Wave-current Interaction Research Articles

A fully nonlinear numerical method for modeling wave–current interactions

The presence of current in the ocean can significantly modify the characteristics of ocean waves, and it is considered as an important factor responsible for the occurrence of extreme waves, e.g., rogue waves, which are well known as great threats to ocean engineering practices. The magnitude and direction of ocean current normally vary spatially and ocean waves can become very large and steep. Accurate and efficient phase-resolved numerical methods of fully nonlinear wave–current interactions on a large scale in three dimensions (3D) are required to understand their properties, but the existing phase-resolved methods are all based on the assumption of linear or weakly nonlinear interactions. This paper will address the issues and present a fully nonlinear numerical method to model the 3D interactions between waves and varying current on a large scale using a phase-resolved formulation. A new set of equations describing the three-dimensional, fully nonlinear interactions between waves and horizontally shearing current is proposed. They are derived by making no assumption on wave steepness or the order of wave–current interactions. The resulting new equations correctly describe the free surface boundary conditions by representing the fully nonlinear wave–current interactions, removing the limitation to the small wave steepness of the existing formulations in literature.On this basis, the recently developed Enhanced Spectral Boundary Integral (short as ESBI) method is further enhanced to be able to model the wave–current interactions using the new equations, by developing the appropriate procedure for dealing with the extra terms related to nonlinear wave–current interactions. The new equations are used as the prognostic equations for updating the free surface in time domain, and a fast converging iterative technique is employed to solve them. The robustness of the newly developed method is demonstrated through comparing with experimental data available in literature and good agreements are observed in the several different cases, including the 3D fully nonlinear interactions between ocean waves and horizontally varying current. A comparison with the Higher-Order Spectrum (HOS) method based on weak-nonlinear formulations of wave–current interactions is also made to confirm larger error does appear if the wave steepness is high by using the HOS. The method presented in the paper can be employed to simulate the real evolution of ocean waves on current in a phase-resolved way to give deep insights to the dynamics of wave–current interactions, which may not be done correctly by the existing methods so far.

Wave-current interaction during Typhoon Nuri (2008) and Hagupit (2008): an application of the coupled ocean-wave modeling system in the northern South China Sea

The northern South China Sea (SCS) is frequently affected by typhoons. During severe storm events, wave-current interactions produce storm surges causing enormous damage in the path of the typhoon. To evaluate the influence of wave-current interactions on storm surge, we used a coupled ocean-atmospherewave- sediment transport (COAWST) modeling system with radiation-stress and vortex-force formulations to simulate two typically intense tropical storms that invaded the SCS, namely Typhoons Nuri (2008) and Hagupit (2008), and compared results with observations from the Hong Kong Observatory. Both radiationstress and vortex-force formulations significantly improved the accuracy of the simulation. Depending on which typhoon and the topography encountered, the influence of surface waves on the oceanic circulation showed different characteristics, including the differences of range and intensity of storm surge between vortex-force and radiation-stress experiments. During typhoon landing, strong sea-surface elevation in concert with wave set-up/set-down caused the adjustment of the momentum balance. In the direction perpendicular to the current, but especially in the cross-shore direction, the pressure gradient and wave effects on the current dominated the momentum balance.

Effects of Wave–Current Interactions on Suspended-Sediment Dynamics during Strong Wave Events in Jiaozhou Bay, Qingdao, China

AbstractWave–current interactions are crucial to suspended-sediment dynamics, but the roles of the associated physical mechanisms, the depth-dependent wave radiation stress, Stokes drift velocity, vertical transfer of wave-generated pressure transfer to the mean momentum equation (form drag), wave dissipation as a source term in the turbulence kinetic energy equation, and mean current advection and refraction of wave energy, have not yet been fully understood. Therefore, in this study, a computationally fast wave model developed by Mellor et al., a Finite Volume Coastal Ocean Model (FVCOM) hydrodynamics model, and the sediment model developed by the University of New South Wales are two-way coupled to study the effect of each wave–current interaction mechanism on suspended-sediment dynamics near shore during strong wave events in a tidally dominated and semiclosed bay, Jiaozhou Bay, as a case study. Comparison of Geostationary Ocean Color Imager data and model results demonstrates that the inclusion of just the combined wave–current bottom stress in the model, as done in most previous studies, is clearly far from adequate to model accurately the suspended-sediment dynamics. The effect of each mechanism in the wave–current coupled processes is also investigated separately through numerical simulations. It is found that, even though the combined wave–current bottom stress has the largest effect, the combined effect of the other wave–current interactions, mean current advection and refraction of wave energy, wave radiation stress, and form drag (from largest to smallest effect), are comparable. These mechanisms can cause significant variation in the current velocities, vertical mixing, and even the bottom stress, and should obviously be paid more attention when modeling suspended-sediment dynamics during strong wave events.

