Ocean Wave Propagation Research Articles

A transport equation for flexural-gravity wave propagation under a sea ice cover of variable thickness

In the polar regions, ocean wave propagation is affected by the presence of sea ice. In particular, the waves are observed to attenuate exponentially due to scattering and dissipative effects. Here we derive a transport equation and the associated attenuation coefficient for linear ocean wave packets in one horizontal dimension due to scattering only, assuming that the ocean is covered with ice of spatially varying thickness. This thickness variation is assumed to occur at length scales that are comparable to the wavelength but short compared to the observation scale over which the attenuation is measured. We use a multiple scale expansion and a Wigner transform to arrive at the transport equation. We find that the resulting attenuation coefficient generally overestimates the attenuation that we expect to see in a real ice-covered ocean. We argue that this is likely to be due to the one-dimensional nature of our model.

Shallow water models for stratified equatorial flows

Our aim is to study the effect of a continuous prescribed density variation on the propagation of ocean waves. More precisely, we derive KdV-type shallow water model equations for unidirectional flows along the Equator from the full governing equations by taking into account a prescribed but arbitrary depth-dependent density distribution. In contrast to the case of constant density, we obtain for each fixed water depth a different model equation for the horizontal component of the velocity field. We derive explicit formulas for traveling wave solutions of these model equations and perform a detailed analysis of the effect of a given density distribution on the depth-structure of the corresponding traveling waves.

Parametric study of a wave energy converter (Searaser) for Caspian Sea

Over the past decades, different types of energy converters have been invented because wave energy is a renewable energy source with high potential for extraction of considerable clean energy. Many numerical and experimental tests have been conducted to calculate the power generation of ocean waves, and these tests have demonstrated the significance of this energy. In this paper, the hydrodynamic performance of a new energy converter called "Searaser" has been evaluated using numerical simulation to study different aspects of this energy converter. Since previous studies have found ocean wave energy converters excellent for implementation in the Caspian Sea, the aim of this study is to investigate its performance for that sea, so this study presents a numerical simulation of Searaser inside an experimental wave tank using commercial software Flow-3D. To model the motion of the energy converter, Reynolds Averaged Navier-Stokes was coupled with a volume-of-fluid (VOF) model to generate three-dimensional numerical linear propagating waves for solving the fluid field. Grid independency was also carried out to determine the best mesh numbers for the original simulations. Finally, the Searaser hydrodynamic performance was numerically calculated for different wave heights, and some of the most important parameters of point absorbers were captured, including output flow rate in different seasons, extractable wave power, and output power. Accordingly, the obtained results indicate that the output flow rate and the power generation are significantly increased by incremental changes in wave height, and using this type of converter device has potential for practical and profitable use in industrial applications.

Well-posedness and analyticity of solutions to a water wave problem with viscosity

The water wave problem models the free-surface evolution of an ideal fluid under the influence of gravity and surface tension. The governing equations are a central model in the study of open ocean wave propagation, but they possess a surprisingly difficult and subtle well-posedness theory. In this paper we establish the existence and uniqueness of spatially periodic solutions to the water wave equations augmented with physically inspired viscosity suggested in the recent work of Dias et al. (2008) [16]. As we show, this viscosity (which can be arbitrarily weak) not only delivers an enormously simplified well-posedness theory for the governing equations, but also justifies a greatly stabilized numerical scheme for use in studying solutions of the water wave problem.

