NH5.2

Despite several strong hypotheses on how rogue waves can be generated in idealized conditions, the real-world causes of these waves are still largely unknown. We credit this to insufficient amounts of observational data and a missing robust probabilistic framework to analyze the available data.

We address these issues by processing over 1 billion wave measurements from offshore buoys and organizing them into a comprehensive catalogue. Through a robust, machine-learning driven analysis, we then identify several characteristic sea conditions that lead to significantly higher risks to encounter a rogue wave. This yields quantitative evidence on the relative importance of the underlying physical mechanisms.

Specifically, we find that by far the most important factor is crest-trough correlation, a parameter related to spectral bandwidth, with other parameters acting as minor corrections. This has profound implications on the nature of "everyday" rogue waves, and suggests a path towards a more reliable extreme wave forecast.

How to cite: Häfner, D., Gemmrich, J., and Jochum, M.: Real-world rogue wave probabilities, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1189, https://doi.org/10.5194/egusphere-egu21-1189, 2021.

Extreme sea waves have a great impact on the safety of navigation and coastal areas, however their prediction in operational forecasts is difficult and is generally based on spectral indices. Numerical simulations of the free surface Euler equations can be of notable help in the understanding of the statistical properties of a given sea state, and therefore to establish also the probability of extreme or rare events. In this study we performed phase-resolved simulations of wave spectra obtained from a WaveWatch III hindcast, using a Higher Order Spectral Method. We analyzed a number of sea-states occurred in a precise area of the Mediterranean sea, near the location of a reported accident, with the objective of relating the probability of extreme events with different sea state conditions. Namely, we produced statistics of the wave field, calculating crest distributions and the probability of extreme events from the analysis of long time-series of the surface elevation. The results show a good matching between the distributions of the numerically simulated field and theory, namely Tayfun second- and third- order ones, while the Rayleigh distribution gives a significant underestimate. 

We looked for several kind of correlations between spectral quantities like angular spreading and wave steepness and the probability of occurrence of extreme events, finding an enhanced probability for high mean steepness seas and narrow spectra. It is also evident how the case study of the reported accident was not amongst the most dangerous sea states. Relating the skewness and kurtosis of the surface elevation to the wave steepness helped us to understand the discrepancy between theoretical and numerical distributions.

How to cite: Innocenti, A. and Brandini, C.: Numerical analysis of extreme waves in the North-Western Mediterranean area, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15017, https://doi.org/10.5194/egusphere-egu21-15017, 2021.

The arc of the Lesser Antilles is one of the most quiet subduction zone in the world. In this region, the convergence of the Atlantic and the Caribbean plates is low (few mm/year) and most of the seismicity is an intraplate and crustal seismicity. Among the Mw>7 earthquakes recorded in the historical catalog (1690 near Barbuda, 1843 near Guadeloupe, 1867 near the Virgin Islands, 1839 offshore Martinica, 1969 offshore Dominica, 1974 near Antigua), only the 1839 and 1843 events are suspected to be interplate earthquakes. The 1867 Virgin Island earthquake generated an important tsunami with waves of 10m that devastated the closest islands. A tsunami followed the 1843 earthquake but without much damage. These two events are the only known damaging tsunami in this region, but another older one might be added to the list. Indeed, an increasing number of tsunami deposits have been identified in the recent years on several islands of the arc, all of them being around 500 years old (~1450 AD). These deposits are all located in the northern segment of the arc, between Antigua and Puerto-Rico, in Anegada, St-Thomas (Virgin Islands), Anguilla and Scrub islands. There is unfortunately no record and no testimonies of an extreme event at that time.

The northern segment of the arc is particularly complex because located at the transition between the Greater Antilles and the Lesser Antilles. It is crossed by the Anegada Passage, a series of faults and basins cutting through the arc, which defines the limit between the Puerto-Rico micro-plate and the Caribbean plate. This passage and the numerous intra-arc fault systems present between the islands are active and likely compensate for the plates motion. The very low slip deficit detected with GPS measurements at the subduction contacts of Puerto-Rico and the Lesser Antilles indicates that the interface from Guadeloupe to Puerto-Rico can be considered as totally uncoupled or holding the characteristics of a very long seismic cycle. A tsunami generated by an extreme event 500 years ago in this region could be related to intra-arc, outer-rise, intraplate or interface fault rupture. The identification of the source would enable a better understanding of the seismic cycle and the dynamic of this part of the arc.

This study lists and set models of all the potential faults that could trigger an earthquake in the area encompassing the three islands : Anguilla, Anegada and StThomas. We have created high-resolution bathymetric grids and performed tsunami simulations for each fault model. We uses run-up models to compare the simulated wave heights and run-up distance to all the deposits heights and positions. The magnitudes of our fault models range between 7 and 9, but very few of them generate a strong enough tsunami to match the observed deposits.

How to cite: Cordrie, L., Gailler, A., and Feuillet, N.: Source identification of Middle Age extreme event deposits in the Lesser Antilles using forward numerical modeling of tsunami, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10908, https://doi.org/10.5194/egusphere-egu21-10908, 2021.

