Wave-current Interaction Research Articles

Development of an unstructured-grid wave-current coupled model and its application

An unstructured grid wave-current coupled model was developed by coupling the SWAN (Simulating Waves Nearshore) wave model and ADCIRC (Advanced Circulation model) ocean model through the Model Coupling Toolkit (MCT). The developed coupled model has high spatial resolution in the coastal area and is efficient for computation. The efficiency of the newly developed SWAN+ADCIRC model was compared with that of the widely-used SWAN+ADCIRC coupled model, in which SWAN and ADCIRC are coupled directly rather than through the MCT. Results show that the directly-coupled model is more efficient when the total number of computational cores is small, but the MCT-coupled model begin to run faster than the directly-coupled model when more computational cores are used. The MCT-coupled model maintains the scalability longer and can increase the simulation efficiency more than 35% by comparing the minimum wall clock time of one day simulation in the test runs.The MCT-coupled SWAN+ADCIRC model was used to simulate the storm surge and waves during the typhoon Usagi which formed in the western Pacific on September 17, 2013 and landed at Shanwei, China. Three numerical experiments were performed to investigate the effect of wave-current interaction on the storm surge and waves. The results show that the coupled model can better simulate the storm surge and waves when considering the wave-induced radiation stress, the wave effect on the wind stress drag coefficient and the modulation of current and water level on waves. During the typhoon Usagi, the effect of wave radiation stress could result in a maximum of 0.75m increase in the extreme storm surge, and the wave induced wind stress could cause a −0.82∼0.48m change of the extreme storm surge near the coastal area. Besides, the radiation stress forced currents cannot be ignored either in the study of mass transport at coastal zones. Results of this study are useful for understanding the wave-current interaction processes and the development of the operational prediction technique for storm surge and waves.

Nonlinear Wave–Current Interaction in Water of Finite Depth

AbstractThe interaction of nonlinear progressive waves and a uniform current in water of finite depth is investigated analytically by means of the homotopy analysis method (HAM). With HAM, the velocity potential of the flow and the surface elevation are expressed by the Fourier series, and the nonlinear free surface boundary conditions are satisfied by continuous mapping. Unlike a perturbation method, the present approach does not depend on any small parameters; thus, the solutions are suitable for steep waves and strong currents. To verify the HAM solutions, experiments are conducted in the wave–current flume of the Education Ministry Key Laboratory of Hydrodynamics at Shanghai Jiao Tong University (SJTU) in Shanghai, China. It is found that the HAM solutions are in good agreement with experimental measurements. Based on the series solutions of the validated analytical model, the influence of water depth, wave steepness, and current velocity on the physical properties of the coexisting wave–current field...

A simplified method to estimate tidal current effects on the ocean wave power resource

Although ocean wave power can be significantly modified by tidal currents, resource assessments at wave energy sites generally ignore this effect, mainly due to the difficulties and high computational cost of developing coupled wave-tide models. Furthermore, validating the prediction of wave-current interaction effects in a coupled model is a challenging task, due to the paucity of observational data. Here, as an alternative to fully coupled numerical models, we present a simplified analytical method, based on linear wave theory, to estimate the influence of tidal currents on the wave power resource. The method estimates the resulting increase (or decrease) in wave height and wavelength for opposing (or following) currents, as well as quantifying the change in wave power. The method is validated by applying it to two energetic locations around the UK shelf – Pentland Firth and Bristol Channel – where wave/current interactions are significant, and for which field data are available. Results demonstrate a good accuracy of the simplified analytical approach, which can thus be used as an efficient tool for making rapid estimates of tidal effects on the wave power resource. Additionally, the method can be used to help better interpret numerical model results, as well as observational data.

An integrated model for pore pressure accumulations in marine sediment under combined wave and current loading

In this paper, an integrated model for the wave (current)-induced seabed response is presented. The present model consists of two parts: hydrodynamic model for wave-current interactions and poro-elastic seabed model for pore accumulations. In the wave-current model, based on the fifth-order wave theory, ocean waves were generated by adding a source function into the mass conservation equation. Then, currents were simulated through imposing a steady inlet velocity on one domain and pressure outlet on the other side. In addition, both of the Reynolds-Averaged Navier-Stokers (RANS) Equations and <TEX>$k-{\varepsilon}$</TEX> turbulence model would be applied in the fluid field. Once the wave pressures on the seabed calculated through the wave-current interaction model, it would be applied to be boundary conditions on the seabed model. In the seabed model, the poro-elastic theory would be imposed to simulate the seabed soil response. After comparing with the experimental data, the effect of currents on the seabed response would be examined by emphasize on the residual mechanisms of the pore pressure inside the soil. The build-up of the pore water pressure and the resulted liquefaction phenomenon will be fully investigated. A parametric study will also be conducted to examine the effects of waves and currents as well as soil properties on the pore pressure accumulation.