Fully nonlinear propagation of waves in a uniform current using NURBS numerical wave tank

A two-dimensional Numerical Wave Tank (NWT) is developed to simulate in the time domain fully nonlinear propagation of ocean waves in uniform currents. Fully nonlinear free surface motion is modeled using Mixed Eulerian-Lagrangian (MEL) scheme and Non-Uniform Rational B-Spline (NURBS) formulation. The potential theory and Laplace equation are solved in the Eulerian frame using a high-order formulation of Boundary Elements Method (BEM) at each time step. The distribution of boundary values is defined based on NURBS to discretize the boundary integral equation. The spatial derivatives of the boundary values are computed precisely based on NURBS. Material node approach and fourth-order Runge-Kutta time integration are employed to update the free surface boundary conditions. Propagation of robust nonlinear wave is simulated to examine the accuracy and convergence of the present fully nonlinear numerical procedure. Propagation the nonlinear regular waves in the uniform flows are also studied and the solutions are compared with the theoretical results. Propagation of the irregular nonlinear waves is studied to compare with the analytical solutions. Furthermore, fully nonlinear irregular wave in the uniform currents is simulated.

Ensuring numerical stability of wave propagation by tuning model parameters using genetic algorithms and response surface methods

The effectiveness of a Metamodel-Embedded Evolution Framework for model parameter identification of a Smoothed Particles Hydrodynamic (SPH) solver, called DualSPHysics, is demonstrated when applied to the generation and propagation of progressive ocean waves. DualSPHysics is an open-source code that provides GP-GPU acceleration, allowing for highly refined simulations. The automatic optimization framework combines the global-convergence capabilities of a Multi-Objective Genetic Algorithm (MOGA) with Response Surface Method (RSM) based on a Kriging approximation. The proposed Metamodel-Embedded Evolutionary framework is used to find the set of SPH model parameters that ensures an accurate reproduction of a 2nd order Stokes wave propagating in a numeric flume tank. In order to demonstrate the consistency of the obtained results, the optimum set of parameters found by the framework is finally used to reproduce other 2nd and 3rd order Stokes waves propagating over the same flume tank.

Integrable aspects and rogue wave solution of Sasa–Satsuma equation with variable coefficients in the inhomogeneous fiber

Under investigation with symbolic computation in this paper, is a variable-coefficient Sasa–Satsuma equation (SSE) which can describe the ultra short pulses in optical fiber communications and propagation of deep ocean waves. By virtue of the extended Ablowitz–Kaup–Newell–Segur system, Lax pair for the model is directly constructed. Based on the obtained Lax pair, an auto-Bäcklund transformation is provided, then the explicit one-soliton solution is obtained. Meanwhile, an infinite number of conservation laws in explicit recursion forms are derived to indicate its integrability in the Liouville sense. Furthermore, exact explicit rogue wave (RW) solution is presented by use of a Darboux transformation. In addition to the double-peak structure and an analog of the Peregrine soliton, the RW can exhibit graphically an intriguing twisted rogue-wave (TRW) pair that involve four well-defined zero-amplitude points.

Simulation of breaking waves using the high-order spectral method with laboratory experiments: wave-breaking energy dissipation

We examine the implementation of a wave-breaking mechanism into a nonlinear potential flow solver. The success of the mechanism will be studied by implementing it into the numerical model HOS-NWT, which is a computationally efficient, open source code that solves for the free surface in a numerical wave tank using the high-order spectral (HOS) method. Once the breaking mechanism is validated, it can be implemented into other nonlinear potential flow models. To solve for wave-breaking, first a wave-breaking onset parameter is identified, and then a method for computing wave-breaking associated energy loss is determined. Wave-breaking onset is calculated using a breaking criteria introduced by Barthelemy et al. (J Fluid Mech https://arxiv.org/pdf/1508.06002.pdf , submitted) and validated with the experiments of Saket et al. (J Fluid Mech 811:642–658, 2017). Wave-breaking energy dissipation is calculated by adding a viscous diffusion term computed using an eddy viscosity parameter introduced by Tian et al. (Phys Fluids 20(6): 066,604, 2008, Phys Fluids 24(3), 2012), which is estimated based on the pre-breaking wave geometry. A set of two-dimensional experiments is conducted to validate the implemented wave breaking mechanism at a large scale. Breaking waves are generated by using traditional methods of evolution of focused waves and modulational instability, as well as irregular breaking waves with a range of primary frequencies, providing a wide range of breaking conditions to validate the solver. Furthermore, adjustments are made to the method of application and coefficient of the viscous diffusion term with negligible difference, supporting the robustness of the eddy viscosity parameter. The model is able to accurately predict surface elevation and corresponding frequency/amplitude spectrum, as well as energy dissipation when compared with the experimental measurements. This suggests the model is capable of calculating wave-breaking onset and energy dissipation successfully for a wide range of breaking conditions. The model is also able to successfully calculate the transfer of energy between frequencies due to wave focusing and wave breaking. This study is limited to unidirectional waves but provides a valuable basis for future application of the wave-breaking model to a multidirectional wave field. By including parameters for removing energy due to wave-breaking into a nonlinear potential flow solver, the risk of developing numerical instabilities due to an overturning wave is decreased, thereby increasing the application range of the model, including calculating more extreme sea states. A computationally efficient and accurate model for the generation of a nonlinear random wave field is useful for predicting the dynamic response of offshore vessels and marine renewable energy devices, predicting loads on marine structures, and in the study of open ocean wave generation and propagation in a realistic environment.