Numerical Simulation of Parabolic Profile of Longshore Currents

Chun, H. and Suh, K.-D., 2018. Numerical simulation of parabolic profile of longshore currents. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 941–945. Coconut Creek (Florida), ISSN 0749-0208.The three-dimensional nearshore currents model well predicted the typical profile of undertow, i.e. the shoreward near-surface currents and the seaward flow below the wave trough level. Meanwhile, the measurements showed that the longshore currents were logarithmically or parabolically distributed over the depth, but the parabolic profile had not been reproduced by the numerical models (Newberger and Allen, 2007b; Uchiyama et al., 2010). However, Chun and Suh (2017) have shown that the wave-current interaction term in the surface wave stress was attributed to the parabolic profile of longshore currents, and then reproduced the profile of longshore currents in DUCK94. In order to see the parabolic profile of longshore currents in other cases, Chun and Suh's (2017) nearshore current model has been applied to Hamilton et al.'s (2001) laboratory experiment in the present study. Then the numerical results were compared with the measurements including the vertical profiles of longshore currents and undertow.

Combined effect of wave and current in rough bed free surface flow

In this paper, detailed experimental results are reported to study the effect of the surface wave of different frequencies on turbulent characteristics of flow over a regular array of cubical roughness. The velocity time series of current-only and combined wave-current flow is analyzed to obtain the distribution of first and the second order turbulence statistics, turbulent kinetic energy production, turbulent dissipation and kinetic energy fluxes at a fixed Reynolds number. To highlight the changes due to combined wave-current flow, a comparative study was made between the velocity profiles for current-only flow and those measured for combined wave-current flow. As expected, the rough profiles are shifted downwards with the amount equivalent to the roughness function (ΔU+), which was obtained directly from mean velocity profiles. Further, the thickness of turbulent boundary layer increases with the superposition of surface wave compared to current-only flow. Particular attention is also given to understand the behavior of kinetic energy flux to explicitly account for turbulent momentum transport characteristics over roughness under wave-current interactions.

Waves and Currents at a River Mouth: The Role of Macrovortices, Sub-Grid Turbulence and Seabed Friction

Numerical experiments of wave-current interaction have been performed to investigate the evolution and dissipation of horizontal large-scale vortical structures generated by differential wave breaking and current shearing at river mouths. Specific focus is on the role played by turbulence of scales smaller than the water depth and by seabed friction on the dissipation of the mentioned macrovortices. The analysis reveals two regions of turbulence generation: at the river mouth, and along the curved seaward boundary of the shoal. In the latter zone, macrovortices are formed due to differential wave breaking induced by the sudden variation in water depth and enhanced by opposing currents which favour wave steepening. Such vortices are then advected towards the shore. Among the dissipative mechanisms, dissipation induced by seabed friction is deemed dominant, in particular in the most shallow waters of the shoal. Sub-grid turbulence dissipation, conversely, is more efficient offshore, although exerting some effect also over the shoal when supported by the continuous action of waves.

Reprint of Mechanisms of maintaining high suspended sediment concentration over tide-dominated offshore shoals in the southern Yellow Sea

An understanding of the dynamics and behaviors of suspended sediments is vital in analysis of morphological, environmental, and ecological processes occurring in coastal marine environments. To study the mechanisms of maintaining high suspended sediment concentrations (SSCs) on a tide-dominated offshore shoal, we measured water depths, current velocities, SSCs, wave parameters and bottom sediment compositions in the southern Yellow Sea. These data were then used to calculate bottom shear stresses generated by currents (τc), waves (τw), and wave–current interactions (τcw). SSCs time series exhibited strong quarter-diurnal peaks during spring tides, in contrast to the semidiurnal signal during neap tides. A Fourier analysis showed that suspended sediment variations within tidal cycles was mainly controlled by resuspension in most stations. There existed relatively stable background SSCs (maintaining high SSCs among tidal cycles) values at all four stations during both windy (wind speed > 9.0 m/s) and normal weather conditions (wind speed < 3.0 m/s). The background SSCs had strong relationship with spring/neap-averaged τcw, indicating background SSCs were mainly controlled by mean bottom shear stress, with a minimum value of 0.21 N/m2. On account of the strong tidal currents, background SSCs of spring tides were greater than that of neap tides. In addition, on the base of wavelet, statistics analyses and turbulence dissipation parameter, background SSCs during slack tide in the study area may be maintained by intermittent turbulence events induced by a combined tidal current and wave action.