Electromagnetic backscattering from one-dimensional drifting fractal sea surface I: Wave–current coupled model**Project supported by the National Natural Science Foundation of China (Grant No. 41276187), the Global Change Research Program of China (Grant No. 2015CB953901), the Priority Academic Development Program of Jiangsu Higher Education Institutions (PAPD), Program for the Innovation Research and Entrepreneurship Team in Jiangsu Province, China, the Canadian Program

To study the electromagnetic backscattering from a one-dimensional drifting fractal sea surface, a fractal sea surface wave–current model is derived, based on the mechanism of wave–current interactions. The numerical results show the effect of the ocean current on the wave. Wave amplitude decreases, wavelength and kurtosis of wave height increase, spectrum intensity decreases and shifts towards lower frequencies when the current occurs parallel to the direction of the ocean wave. By comparison, wave amplitude increases, wavelength and kurtosis of wave height decrease, spectrum intensity increases and shifts towards higher frequencies if the current is in the opposite direction to the direction of ocean wave. The wave–current interaction effect of the ocean current is much stronger than that of the nonlinear wave–wave interaction. The kurtosis of the nonlinear fractal ocean surface is larger than that of linear fractal ocean surface. The effect of the current on skewness of the probability distribution function is negligible. Therefore, the ocean wave spectrum is notably changed by the surface current and the change should be detectable in the electromagnetic backscattering signal.

Hydrodynamic modelling and characterisation of a shallow fluvial lake: a study on the Superior Lake of Mantua

This paper presents a numerical modelling framework developed to simulate circulations and to generally characterise the hydrodynamics of the Superior Lake of Mantua, a shallow fluvial lake in Northern Italy. Such eutrophied basin is characterised by low winds, reduced discharges during the summer and by the presence of large lotus flower (&lt;em&gt;Nelumbo&lt;/em&gt; &lt;em&gt;nucifera&lt;/em&gt;) meadows, all contributing to water stagnation. A hydrodynamic numerical model was built to understand how physical drivers shape basic circulation dynamics, selecting appropriate methodologies for the lake. These include a 3D code to reproduce the interaction between wind and through-flowing current, a fetch-dependent wind stress model, a porous media approach for canopy flow resistance and the consideration of wave-current interaction. The model allowed to estimate the circulation modes and water residence time distributions under identified typical ordinary, storm and drought conditions, the hydrodynamic influence of the newly-opened secondary outlet of the lake, the surface wave parameters, their influence on circulations and the bottom stress they originate, and the adaptation time scales of circulations to storm events. Some probable effects of the obtained hydrodynamic characteristics of the Superior Lake of Mantua on its biochemical processes are also introduced.

The influence of blade pitch angle on the performance of a model horizontal axis tidal stream turbine operating under wave–current interaction

Tidal stream turbines offer a promising means of producing renewable energy at foreseeable times and of predictable quantity. However, the turbines may have to operate under wave-current conditions that cause high velocity fluctuations in the flow, leading to unsteady power output and structural loading and, potentially, to premature structural failure. Consequently, it is important to understand the effects that wave-induced velocities may have on tidal devices and how their design could be optimised to reduce the additional unsteady loading.This paper describes an experimental investigation into the performance of a scale-model three-bladed HATT (horizontal axis tidal stream turbine) operating under different wave-current combinations and it shows how changes in the blade pitch angle can reduce wave loading. Tests were carried out in the recirculating water channel at the University of Liverpool, with a paddle wavemaker installed upstream of the working section to induce surface waves travelling in the same direction as the current. Three wave conditions were employed in a current-dominated flow. The wave kinematics were measured using an acoustic Doppler velocimeter and there was generally good agreement with Stokes' second-order wave theory. Power and thrust measurements were taken under both current-alone and wave-current conditions for different blade pitch angles. It was observed that, as the blade pitch angle was increased from optimum, both the mean power and thrust on the turbine decreased and the reductions in thrust were always greater than in power. The fluctuations in power and thrust also decreased with an increase in the blade pitch angle. Therefore, changes in blade pitch angle can be used as a mechanism for reducing the loading on a HATT when operating with excessive wave-induced loads, while still enabling a significant amount of the available power in the unsteady tidal stream to be extracted.