Modeling and simulation of ocean wave propagation using lattice Boltzmann method

In this paper, we present on modeling and simulation of ocean wave propagation from the deep sea to the shoreline. This requires high computational cost for simulation with large domain. We propose to couple a 1D shallow water equations (SWE) model with a 2D incompressible Navier-Stokes equations (NSE) model in order to reduce the computational cost. The coupled model is solved using the lattice Boltzmann method (LBM) with the lattice Bhatnagar-Gross-Krook (BGK) scheme. Additionally, a special method is implemented to treat the complex behavior of free surface close to the shoreline. The result shows the coupled model can reduce computational cost significantly compared to the full NSE model.

Linking source region and ocean wave parameters with the observed primary microseismic noise

In previous studies, the contribution of Love waves to the primary microseismic noise field was found to be comparable to those of Rayleigh waves. However, so far only few studies analysed both wave types present in this microseismic noise band, which is known to be generated in shallow water and the theoretical understanding has mainly evolved for Rayleigh waves only. Here, we study the relevance of different source region parameters on the observed primary microseismic noise levels of Love and Rayleigh waves simultaneously. By means of beamforming and correlation of seismic noise amplitudes with ocean wave heights in the period band between 12 and 15 s, we analysed how source areas of both wave types compare with each other around Europe. The generation effectivity in different source regions was compared to ocean wave heights, peak ocean gravity wave propagation direction and bathymetry. Observed Love wave noise amplitudes correlate comparably well with near coastal ocean wave parameters as Rayleigh waves. Some coastal regions serve as especially effective sources for one or the other wave type. These coincide not only with locations of high wave heights but also with complex bathymetry. Further, Rayleigh and Love wave noise amplitudes seem to depend equally on the local ocean wave heights, which is an indication for a coupled variation with swell height during the generation of both wave types. However, the wave-type ratio varies directionally. This observation likely hints towards a spatially varying importance of different source mechanisms or structural influences. Further, the wave-type ratio is modulated depending on peak ocean wave propagation directions which could indicate a variation of different source mechanism strengths but also hints towards an imprint of an effective source radiation pattern. This emphasizes that the inclusion of both wave types may provide more constraints for the understanding of acting generation mechanisms.