The influences of Doppler shift on the wave dissipation and soil responses over the porous medium

ABSTRACTThe influences combined the porous seabed and the uniform current on the energy dissipation and the soil responses in the wave–current interaction over the ideal porous seabed are presented in this paper by using the 1D linear wave theory and the linearized porous flow. The relative wave damping rate can be numerically determined by using the complex dispersion relationship. The influences of Doppler shift and the thickness of porous seabed on the wave damping rate, the pore water pressure and its phase shift are discussed, respectively. In addition, the differences using numerous common porous flow model is also compared. Present results find that the energy dissipation is affected by the Doppler shift because the soil responses and the discharge velocity is changed due to the current induced the adjustment of wavenumber or the wavelength. In the case of following current, the interfacial vertical velocity is decreased with the increase of the current velocity. On the other hand, before reaching up the kinematic limit, the magnitude of interfacial vertical velocity is proportional to the flow velocity in the cases of opposing current. Respectively, clarifying the relative importance of the Doppler shift and the thickness of porous media on the energy loss and the soil responses are found that the influence of the thickness of the porous seabed on the energy dissipation has better efficiency. Relative to the thickness of the permeable seabed, the flow velocities and its direction is the important factor on calculating the soil responses.

Estimation of oceanic subsurface mixing under a severe cyclonic storm using a coupled atmosphere–ocean–wave model

Abstract. A coupled atmosphere–ocean–wave model was used to examine mixing in the upper-oceanic layers under the influence of a very severe cyclonic storm Phailin over the Bay of Bengal (BoB) during 10–14 October 2013. The coupled model was found to improve the sea surface temperature over the uncoupled model. Model simulations highlight the prominent role of cyclone-induced near-inertial oscillations in subsurface mixing up to the thermocline depth. The inertial mixing introduced by the cyclone played a central role in the deepening of the thermocline and mixed layer depth by 40 and 15 m, respectively. For the first time over the BoB, a detailed analysis of inertial oscillation kinetic energy generation, propagation, and dissipation was carried out using an atmosphere–ocean–wave coupled model during a cyclone. A quantitative estimate of kinetic energy in the oceanic water column, its propagation, and its dissipation mechanisms were explained using the coupled atmosphere–ocean–wave model. The large shear generated by the inertial oscillations was found to overcome the stratification and initiate mixing at the base of the mixed layer. Greater mixing was found at the depths where the eddy kinetic diffusivity was large. The baroclinic current, holding a larger fraction of kinetic energy than the barotropic current, weakened rapidly after the passage of the cyclone. The shear induced by inertial oscillations was found to decrease rapidly with increasing depth below the thermocline. The dampening of the mixing process below the thermocline was explained through the enhanced dissipation rate of turbulent kinetic energy upon approaching the thermocline layer. The wave–current interaction and nonlinear wave–wave interaction were found to affect the process of downward mixing and cause the dissipation of inertial oscillations.

Effects of Wave–Current Interaction on Salt Intrusion During a Typhoon Event in a Highly Stratified Estuary

Wave–current interaction (WCI) is important in modulating hydrodynamics and water mixing in estuaries, and thereby the transport of water-borne materials. However, the effects of WCI on salt transport and salt intrusion in estuaries during storm events have been rarely examined. In the present study, we use a coupled atmosphere–ocean–wave–sediment transport (COAWST) modeling system to investigate the effects of WCI on salt intrusion in the highly stratified Modaomen Estuary during Typhoon Hagupit (2008). The model is validated by the measured wave, water elevation, and surface salinity data, and several diagnostic model experiments are conducted. WCI increases the storm surge by 0.8 m at the peak surge (25% of the total surge height). The wave-breaking-induced momentum flux and the Stokes drift increase the magnitude of the landward flow by 0.3 m s−1 (30% of the total landward flow). In addition, the waves increase water mixing by 2–4 times compared with that without waves. Hence, WCI significantly increases the landward advective salt transport and decreases the steady shear transport. The net effect of the WCI is a significant increase of salt import and salt intrusion during the typhoon event. However, in the aftermath of the storm, the imported salt water is rapidly flushed out by the increased river discharge, and the estuary regains its stratification within one day.

