Freak wave generation in shallow water
Tatiana TalipovaComptes Rendus de l Académie des Sciences - Series IIB - Mechanics
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
The influence of wind on extreme wave events in shallow water is investigated numerically. A series of numerical simulations using a pressure distribution over the steep crests given by the modified Jeffreys' sheltering theory shows that wind blowing over a strongly modulated wave group due to the dispersive focusing of a chirped long wave packet increases the time duration and maximal amplitude of the extreme wave event. These results are coherent with those obtained within the framework of deep water. However, steep wave events are less unstable to wind perturbation in shallow water than in deep water.
Related papers
Focusing wave group in shallow water in the presence of wind
Discrete and Continuous Dynamical Systems-series B, 2010
The influence of wind on extreme wave events in shallow water is investigated numerically. A series of numerical simulations using a pressure distribution over the steep crests given by the modified Jeffreys' sheltering theory shows that wind blowing over a strongly modulated wave group due to the dispersive focusing of a chirped long wave packet increases the time duration and maximal amplitude of the extreme wave event. These results are coherent with those obtained within the framework of deep water. However, steep wave events are less unstable to wind perturbation in shallow water than in deep water.
ESTIMATION OF FREAK WAVE OCCURRENCE FROM DEEP TO SHALLOW WATER REGIONS
Coastal Engineering Proceedings, 2014
Nonlinear four-wave interactions amplify wave heights of deep-water generating extreme wave such as a freak wave. However, it is not clear the behavior of generated freak waves in deep-water shoaling to shallow water regions. In this study, a series of physical experiments and numerical simulations with several bathymetry configurations were conducted for unidirectional random waves from deep to shallow water regions. The maximum wave heights increase with an increase in kurtosis by third-order nonlinear interactions in deep water regions. The dependence of the kurtosis on the freak wave occurrence is weakened due to second-order nonlinear interactions associated with wave shoaling on the slope. Moreover, it is possible to understand the behavior of the high-order nonlinearity and the freak wave occurrence in shallow water regions if appropriate correction of the insufficient nonlinearity of more than O(ε 2 ) to the standard Boussinesq equation are considered analytically.
Freak waves under the action of wind: experiments and simulations
European Journal of Mechanics - B/Fluids, 2006
The freak wave formation due to the dispersive focusing mechanism is investigated experimentally without wind and in presence of wind. An asymmetric behaviour between the focusing and defocusing stages is found when the wind is blowing over the mechanically generated gravity wave group. This feature corresponds physically to the sustain of the freak wave mechanism on longer periods of time. Furthermore, a weak amplification of the freak wave and a shift in the downstream direction of the point where the waves merge are observed. The experimental results suggest that the Jeffreys' sheltering mechanism could play a key role in the coherence of the group of the freak wave. Hence, the Jeffreys' sheltering theory is introduced in a fully nonlinear model. The results of the numerical simulations confirm that the duration of the freak wave event increases with the wind velocity.
Influence of wind on extreme wave events: experimental and numerical approaches
Journal of Fluid Mechanics, 2008
The influence of wind on extreme wave events is investigated experimentally and numerically. A series of experiments conducted in the Large Air-Sea Interactions Facility (LASIF) shows that a wind blowing over a short wave group due to the dispersive focusing of a longer frequency modulated wave train (chirped wave packet) may increase the time duration of the extreme wave event by delaying the defocusing stage. A detailed analysis of the experimental results suggests that the air flow separation that occurs on the leeward side of the steep crests may sustain longer the maximum of modulation of the focusing-defocusing cycle. Furthermore it is found that the frequency downshifting observed during the formation of the extreme wave event is more important when the wind velocity is larger. The experiments have pointed out that the transfer of momentum and energy is strongly increased during extreme wave events. Two series of numerical simulations have been performed using a pressure distribution over the steep crests given by the Jeffreys'sheltering theory. The first series corresponding to the dispersive focusing confirms the experimental results. The second series that corresponds to extreme wave events due to modulational instability shows that wind sustains steep waves which then evolve into breaking waves. Furthermore, it was shown numerically that during extreme wave events the wind-driven current may play a significant role in their persistence.