Statistical wave climate projections for coastal impact assessments

AbstractGlobal multimodel wave climate projections are obtained at 1.0° × 1.0° scale from 30 Coupled Model Intercomparison Project Phase 5 (CMIP5) global circulation model (GCM) realizations. A semi‐supervised weather‐typing approach based on a characterization of the ocean wave generation areas and the historical wave information from the recent GOW2 database are used to train the statistical model. This framework is also applied to obtain high resolution projections of coastal wave climate and coastal impacts as port operability and coastal flooding. Regional projections are estimated using the collection of weather types at spacing of 1.0°. This assumption is feasible because the predictor is defined based on the wave generation area and the classification is guided by the local wave climate. The assessment of future changes in coastal impacts is based on direct downscaling of indicators defined by empirical formulations (total water level for coastal flooding and number of hours per year with overtopping for port operability). Global multimodel projections of the significant wave height and peak period are consistent with changes obtained in previous studies. Statistical confidence of expected changes is obtained due to the large number of GCMs to construct the ensemble. The proposed methodology is proved to be flexible to project wave climate at different spatial scales. Regional changes of additional variables as wave direction or other statistics can be estimated from the future empirical distribution with extreme values restricted to high percentiles (i.e., 95th, 99th percentiles). The statistical framework can also be applied to evaluate regional coastal impacts integrating changes in storminess and sea level rise.

Implementation of a two-way coupled atmosphere-ocean wave modeling system for assessing air-sea interaction over the Mediterranean Sea

It is generally accepted that the fluid layer surrounding Earth should be considered as a single system at short and longer spatiotemporal scales. The current knowledge on the complex mechanisms of atmosphere-ocean interactions is still insufficient. This translates to the simulation of atmosphere and ocean as a single fully coupled system constructing multi-scale, multi-model integrated modeling systems. In this study, a new two-way coupled atmosphere-ocean wave modeling system is introduced with overarching aim to thoroughly unveil the impact of waves on the sea surface roughness and the atmospheric properties. The newly developed system consists of the Weather Research Forecasting (WRF) model with Chemistry (WRF-Chem) and Hydrology (WRF-Hydro) as the atmospheric component and the Wave model (WAM) as the ocean wave component. WRF and WAM models are coupled using the OASIS Model Coupling Toolkit (OASIS3-MCT) that enables models to communicate and exchange the information required to refine their simulation results. CHAOS (Chemical Hydrological Atmospheric Ocean wave System) has been tested in a high-impact cyclonic system over the Mediterranean Sea employing one-way and two-way coupling simulations to assess the air-sea interactions, currently neglecting the chemical and hydrological capabilities. The encapsulation of the ocean waves in the atmospheric surface layer processes modifies the characteristics of atmospheric flow and determines the ocean wave generation. A remarkable finding is that the coupling of the two systems affects the air-sea momentum, enthalpy and moisture transfer determining the evolution of the cyclonic system. The interactions along the air-sea interface are also reflected in the vertical structure of troposphere and its properties. CHAOS in two-way coupling mode shows an overall improvement of the forecast skill up to 20% over the sea while positively affects the atmospheric predictability over the land.

Wave energy assessment in the central-south coast of Chile

This paper presents an assessment of the wave energy resource in nearshore waters along the central coast of Chile (Lat.:32.5° S to 42.5° S). The assessment is built upon the combined use of hindcast and measured data collected specifically for this goal. Offshore and nearshore data at a number of locations were collected with buoys and ADCPs, with dwell times ranging from 3 up to 12 months. These were used to assess the accuracy of modeled data at the both offshore and nearshore locations. Modeled offshore data comprises three hourly sea states obtained from a third generation ocean wave model, covering the 1989–2013 period, thereby allowing long-term estimates. By using the wave model SWAN, these data was propagated to the nearshore shallow waters to obtain modeled wave climate along the entire section of coast. Validation results indicate good model skill, where both offshore and nearshore results are within 10% of the measured data, with an over prediction of wave power. The long-term wave power estimates show an increase of the median power with increasing latitude, fluctuating between 20 and 35 kW/m in areas near the coast. Monthly and seasonal variability also increase with latitude, with higher energy events present during the winter season. These results are qualitatively consistent with previous assessments in the area, albeit the present results are consistently 5–10 kW/m smaller, which suggests that previous non calibrated assessments may have overpredicted the wave power by about 20%.