Hamiltonian Formulation for Wave-Current Interactions in Stratified Rotational Flows

We show that the Hamiltonian framework permits an elegant formulation of the nonlinear governing equations for the coupling between internal and surface waves in stratified water flows with piecewise constant vorticity.

The influence of surface wave on water exchange in the Bohai Sea

A three-dimensional wave-current coupled modeling system has been applied to analyze the water motions for the Bohai Sea and its adjacent waters. Two different methods of estimating the water exchange through the Bohai Strait have been employed, consisting of particle tracking and passive dye. The objectives of this study are to account for the surface wave role in the water exchange processes between the Bohai Sea and the outer waters, to test the response of the flushing characteristics of the Bohai Sea to different aspects of wave actions, and to obtain a quantitative and qualitative estimate of the half-life time under different experiment conditions. By comparing the simulations of water exchange with or without wave-current interactions, we find that waves can improve the Bohai Sea vertically mean water exchange capability, with more obvious enhancements for the surface layer where concentrated actions function. A series of numerical experiments indicate that turbulent kinetic energy from wave dissipation is the major positive influence, while wave-dependent surface stress, radiation stress, and Stokes drift have a minor effect. These results suggest that wave-driven mixing should be considered in the Bohai Sea water exchange processes, preferably using a half-life model based on concentration advection-diffusion model.

Applicability of 3D Beach Evolution Model with Wave-current Interaction to River-mouth Bar Formation

ABSTRACT Kuroiwa, M.; Shibutani, Y.; Yasumoto,; Mase, H, and Matsubara, Y., 2016. Applicability of 3D beach evolution model with wave-current interaction to river-mouth bar formation. In: Vila-Concejo, A.; Bruce, E.; Kennedy, D.M., and McCarroll, R.J. (eds.), Proceedings of the 14th International Coastal Symposium (Sydney, Australia). Journal of Coastal Research, Special Issue, No. 75, pp. 73–77. Coconut Creek (Florida), ISSN 0749-0208. A coastal area model with wave-current interaction was presented, and then the performance and applicability of the numerical to morphodynamics around river mouths due to waves, wave-induced currents and river flows were investigated. First, model tests were carried out under a variety of wave and river discharge conditions to investigate their capability of predicting the formation of sand spit and terrace topographies. Second, model verification using a field site was conducted and the applicability was investigated. From the computed results, it was confirmed that the p...

Nonlinear Wave–Current Interactions in Shallow Water

We study here the propagation of long waves in the presence of vorticity. In the irrotational framework, the Green–Naghdi equations (also called Serre or fully nonlinear Boussinesq equations) are the standard model for the propagation of such waves. These equations couple the surface elevation to the vertically averaged horizontal velocity and are therefore independent of the vertical variable. In the presence of vorticity, the dependence on the vertical variable cannot be removed from the vorticity equation but it was however shown in that the motion of the waves could be described using an extended Green–Naghdi system. In this paper, we propose an analysis of these equations, and show that they can be used to get some new insight into wave–current interactions. We show in particular that solitary waves may have a drastically different behavior in the presence of vorticity and show the existence of solitary waves of maximal amplitude with a peak at their crest, whose angle depends on the vorticity. We also show some simple numerical validations. Finally, we give some examples of wave–current interactions with a nontrivial vorticity field and topography effects.

The impact of surface currents and sea level on the wave field evolution during St. Jude storm in the eastern Baltic Sea

Summary A third generation numerical wave model SWAN (Simulating WAves Nearshore) was applied to study the spatio-temporal effect of surface currents and sea level height on significant wave height; and to describe the mechanisms responsible for wave–current interaction in the eastern Baltic Sea. Simulation results were validated by comparison with in situ wave measurements in deep and shallow water, carried out using the directional wave buoy and RDCP respectively, and with TerraSAR-X imagery. A hindcast period from 23 to 31 October 2013 included both a period of calm to moderate weather conditions and a severe North-European windstorm called St. Jude. The prevailing wind directions were southerly to westerly. Four simulations with SWAN were made: a control run with dynamical forcing by wind only; and simulations with additional inputs of surface currents and sea level, both separately and combined. A clear effect of surface currents and sea level on the wave field evolution was found. It manifested itself as an increase or decrease of significant wave height of up to 20%. The strength of the interaction was influenced by the propagation directions of waves and surface currents and the severity of weather conditions. An increase in the wave height was mostly seen in shallower waters and in areas where waves and surface currents were propagating in opposite directions. In deeper parts of the eastern Baltic Sea and in case of waves and surface currents propagating in the same direction a decrease occurred.