Turbulent oscillatory flow along unidirectional current over square ribs

The objective of this research is to examine the turbulent flow characteristics over a series of square rib elements under the combined action of surface wave and unidirectional current. The velocity data were analyzed to determine the distributions of the mean velocity, turbulent kinetic energy, Reynolds shear stress, and the contribution of burst-sweep cycles. These were used for the characterization of flow over square rib due to the superposition of surface waves of different frequencies and thereby compare the results with the current-only case. Mean velocity profiles over the rib roughness, illustrate the well-known downward shift from the flat surface data. Also, the thickness of turbulent boundary layer increases with the superposition of surface wave when compared to current-only flow. Particular attention is also given to understand the behaviour of higher-order moments to explicitly account for turbulent momentum transport characteristics over rib roughness under wave-current interactions.

Steady solution of solitary wave and linear shear current interaction

• Solitary wave in the presence of a linear shear background current is studied. • The wave profile, wave speed, velocity field are studied. • The horizontal velocity under the wave crest is presented. The steady solution of a solitary wave propagating in the presence of a linear shear background current is investigated by the Green–Naghdi (GN) equations. The steady solution is obtained by use of the Newton–Raphson method. Three aspects are investigated; they are the wave speed, wave profile and velocity field. The converged GN results are compared with results from the literature. It is found that for the opposing-current case of the solitary wave with a small amplitude, the results of the GN equations match results from the literature well, while for the solitary wave with a large amplitude, results from the literature are seen to be not as accurate. In the following-current case, though the amplitude of the solitary wave is small, the GN results are shown to be accurate. The velocity along the water column at the wave crest and the velocity field for different cases are calculated by the GN equations. The results of the GN equations show obvious differences when compared with the results obtained by superposing the no-current results and linear shear current linearly. We find that for the same current strength, the vortex is stronger for the steep solitary-wave case than that for the small solitary-wave case.

Higher order turbulent flow characteristics of oscillatory flow over a wall-mounted obstacle

The paper presents an experimental study in a laboratory flume to investigate the combined wave–current flow over a wall-mounted cubic obstacle. Detailed velocity data were collected using three-dimensional (3D) micro-acoustic Doppler velocimeter from upstream to downstream of the cube along the centerline of the flume. This study examines the spectra, co-spectra, and turbulence kinetic energy flux analysis under the influence of cube in the turbulent boundary layer. It is observed that stream-wise spectral and co-spectral energy distributions vary with the addition of surface wave. Particular attention is also given to understand the behavior of higher order moments to explicitly account for turbulent momentum transport characteristics over wall-mounted cube under wave–current interactions.

Flow fields and particle trajectories beneath a tidal bore: A numerical study

Tidal bores may appear in some estuaries when the tides quickly reach a high level. This phenomenon is rare but has a strong impact during its short duration: i.e. the river bed is significantly eroded and sediments are then transported. In this paper, the trajectories of suspended particles induced by this flow are numerically studied. Four undular bores with Froude numbers between 1.1 and 1.2 are studied. Despite similar Froude numbers, various initial flow conditions were selected to produce or not an inversion of the flow direction during the bore passage. The particle trajectories associated with each distinct flow configuration are presented and analyzed. These trajectories, estimated by solving the Maxey-Riley equation, appear to be very different even though the Froude numbers of flows are similar. These observations are important because the Froude number is often used to characterize a tidal bore as it describes well the free surface, however, it cannot describe the sediment transport. Finally, Chen's model of wave-current interactions is adapted to fit the cases studied and is applied to the four bores simulated. The results highlight that this latter model can reproduce the observed trajectories and dissociate their different components. From this model, it is shown that the inertial and Basset history effects can be neglected compared to the gravity and flow entrainment effects due to the viscous drag when one wants to determine the long-term trajectories of suspended particles.

FVCOM one-way and two-way nesting using ESMF: Development and validation

Built on the Earth System Modeling Framework (ESMF), the one-way and two-way nesting methods were implemented into the unstructured-grid Finite-Volume Community Ocean Model (FVCOM). These methods help utilize the unstructured-grid multi-domain nesting of FVCOM with an aim at resolving the multi-scale physical and ecosystem processes. A detail of procedures on implementing FVCOM into ESMF was described. The experiments were made to validate and evaluate the performance of the nested-grid FVCOM system. The first was made for a wave-current interaction case with a two-domain nesting with an emphasis on qualifying a critical need of nesting to resolve a high-resolution feature near the coast and harbor with little loss in computational efficiency. The second was conducted for the pseudo river plume cases to examine the differences in the model-simulated salinity between one-way and two-way nesting approaches and evaluate the performance of mass conservative two-way nesting method. The third was carried out for the river plume case in the realistic geometric domain in Mass Bay, supporting the importance for having the two-way nesting for coastal-estuarine integrated modeling. The nesting method described in this paper has been used in the Northeast Coastal Ocean Forecast System (NECOFS)-a global-regional-coastal nesting FVCOM system that has been placed into the end-to-end forecast and hindcast operations since 2007.