Global historical archive of wind waves based on Voluntary Observing Ship data

A new global archive of wind wave characteristics has been developed based on Voluntary Observing Ship (VOS) data for the period of 1888–2015. In addition to the basic meteorological variables, we have derived the records of visually observed heights, periods, and wind sea and swell directions. The main parameters have been supplemented by significant wave height and dominant period estimates, as well as wave geometry characteristics: steepness, wave age, and wavelength. Multistage quality control has been applied to correct or eliminate spurious values. Data are presented as individual records for every month and as original monthly means fields for every parameter. Easy access and use, along with representative data, make the new archive particularly special and applicable in different ways without any additional preprocessing. Visual wave observations assimilated in the new archive can be used to develop global and regional climatologies, estimate extreme wave characteristics and long-term trends in wave climate, verify and compare them with satellite measurements and model analysis, and test the theoretical laws of ocean wave development and propagation.

Processes involved in the second-year warming of the 2015 El Niño event as derived from an intermediate ocean model

The tropical Pacific experienced a sustained warm sea surface condition that started in 2014 and a very strong El Nino event in 2015. One striking feature of this event was the horseshoe-like pattern of positive subsurface thermal anomalies that was sustained in the western-central equatorial Pacific throughout 2014–2015. Observational data and an intermediate ocean model are used to describe the sea surface temperature (SST) evolution during 2014–2015. Emphasis is placed on the processes involved in the 2015 El Nino event and their relationships with SST anomalies, including remote effects associated with the propagation and reflection of oceanic equatorial waves (as indicated in sea level (SL) signals) at the boundaries and local effects of the positive subsurface thermal anomalies. It is demonstrated that the positive subsurface thermal anomaly pattern that was sustained throughout 2014–2015 played an important role in maintaining warm SST anomalies in the equatorial Pacific. Further analyses of the SST budget revealed the dominant processes contributing to SST anomalies during 2014–2015. These analyses provide an improved understanding of the extent to which processes associated with the 2015 El Nino event are consistent with current El Nino and Southern Oscillation theories.

Effect of RANS-based turbulence models on nonlinear wave generation in a two-phase numerical wave tank

Ocean waves are the most important exciting source acting on marine structures such as ships, offshore platforms and wave energy converters. To efficiently design such structures, accurate modelling of these waves is of importance. This paper utilised a two-dimensional numerical wave tank based on the Reynolds-averaged Navier-Stokes (RANS) equations and volume of fluid (VOF) method and a commercial software code to numerically investigate ocean wave generation. Impact of different turbulence models such as standard k-ε, realisable k-ε, shear stress transport (SST) and Reynolds stress models (RSM) on the generated waves were investigated. Experimental wave measurements have been conducted to validate the numerical results. Excessive generation of eddy viscosity can lead to significant damping. Good numerical agreement with both experimental measurements and analytical wave theory was only successfully achieved either with the RSM or implementing artificial turbulence damping at the air-water interface with the SST model.

Wave energy resource assessment for Red Sea

Accurate assessment of wave energy potential has not been done so far in the offshore and nearshore waters of the Red Sea. In this paper, we present an assessment of wave energy resources in the Red Sea using numerical modelling. The wave conditions are simulated for 1979 to 2010 using a third generation ocean wave model, WAVEWATCH-III by forcing with CFSR winds. The model results are validated against in situ measurements in the Red Sea. The simulated wave parameters are used to estimate the wave power in the Red Sea during the 32 years – a reasonable long-term period for accurate assessment. The estimated wave power has been analyzed on a monthly, seasonal and inter-annual basis. The results indicate robust spatial and seasonal variations in mean wave power. Detailed investigations on wave energy potential have been carried out at a number of coastal locations in the Red Sea that consists of the coasts of Saudi Arabia, Yemen, Egypt, Sudan and Eritrea. Inter-annual variability in the mean wave power is also analyzed and discussed.