Video-based nearshore bathymetry estimation in macro-tidal environments

Video-based depth inversion through the linear dispersion relation for free surface waves using the cross spectral correlation analysis, cBathy (Holman et al., 2013), is applied for the first time in a highly energetic macro-tidal environment in the South West of England at Porthtowan. This application of cBathy reveals two main issues: 1) inaccurate depth estimations on inter camera boundaries when multiple cameras are used and 2) significantly less accurate depth estimates over the whole domain during spring tide compared to neap tide (inaccuracies of around 35% of the local depths are found during spring tide). These two issues are not only important in macro-tidal environments: the camera boundary issue has been reported in numerous video-camera sites and the deviation in accuracy during tidal levels is a function of the tidal range in combination of the vertical camera position. To overcome the two issues, a camera boundary solution and a floating pixel solution (meaning moving pixels in a horizontal plane as function of the tidal elevation) are proposed here. With the modifications, cBathy is capable of estimating depths in the sub-tidal zone with an accuracy in the order of 10% of the local depth irrespective to the local tidal regime. However, for the very upper part of the beach face less accurate results are found due to the reduced validity of the linear dispersion relation in that region due to the non-linear behaviour of breaking waves and wave–current interactions. The improvements persist across all bathymetry survey campaigns at Porthtowan and when compared to other well known Argus video-system sites the importance of the floating pixels is apparent.

A numerical model for wave-current interaction at the scale of marine engineering

ABSTRACTIn the present paper a numerical method for marine and coastal hydrodynamics is presented. It aims at developing a formulation for the complete wave-current coupling in the time domain. In this framework, both waves and currents are handled by complete Navier–Stokes equations. Indeed, waves are modified by currents and interaction with structures, the flow is forced by waves and structures as well. The numerical solution for fully 3D equations is outlined, showing that the proposed procedure is a revisited version of the fractional step method, i.e. the free surface fractional step method. Some numerical test cases in simple 2D geometries (vertical direction vs direction of wave propagation) are shown.

Modulation of wave–current interactions by horizontal mixing and spatial resolution

The mechanics of rip currents are complex, involving interactions between waves, currents, water levels and bathymetry that pose particular challenges for numerical modeling. Horizontal turbulent diffusion in a rip system is difficult to measure using dye dilution or surfzone drifters, as shown by the range of published values for the horizontal diffusion coefficient. Here, we studied the effects of horizontal mixing on wave–current interactions by testing several diffusivity estimates in a fully coupled 3D wave–current model run at two different spatial resolutions. Published results using very low diffusion have found that near the shore the wave rays converge towards the rip channel because of refraction by the currents. We showed that this process is modulated by both horizontal mixing and spatial resolution. We found that, without the feedback of currents on waves, the flow is more sensitive to horizontal mixing, with large alterations, especially offshore, and generally lower velocities. These modifications ascribed to mixing are similar to those induced by the feedback mechanism. When a large mixing coefficient is used: (i) the behavior of the rip system is similar for both coupling modes (i.e., with and without the feedback of currents on waves) and for each resolution; and (ii) the evolution of the flow is more stable over time. Lastly, we show that the horizontal mixing strongly decreases the intensity of the 3D rip velocity, but not its vertical shear, which is mainly dependent on the vertical mixing scheme and on the forcing terms.

Evolution of Mid-Atlantic Coastal and Back-Barrier Estuary Environments in Response to a Hurricane: Implications for Barrier-Estuary Connectivity

Assessments of coupled barrier island-estuary storm response are rare. Hurricane Sandy made landfall during an investigation in Barnegat Bay-Little Egg Harbor estuary that included water quality monitoring, geomorphologic characterization, and numerical modeling; this provided an opportunity to characterize the storm response of the barrier island-estuary system. Barrier island morphologic response was characterized by significant changes in shoreline position, dune elevation, and beach volume; morphologic changes within the estuary were less dramatic with a net gain of only 200,000 m3 of sediment. When observed, estuarine deposition was adjacent to the back-barrier shoreline or collocated with maximum estuary depths. Estuarine sedimentologic changes correlated well with bed shear stresses derived from numerically simulated storm conditions, suggesting that change is linked to winnowing from elevated storm-related wave-current interactions rather than deposition. Rapid storm-related changes in estuarine water level, turbidity, and salinity were coincident with minima in island and estuarine widths, which may have influenced the location of two barrier island breaches. Barrier-estuary connectivity, or the transport of sediment from barrier island to estuary, was influenced by barrier island land use and width. Coupled assessments like this one provide critical information about storm-related coastal and estuarine sediment transport that may not be evident from investigations that consider only one component of the coastal system.