Longitudinal Pipeline Scour Propagation Induced by Wave-Current Interaction For the South Sumatra-West Java Submarine Pipeline

Scouring process around subsea pipelines could reduce the soil bearing capacity which affected to the pipe stability. Scouring initial process against time should be known to discover scouring propagation. This paper aims to analyze the time scale calculation of 32 inch diameter in-trench pipe, until meet the maximum-scouring-depth stage. Embedment (e/D) variation is given to know the impact to the scour propagation. Wave and current condition presented to meet the real condition. Wave orbital particle velocity (Uw) is calculated to obtain the non-dimensional factors (Uc/(Uc+Uw)) and KC. The results showed according to the deeper pipe embedment, it takes longer time to reach the maximum scouring depth.

Linear and Nonlinear Wave-Current Interactions over Constant Water Depth

Linear and Nonlinear Wave-Current Interactions over Constant Water Depth

Do High-Frequency Radars Measure the Wave-Induced Stokes Drift?

ABSTRACTHigh-frequency (HF) radars remotely measure ocean near-surface currents based on the Doppler shift of electromagnetic waves backscattered by surface gravity waves with half the electromagnetic wavelength, called Bragg waves. Since their phase velocity is affected not only by wave–current interactions with vertically sheared mean Eulerian currents but also by wave–wave interactions with all the other waves present at the sea surface, HF radars should measure a quantity related to the Stokes drift in addition to mean Eulerian currents. However, the literature is inconsistent—both theoretically and experimentally—on the specific expression and even on the existence of the Stokes drift contribution to the HF radar measurements. Three different expressions that have been proposed in the literature are reviewed and discussed in light of the relevant published experimental results: 1) the weighted depth-averaged Stokes drift, 2) the filtered surface Stokes drift, and 3) half of the surface Stokes drift. Effective measurement depths for these three expressions are derived for the Phillips wave spectrum. Recent experimental results tend to discard the second expression but are not inconsistent with the first and third expressions. The latter is physically appealing, since it is a quasi-Eulerian quantity that would be measured by a current meter at a fixed horizontal position but allowed to follow the free surface moving vertically up and down with the passage of the waves. A definitive answer will require further experimental investigations.

Numerical solutions of waves-current interactions by generalized finite difference method

In this paper, a meshless numerical wave flume, based on the generalized finite difference method (GFDM), is adopted to accurately and efficiently simulate the interactions of water waves and current. The GFDM, a newly-developed meshless method, is truly free from mesh generation and numerical quadrature. The proposed meshless numerical wave flume is the combination of the GFDM, the second-order Runge–Kutta method, the semi-Lagrangian approach, the sponge layer and the ramping function. The problems of wave-current interactions in flumes with horizontal and inclined bottoms are accurately and stably investigated by the proposed meshless scheme, respectively. The changes of waveform can be obviously found, while the cases of coplanar, opposing and no currents are stably simulated. Besides, the distribution of steady current in the flume with inclined bottom, which is governed by an inverse Cauchy problem, is acquired by the GFDM in a stable manner. Numerical results of wave-current interactions are compared with other solutions to verify the accuracy of the proposed meshless scheme. Additionally, different parameters of the proposed meshless numerical scheme are examined to validate the consistency and stability of the proposed numerical wave flume for solutions of wave-current interactions.

Wave current interaction: Effect on force prediction for fixed offshore structures

MetOcean conditions in the South China Sea (SCS) indicates that unlike other locations such as the North Sea, the magnitude of the currents can be relatively large. In addition, these currents are strongly sheared. The present study focused on the typical design problem of calculating the ultimate base shear and overturning moments for slender fixed structureswiththe inclusion of the interaction between the currents and the wave field. It has been found that the loads on average can be around 15% larger when this interaction is accounted for in the calculation of the loads, highlighting the importance. In addition, the level of these amplifications were found to be dependent on the sea state steepness and the relative water depth. While no clear trend was found (changed case by case) in the present work, incorporating the vertical structure of the current was found to change the pattern of the amplification of the loads.