An ENSO prediction approach based on ocean conditions and ocean–atmosphere coupling

A simple statistical model for the El Nino–Southern Oscillation (ENSO) prediction is derived based on the evolution of the ocean heat condition and the oceanic Kelvin wave propagation associated with westerly wind events (WWEs) and easterly wind surges (EWSs) in the tropical Pacific. The multivariate linear regression model solely relies on the pentad thermocline depth anomaly evolution in 25 days along with the zonal surface wind modulation. It successfully hindcasts all ENSOs except for the 2000/01 La Nina, using the pentad (or monthly) mean tropical atmosphere ocean array data since 1994 with an averaged skill (measured by anomaly correlation) of 0.62 (or 0.67) with a 6-month lead. The exception is mainly due to the long-lasting cold sea surface temperature anomalies in the subtropics resulting from the strong 1998/99 La Nina, even though the tropical warm water volume (WWV) had rebounded and turned phases after 2000. We also note that the hindcast skill is comparable using pentad or monthly mean NCEP global ocean data assimilation system data for the same time period. The hindcast skill of the proposed statistical model is better than that based on the WWV index in terms of the monthly correlation, normalized RMSEs and ENSO occurrences, which suggest that including the evolution of the subsurface ocean temperature anomaly and the WWEs/EWSs in the central tropical Pacific can enhance the ability to predict ENSO. The hindcast skill is also comparable to the predictions using other dynamical and statistical models, indicating that these processes are the keys to ENSO development. The dynamics behind the statistical model are consistent with the physical processes of ENSO development as follows: the tropical WWV resulting from the interannually-varying meridional subtropical cell transport provides a sufficient heat source. When the seasonal phase lock of ocean–atmosphere coupling triggers the positive (negative) zonal wind anomaly in boreal summer and fall, an El Nino (a La Nina) will develop as evidenced by the Kelvin wave propagation. The triggering dynamic may be suppressed or enhanced by the influence of extratropical Pacific sea surface temperature.

A reformulation of the ΛΦ diagram for the prediction of ocean acoustic wave propagation regimes

The ΛΦ diagram was a tool introduced in the late 1970s to predict ocean acoustic fluctuation regimes termed unsaturated, partially saturated, and fully saturated, where internal wave sound-speed fluctuations play a dominant role. The ΛΦ parameters reflect, respectively, the strength of diffraction and the root mean square phase fluctuation along a ray path. New oceanographic knowledge of the small scale part of the internal wave spectrum, and high angle Fresnel zone formulations now allow a more stable and accurate calculation of these parameters. An empirical relation between the variance of log-intensity and ΛΦ provides a more accurate border between the unsaturated regime and stronger fluctuations. The new diagram is consistent with six short-range, deep-water experiments in the Pacific, Atlantic, and Arctic oceans with frequencies ranging from 75 to 16 000 Hz. The utility of the ΛΦ diagram is that it provides one of the few means to inter-compare experiments at different geographic locations, differen...

Effect of RANSbased Turbulence Models on Nonlinear Wave Generation in a TwoPhase Numerical Wave Tank

Ocean waves are the most important exciting source acting on marine structures such as ships, offshore platforms, wave energy converters and wavebreakers. In order to efficiently design the aforementioned structures, accurate modelling of these waves is of importance. In this paper a two dimensional Numerical Wave Tank (NWT) has been established based on the Reynoldsaveraged NavierStokes (RANS) equations for viscous, incompressible fluid and Volume of Fluid (VOF) method and a commercial software code ANSYS FLUENT (Release 15.0) has been used to numerically investigate ocean wave generation. Impact of different turbulence models such as standard k-ɛ, realizable k-ɛ, Shear Stress Transport (SST) and Reynolds Stress Models (RSM) on the generated ocean surface waves were investigated. With all uncertainties associated with various numerical setting aspects, experimental wave measurements over a wide range of wave conditions covering intermediate and deep water regimes have been conducted in a physical wave basin to validate the numerical results. The excessive generation of eddy viscosity resulted from using eddy viscosity turbulence models especially at the free surface interface, leads to a significant unphysical damping on the generated waves. Good numerical agreement with both experimental measurements and analytical wave theory was successfully achieved either with the RSM or implementing artificial turbulence damping at the airwater interface with the SST model.