Influence of crest and group length on the occurrence of freak waves
Journal of Fluid Mechanics, 2007
A large number of simulations have been performed to reveal how the occurrence of freak waves on deep water depends on the group and crest lengths for fixed steepness. It is found that there is a sharp qualitative transition between short- and long-crested sea, for a crest length of approximately ten wavelengths. For short crest lengths the statistics of freak waves deviates little from Gaussian and their occurrence is independent of group length (or Benjamin–Feir index, BFI). For long crest lengths the statistics of freak waves is strongly non-Gaussian and the group length (or BFI) is a good indicator of increased freak wave activity.
Enhanced extreme wave statistics of irregular waves due to accelerating following current over a submerged bar
Journal of Fluid Mechanics, 2023
We present experimental results of irregular long-crested waves propagating over a submerged trapezoidal bar with the presence of a background current in a wave flume. We investigate the non-equilibrium phenomenon (NEP) induced by significant changes of water depth and mean horizontal flow velocity as the wave trains pass over the bar. Using statistical moments skewness and kurtosis as proxies, we show evidence that an accelerating following current could increase the sea-state non-Gaussianity and enhance both the magnitude and spatial extent of NEP. We also find that below a "saturation relative water depth" 𝑘 𝑝 ℎ 2 ≈ 0.5 (𝑘 𝑝 being the peak wave number in the shallow area of depth ℎ 2 ), although the NEP manifests, the decrease of the relative water depth does not further enhance the maximum skewness and kurtosis over the bar crest. This work highlights the nonlinear physics according to which a following current could provoke higher freak wave risk in coastal areas where the modulation instability plays an insignificant role.
On the characteristics of observed coastal freak waves
Coastal …, 2002
The purpose of this study is to describe the characteristics of occurrence of coastal freak waves and to investigate their statistical and spectral structures. According to Ochi's definition of freak wave, 175 coastal freak waves were obtained from a long-term full scale wave data bank, in which there are more than 4500 wave records. The probability distribution of occurrence of coastal freak waves was investigated. The goodness-of-fit testing shows that the Rayleigh distribution is more appropriate for describing the occurrence probability of coastal freak waves when the ratio of its wave height to the corresponding significant wave height is more than 2.4. However, the occurrence probability of coastal freak waves remains below the Rayleigh distribution. The relationship between coastal freak waves and the related sea states shows that the occurrence possibility of coastal freak waves may significantly increase in the sea of grouping waves or in the wave field of bimodal spectra. Wavelet Transform was applied to the in situ wave records to investigate the energy distribution on the time-frequency domain. It justified the previous conclusions and demonstrated that the wave groups and superposition of the swell and wind wave energy, which occupies 70% of the coastal freak samples, play major roles of inducing the coastal freak waves.
Numerical simulation of freak waves in random sea state
The generation of freak waves in a 2-dimensional random sea state characterized by the JONSWAP spectrum are simulated employing a nonlinear fourth-order Schrödinger equation. The evolution of the freak waves in deep water are analyzed. We investigate the effect of initial wave parameters on kurtosis and occurrence of freak waves. The results show that Benjamin-Feir index (BFI) is an important parameter to identify the presence of instability. The kurtosis presents a similar spatial evolution trend with the occurrence probability of freak waves. Freak waves in a random sea state are more likely to occur for narrow spectrum and small values of significant wave height.
Modeling freak waves from the North Sea
Applied Ocean Research, 2005
Four freak events registered in the North Sea during a storm are presented and studied. The spatial evolution of the freak waves backward and forward wave propagation is simulated within the framework of the Dysthe equation. The lifetimes and travel distances of the freak waves are determined based on the results of the simulations. The wave evolution predicted by the
Wind-wave amplification mechanisms: possible models for steep wave events in finite depth
Natural Hazards and Earth System Science, 2013
We extend the Miles mechanism of wind-wave generation to finite depth. A β-Miles linear growth rate depending on the depth and wind velocity is derived and allows the study of linear growth rates of surface waves from weak to moderate winds in finite depth h. The evolution of β is plotted, for several values of the dispersion parameter kh with k the wave number. For constant depths we find that no matter what the values of wind velocities are, at small enough wave age the β-Miles linear growth rates are in the known deep-water limit. However winds of moderate intensities prevent the waves from growing beyond a critical wave age, which is also constrained by the water depth and is less than the wave age limit of deep water. Depending on wave age and wind velocity, the Jeffreys and Miles mechanisms are compared to determine which of them dominates. A wind-forced nonlinear Schrödinger equation is derived and the Akhmediev, Peregrine and Kuznetsov-Ma breather solutions for weak wind inputs in finite depth h are obtained.
