect of following currents on vegetation-induced wave dissipation.     

The application of wave refraction-diffraction model with friction

In this paper a refraction-diffraction model with friction is used to compute wave characteristics in a region near a certain port. Comparing with the results from refraction model, and with the data observed during a typhoon in 1985, it is found that the characteristics from the refraction-diffraction model with friction are reasonable, and that the results are in rather good agreement with observations. Thus it can be concluded that the model is effective for computing coastal wave characteristics over complicated bottom topography.     

A model for the response of wave directions in slowly turning wind fields

On the basis of the wave energy balance equation, the response model of mean directions of locally wind-generated waves in slowly turning wind fields has been derived. The results show that in a homogeneous field, the time scale of the response is not only related to the rate of wave growth, but also to the directional energy distribution and the angle between the wind direction and the mean wave direction. Furthermore, the law of change in the mean wave direction has been derived. The numerical computations show that the response of wave directions to slowly turning wind directions can be treated as the superposition of the responses of wave directions to a series of sudden small-angle changes of wind directions and the turning rate of the mean wave direction depends on the turning rate and the total turning angles of the wind direction. The response of wave directions is in agreement with the response for a sudden change of wind directions if the change in wind directions is very fast. Based on the no     

Exact solution of entanglement of the double Jaynes—Cummings model without rotating wave approximation

This paper investigates the influences of atom--field coupling and dipole--dipole coupling for atoms on the entanglement between two atoms by means of concurrence. The results show that the sudden death occurs when the atom--field coupling is strong enough, and the collapse and the revival appear when the dipole--dipole interaction is strong enough.     

The effect of wave–current interactions on the storm surge and inundation in Charleston Harbor during Hurricane Hugo 1989

The effects of wave–current interactions on the storm surge and inundation induced by Hurricane Hugo in and around the Charleston Harbor and its adjacent coastal regions are examined by using a three-dimensional (3-D) wave–current coupled modeling system. The 3-D storm surge and inundation modeling component of the coupled system is based on the Princeton ocean model (POM), whereas the wave modeling component is based on the third-generation wave model, simulating waves nearshore (SWAN). The results indicate that the effects of wave-induced surface, bottom, and radiation stresses can separately or in combination produce significant changes in storm surge and inundation. The effects of waves vary spatially. In some areas, the contribution of waves to peak storm surge during Hurricane Hugo reached as high as 0.76 m which led to substantial changes in the inundation and drying areas simulated by the storm surge model.     

A Eulerian–Lagrangian method for the simulation of wave propagation

A Eulerian–Lagrangian method (ELM) is employed for the simulation of wave propagation in the present research. The wave action conservation equation, instead of the wave energy balance equation, is used. The wave action is conservative and the action flux remains constant along the wave rays. The ELM correctly accounts for this physical characteristic of wave propagation and integrates the wave action spectrum along the wave rays. Thus, the total derivative for wave action spectrum may be introduced into the numerical scheme and the complicated partial differential wave action balance equation is simplified into an ordinary differential equation. A number of test cases on wave propagation are carried out and show that the present method is stable, accurate and efficient. The results are compared with analytical solutions and/or other computed results. It is shown that the ELM is superior to the first-order upwind method in accuracy, stability and efficiency and may better reflect the complicated dynamics due to the complicated bathymetry features in shallow water areas.     

Combined classifier–quantifier model: A 2-phases neural model for prediction of wave overtopping at coastal structures

A 2-phases neural prediction method for wave overtopping is developed. The ‘classifier’ predicts whether overtopping occurs or not, i.e. q = 0 or q > 0. If the classifier predicts overtopping q > 0, then the ‘quantifier’ is used to determine the mean overtopping discharge. The overtopping database set up within the EC project CLASH (De Rouck, J., Geeraerts, J., 2005. CLASH Final Report, Full Scientific and Technical Report, Ghent University, Belgium) is used to train the networks of the prediction method.     

Modeling nonlinear wave–wave interactions with the elliptic mild slope equation

An approach is developed to simulate wave–wave interactions using nonlinear elliptic mild-slope equation in domains where wave reflection, refraction, diffraction and breaking effects must also be considered. This involves the construction of an efficient solution procedure including effective boundary treatment, modification of the nonlinear equation to resolve convergence issues, and validation of the overall approach. For solving the second-order boundary-value problem, the Alternating Direction Implicit (ADI) scheme is employed, and the use of approximate boundary conditions is supplemented, for improved accuracy, with internal wave generation method and dissipative sponge layers. The performance of the nonlinear model is investigated for a range of practical wave conditions involving reflection, diffraction and shoaling in the presence of nonlinear wave–wave interactions. In addition, the transformation of a wave spectrum due to nonlinear shoaling and breaking, and nonlinear resonance inside a rectangular harbor are simulated. Numerical calculations are compared with the results from other relevant nonlinear models and experimental data available in literature. Results show that the approach developed here performs reasonably well, and has thus improved the applicability of this class of wave transformation models.     