Turbulence between two inline hemispherical obstacles under wave–current interactions

This paper reports an experimental investigation of open channel turbulent flow between two inline surface mounted hemispherical obstacles in tandem arrangement. A series of experiments are performed under combined wave–current interaction with seven relative spacing L/h, where L is center to center spacing distance and h is the obstacle height for Reynolds number Re = 5.88 × 104. The observations are particularly focused on the changes induced in the mean velocity components, turbulence intensities and Reynolds shear stress due to superposition of surface waves on the ambient flow, and are compared to that of flat-surface and a single hemisphere. The paper also investigates the dominant turbulent bursting events that contribute to the Reynolds shear stress for different relative depth influenced by hemispheres. It is observed that the contributions to the total shear stress due to ejection and sweep are dominant at the wake region for single and double hemisphere near the bed, while towards the surface outward and inward interactions show significant effect for wave–current interactions which is largely different from that over the flat-surface case. Spectral analysis of the observed velocity fluctuations reveals the existence of two distinct power law scaling regime near the bed. At high frequency, an inertial sub-range of turbulence with −5/3 Kolmogorov scaling is observed for the flat-surface. The spectral slope is calculated to show the shifting of standard Kolmogorov scale for both only current and wave-induced tests.

Large-scale 3-D experiments of wave and current interaction with real vegetation. Part 2: Experimental analysis

This paper assesses the influence of different flow and vegetation parameters on the wave attenuation provided by two contrasting salt marsh species: Puccinellia maritima and Spartina anglica. Different water depths and wave parameters (height and period) are considered for both regular and irregular waves with and without an underlying uniform current coming from different directions. The study of the submergence ratio (h/hv) influence shows that wave damping coefficient rapidly decreases as the plant submergence ratio increases. The high nonlinearities found in the wave–current interaction lead to different wave damping patterns in comparison to wave-only conditions. A smaller wave damping is found for waves and current acting in the same direction and an increase in the wave damping rate is obtained for waves and current flowing in the opposite direction. These wave and current tests allow for the studying of the energy dissipation produced by the vegetation, increasing our knowledge about flow and plant interaction in estuarine conditions. The biomechanical properties of the two real salt marshes used in the experiments are also evaluated and related to wave damping revealing a higher attenuation for stiffer vegetation. Both, the vegetation density and the biomass strongly influence wave damping. Higher density and biomass values lead to higher attenuation rates for both species.

Wave–current interaction effects on tidal stream turbine performance and loading characteristics

The transient interaction between tidal currents and the rotation of a horizontal axis turbine rotor have the potential to induce high asymmetric loadings, which are subsequently transmitted to the drive shaft and potentially high speed drive train components. To mitigate the potential for early component failure, analysis of asymmetric loading on marine turbines is fundamental to the design process. To investigate these loads a turbine mounted on a circular stanchion has been used to highlight the effects of introducing more realistic boundary conditions. Depending on their wavelength, waves can also have a significant effect on the overall design decisions and placement of devices. Thrust loading and bending moments applied to the drive shaft can be of the order of hundreds of kN and kNm respectively.Knowledge of the flow regime can allow designers to evaluate material selection for components and incorporate some deformation capability of the turbine blades to increase the power output and potentially alleviate some of the stress distribution through key structural points. The resulting data can then be used to estimate component life via fatigue prediction.This paper includes a multi-physics approach to modelling tidal energy devices and the potential for modelling to inform device condition monitoring.

A coupled "AB" system: Rogue waves and modulation instabilities.

Rogue waves are unexpectedly large and localized displacements from an equilibrium position or an otherwise calm background. For the nonlinear Schrödinger (NLS) model widely used in fluid mechanics and optics, these waves can occur only when dispersion and nonlinearity are of the same sign, a regime of modulation instability. For coupled NLS equations, rogue waves will arise even if dispersion and nonlinearity are of opposite signs in each component as new regimes of modulation instability will appear in the coupled system. The same phenomenon will be demonstrated here for a coupled "AB" system, a wave-current interaction model describing baroclinic instability processes in geophysical flows. Indeed, the onset of modulation instability correlates precisely with the existence criterion for rogue waves for this system. Transitions from "elevation" rogue waves to "depression" rogue waves are elucidated analytically. The dispersion relation as a polynomial of the fourth order may possess double pairs of complex roots, leading to multiple configurations of rogue waves for a given set of input parameters. For special parameter regimes, the dispersion relation reduces to a cubic polynomial, allowing the existence criterion for rogue waves to be computed explicitly. Numerical tests correlating modulation instability and evolution of rogue waves were conducted.