Related topics
Related papers
Nonlinear-dispersive mechanism of the freak wave formation in shallow water
Physica D: Nonlinear Phenomena, 2000
The mechanism of the freak wave formation related to the spatial-temporal focusing is studied within the framework of the Korteweg-de Vries equation. A method to find the wave trains whose evolution leads to the freak wave formation is proposed. It is based on the solution of the Korteweg-de Vries equation with an initial condition corresponding to the expected freak wave. All solutions of this Cauchy problem by the reversal of abscissa represent the possible forms of wave trains which evolve into the freak wave. It is found that freak waves are almost linear waves, and their characteristic Ursell parameter is small. The freak wave formation is possible also from the random wave field and the numerical simulation describes the details of this phenomenon. It is shown that freak waves can be generated not only for specific conditions, but also for relative wide classes of the wave trains. This mechanism explains the rare and short-lived character of the freak wave.
Numerical modelling of nonlinear extreme waves in presence of wind
A numerical wave flume with fully nonlinear free surface boundary conditions is adopted to investigate the temporal characteristics of extreme waves in the presence of wind at various speeds. Incident wave trains are numerically generated by a piston-type wave maker, and the wind-excited pressure is introduced into dynamic boundary conditions using a pressure distribution over steep crests, as defined by Jeffreys' sheltering mechanism. A boundary value problem is solved by a higher-order boundary element method (HOBEM) and a mixed Eulerian-Lagrangian time marching scheme. The proposed model is validated through comparison with published experimental data from a focused wave group. The influence of wind on extreme wave properties, including maximum extreme wave crest, focal position shift, and spectrum evolution, is also studied. To consider the effects of the wind-driven currents on a wave evolution, the simulations assume a uniform current over varying water depth. The results show that wind causes weak increases in the extreme wave crest, and makes the nonlinear energy transfer non-reversible in the focusing and defocusing processes. The numerical results also provide a comparison to demonstrate the shifts at focal points, considering the combined effects of the winds and the wind-driven currents.
On the role of the Jeffreys' sheltering mechanism in sustaining extreme water waves
2006
The effect of the wind on the sustain of extreme water waves is investigated experimentally and numerically. A series of experiments conducted in the Large Air-Sea Interactions Facility (LASIF) showed that a wind blowing over a strongly nonlinear short wave group due to the linear focusing of a modulated wave train may increase the life time of the extreme wave event. The expriments suggested that the air flow separation that occurs on the leeward side of the steep crests may sustain longer the maximum of modulation of the focusing-defocusing cycle. Based on a Boundary-Integral Equation Method and a pressure distribution over the steep crests given by the Jeffreys'sheltering theory, similar numerical simulations have confirmed the experimental results.
On The Birth of Freak Waves Due To The Nonlinear Interaction of Swell and Wind Waves Crossing Each Other With Finite Angle
Lately, strange waves originating from an unknown source even under mild weather conditions have been frequently reported along the coast of South Korea. These waves can be characterized by abnormally high run-up height and unpredictability, and have evoked the imagination of many people. However, how these waves are generated is a very controversial issue within the coastal community of South Korea. In 2006, Shukla numerically showed that extremely high waves of modulating amplitude can be generated when swell and locally generated wind waves cross each other with finite angle, by using a pair of nonlinear cubic Schrodinger Equations. Shukla (2006) also showed that these waves propagate along a line, that evenly dissects the angles formed by the propagating directions of swell and wind waves. Considering that cubic Schrodinger Equations are only applicable for a narrow banded wave train, which is very rare in the ocean field, Shukla (2006)'s work is subject to more severe testing. Based on this rationale, in this study, first we relax the narrow banded assumption, and numerically study the feasibility of the birth of freak waves due to the nonlinear interaction of swell and wind waves crossing each other with finite angle, by using a more robust wave model, the Navier-Stokes equation.