Interannual variability of Kelvin wave propagation in the wave guides of the equatorial Indian Ocean,the coastal Bay of Bengal and the southeastern Arabian Sea during 1993–2006

The observed variability of the Kelvin waves and their propagation in the equatorial wave guide of the Indian Ocean and in the coastal wave guides of the Bay of Bengal (BoB) and the southeastern Arabian Sea (AS) on seasonal to interannual time scales during years 1993–2006 is examined utilizing all the available satellite and in-situ measurements. The Kelvin wave regime inferred from the satellite-derived sea surface height anomalies (SSHA) shows a distinct annual cycle composed of two pairs of alternate upwelling (first one occurring during January–March and the second one occurring during August–September) and downwelling (first one occurring during April–June and the second one occurring during October–December) Kelvin waves that propagate eastward along the equator and hit the Sumatra coast and bifurcate. The northern branches propagate counterclockwise over varied distances along the coastal wave guide of the BoB. The potential mechanisms that contribute to the mid-way termination of the first upwelling and the first downwelling Kelvin waves in the wave guide of the BoB are hypothesized. The second downwelling Kelvin wave alone reaches the southeastern AS, and it shows large interannual variability caused primarily by similar variability in the equatorial westerly winds during boreal fall. The westward propagating downwelling Rossby waves triggered by the second downwelling Kelvin wave off the eastern rim of the BoB also shows large interannual variability in the near surface thermal structure derived from SODA analysis. The strength of the equatorial westerlies driven by the east–west gradient of the heat sources in the troposphere appears to be a critical factor in determining the observed interannual variability of the second downwelling Kelvin wave in the wave guides of the equatorial Indian Ocean, the coastal BoB, and the southeastern AS.     

Eddies and a mesoscale deflection of the slope current in the Faroe–Shetland Channel

The mesoscale dynamics of the Scottish side of the Faroe–Shetland Channel have been investigated using synoptic in situ and remote sensing observations. A cold core cyclonic eddy, identified from an AVHRR image, had a diameter of about 50 km and surface current speeds of up to 50 cm s^-1; it appeared to be attached to the 800 m isobath as it moved north-eastward along the edge of the channel at about 8 cm s^-1. Speeds in the slope current were about 50 cm s^-1 but increased to 70 cm s^-1 where the current was compressed by the eddy. Offshore, over the 1000 m isobath in the cooler water, speeds in the current were slower (ca. 20 cm s^-1). North-west of the Shetlands the offshore edge of the slope current was deflected across the channel for a distance of about 70 km from the shelf edge. The speed of drifters in the slope current increased to over 60 cm s^-1 as they moved anti-cyclonically around this deflection. CTD profiles suggest that the movement of the surface waters was mirrored in the deep water of the channel. The deflection carried a very large quantity of North Atlantic Water into the central part of the channel; its cause and ultimate fate are not known, although it is likely to have had a significant impact on the dynamics of the channel.     

Compression–shear coupling rheological constitutive model of the deep-sea sediment

In deep-sea mining engineering, the compression–shear coupling effect of the sediment on the moving tracked mining vehicle must be considered, since it is proved to be existing in compression–shear creep test of the sediment simulant. Based on the endochronic theory, the compression–shear coupling rheological model is established by the definition of intrinsic time and calculation of deviatoric tensor, where the coupling rheological parameters can be obtained by the compression–shear creep test. For simulating sinkage and traction force of the moving tracked mining vehicle, the compression–shear coupling rheological model as well as compressive rheological model and direct shear rheological model (regardless of coupling rheological effect) is programmed and introduced into RecurDyn software (with only traditional elastic–plastic constitutive model) for comparison. Research results show that the sinkage is the largest, and the traction force is the smallest under the compression–shear coupling rheological model, which could better reflect the worse working situation. The compression–shear coupling rheological model could provide theoretical basis for optimal design and safety assessment of the tracked mining vehicle.     

Wave refraction–diffraction effect in the wind wave model WWM

Based on the extended mild-slope equation, the wind wave model (WWM; Hsu et al., 2005) is modified to account for wave refraction, diffraction and reflection for wind waves propagating over a rapidly varying seabed in the presence of current. The combined effect of the higher-order bottom effect terms is incorporated into the wave action balance equation through the correction of the wavenumber and propagation velocities using a refraction–diffraction correction parameter. The relative importance of additional terms including higher-order bottom components, the wave–bottom interaction source term and wave–current interaction that influence the refraction–diffraction correction parameter is discussed. The applicability of the proposed model to calculate a wave transformation over an elliptic shoal, a series of parallel submerged breakwater induced Bragg scattering and wave–current interaction is evaluated. Numerical results show that the present model provides better predictions of the wave amplitude as compared with the phase-decoupled model of Holthuijsen et al. (2003).     

A simple approximation for wave refraction – Application to the assessment of the nearshore wave directionality

This work presents a simple and relatively quick methodology to obtain the nearshore wave angle. The method is especially valuable for curvilinear coasts where Snell’s law may provide excessively inaccurate results. We defined a correction factor, K, that depends on the geometry of the coast and on the wave climate. The values of this coefficient were obtained minimizing the differences with a sophisticated numerical model. The limitations and performance of the methodology are further discussed. The procedure was applied to a beach in Southern Spain to analyze the influence of shoreline geometry on nearshore wave directionality. Offshore and nearshore distributions of wave period and directions were analyzed, and the results showed that the geometry of the coast played a crucial role in the directionality of the nearshore waves, which also plays an important role in hydrodynamics. The methodology presented here is able to analyze and quantify the importance of this directionality without a noticeable computational cost, even when a long time series of wave data are considered. Hence, this methodology constitutes a useful and efficient tool for practical applications in Coastal and Ocean Engineering, such as sedimentary, wave energy, and wave climate studies.