Sea-swell interaction as a mechanism for the generation of freak waves
Physics of Fluids, 2008
The probability of freak waves in an inhomogeneous ocean is studied by integration of Alber's equation. The special phase structure of the inhomogeneous disturbance, required for instability, is provided by bound waves, generated by the quadratic interaction of the stochastic sea with a deterministic, long swell. The probability of freak waves higher than twice the significant wave height increases by a factor of up to 20 compared to the classical value given by Rayleigh's distribution. The probability of exceptionally high freak waves, with height larger than three times the significant wave height, is shown to increase some 30 000-fold compared to that given by the Rayleigh distribution, which renders their encounter feasible.
Generation of two-dimensional steep water waves on finite depth with and without wind
European Journal of Mechanics B-fluids, 2010
This paper reports on a series of numerical simulations designed to investigate the action of wind on steep waves and breaking waves generated through the mechanism of dispersive focusing on finite depth. The dynamics of the wave packet propagating without wind at the free surface are compared to the dynamics of the packet propagating in the presence of wind. Wind is introduced in the numerical wave tank by means of a pressure term, corresponding to the modified Jeffreys' sheltering mechanism. The wind blowing over a strongly modulated wave group due to the dispersive focusing of an initial long wave packet increases the duration and maximal amplitude of the steep wave event. These results are coherent with those obtained within the framework of deep water. However, steep wave events are less unstable to wind perturbation in shallow water than in deep water.
Freak waves in weakly nonlinear unidirectional wave trains over a sloping bottom in shallow water
Physics of Fluids, 2013
Using a Boussinesq model with improved linear dispersion, we show numerical evidence that bottom non-uniformity can provoke significantly increased probability of freak waves as a wave field propagates into shallower water, in agreement with recent experimental results [K. Trulsen, H. Zeng, and O. Gramstad, "Laboratory evidence of freak waves provoked by non-uniform bathymetry," Phys. Fluids 24, 097101 (2012)]. Increased values of skewness, kurtosis, and probability of freak waves can be found on the shallower side of a bottom slope, with a maximum close to the end of the slope. The increased probability of freak waves is typically seen to endure some distance into the shallower domain, before it decreases and reaches a stable value depending on the depth. The maxima of the statistical parameters are observed both in the case where there is a region of constant depth after the slope, and in the case where the uphill slope is immediately followed by a downhill slope. In the case that waves propagate over a slope from shallower to deeper water, however, we do not find any increase in freak wave occurrence.
Statistics of Extreme Waves in Coastal Waters: Large Scale Experiments and Advanced Numerical Simulations
Fluids, 2019
The formation mechanism of extreme waves in the coastal areas is still an open contemporary problem in fluid mechanics and ocean engineering. Previous studies have shown that the transition of water depth from a deeper to a shallower zone increases the occurrence probability of large waves. Indeed, more efforts are required to improve the understanding of extreme wave statistics variations in such conditions. To achieve this goal, large scale experiments of unidirectional irregular waves propagating over a variable bottom profile considering different transition water depths were performed. The validation of two highly nonlinear numerical models was performed for one representative case. The collected data were examined and interpreted by using spectral or bispectral analysis as well as statistical analysis. The higher probability of occurrence of large waves was confirmed by the statistical distributions built from the measured free surface elevation time series as well as by the local maximum values of skewness and kurtosis around the end of the slope. Strong second-order nonlinear effects were highlighted as waves propagate into the shallower region. A significant amount of wave energy was transmitted to low-frequency modes. Based on the experimental data, we conclude that the formation of extreme waves is mainly related to the second-order effect, which is also responsible for the generation of long waves. It is shown that higher-order nonlinearities are negligible in these sets of experiments. Several existing models for wave height distributions were compared and analysed. It appears that the generalised Boccotti's distribution can predict the exceedance of large wave heights with good confidence.
A possible mechanism of generation of extreme waves in shallow water
Eprint Arxiv Nlin 0702052, 2007
We consider a mechanism of generation of huge waves by multi-soliton resonant interactions. A non-stationary wave amplification phenomenon is found in some exact solutions of the Kadomtsev-Petviashvili (KP) equation. The mechanism proposed here explains the character of extreme waves and of those in Tsunami.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.