(manuscript accepted into Applied Ocean Research https://www.researchgate.net/publication/344786014)

Abstract

Nearly four decades have elapsed since the first efforts to obtain a realistic narrow-banded model for extreme wave crests and heights were made, resulting in a couple of dozen different exceeding probability distributions. These models reflect results of numerical simulations and storm records measured from oil platforms, buoys, and more recently, satellite data. Nevertheless, no consensus has been achieved in either deterministic or operational approaches. Typically, distributions found in the literature analyze a very large set of waves with large variations in sea-state parameters while neglecting homogeneous smaller samples, such that we lack a suitable definition for the sample size and homogeneity of sea variables, also known as sampling variability (Bitner-Gregersen et al., 2020). Naturally, a possible consequence of such sample size inconsistency is the apparent disagreement between several studies regarding the prediction of rogue wave occurrence, as some studies can report less rogue wave heights while others report more rogue waves or the same statistics predicted by Longuet-Higgins (1952), sometimes a combination of the three in the very same study (Stansell, 2004; Cherneva et al., 2005). In this direction, we have obtained a dimensionless parameter capable of measuring how large the deviations in sea state variables can be so that accuracy in wave statistics is preserved.  In particular, we have defined which samples are too heterogeneous to create an accurate description of the uneven distribution of rogue wave likelihood among different storms (Stansell, 2004). Though the literature is rich in physical bounds for single waves, here we describe empirical physical limits for the ensemble of waves (such as the significant steepness) devised to bound these variables within established and prospective wave distributions. Furthermore, this work supplies a combination of sea state parameters that provide guidance on the influence of sea states influence on rogue wave occurrence. Based on these empirical limits, we conjecture a mathematical model for the dependence of the expected maximum of normalized wave heights and crests on the sea state parameters, thus explaining the uneven distribution of rogue wave likelihood among different storms collected by infrared laser altimeters of the North Alwyn oil platform discussed in Stansell (2004). Finally, we demonstrate that for heights and crests beyond 90% of their thresholds (H>2H_1/3 for heights), the exceeding probability becomes stratified, i.e. they resemble layers of probability curves according to each sea state, suggesting the existence of a dynamical definition for rogue waves rather than purely statistical.

References

Bitner-Gregersen, E. M., Gramstad, O., Magnusson, A., Malila, M., 2020. Challenges in description of nonlinear waves due to sampling variability. J. Mar. Sci. Eng. 8, 279.

Longuet-Higgins, M., 1952. On the statistical distribution of the heights of sea waves. Journal of Marine Research 11, 245–265.

Stansell, P., 2004. Distribution of freak wave heights measured in the north sea. Appl. Ocean Res. 26, 35–48.

Cherneva, Z., Petrova, P., Andreeva, N., Guedes Soares, C., 2005. Probability distributions of peaks, troughs and heights of wind waves measured in the black sea coastal zone. Coastal Engineering 52, 599–615.

How to cite: Mendes, S., Scotti, A., and Stansell, P.: On the physical constraints for the exceeding probability of deep water rogue waves, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3961, https://doi.org/10.5194/egusphere-egu21-3961, 2021.

Long-living coherent wave patterns embedded into the irregular wave fields are studied using the data of extensive numerical simulations of the Euler equations in deep water. The distributions of the rogue wave lifetimes according to the numerical simulations of JONSWAP waves with narrow and broad angle spectra are discussed. The observation of a wave group persisting for more than 200 periods in the direct numerical simulation of nonlinear unidirectional irregular water waves is discussed. Through solution of the associated scattering problem for the nonlinear Schrodinger equation, the persisting group is identified as the intense envelope soliton with remarkably stable parameters. Most of extreme waves occur on top of this group, resulting in higher and longer rogue wave events. It is shown that the persisting wave structure survives under the conditions of directional waves with moderate spread of directions. The survivability of coherent wave patterns is expected to further increase when the waves are guided by currents or the topography.

The research is supported by the RSF grant No. 19-12-00253; the study of trapped waves is performed for the RFBR grant No. 21-55-15008.

How to cite: Slunyaev, A. and Kokorina, A.: Long-living coherent patterns in the fields of irregular waves in deep water, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1768, https://doi.org/10.5194/egusphere-egu21-1768, 2021.

               The work presents the results of studying the bound coherent structures propagating on the free surface of ideal incompressible fluid of infinite depth. Examples of such structures are bi-solitons which are exact solutions of the known approximate model for deep water waves — the nonlinear Schrödinger equation (NLSE). Recently, when studying multiple breathers collisions, the occurrence of such objects was found in a more accurate model of the supercompact equation for unidirectional water waves [1]. The aim of this work is obtaining and further studying such structures with different parameters in the supercompact equation and in the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. The algorithm used for finding the bound coherent objects was similar to the one described in [2]. As the initial conditions for obtaining such structures in the framework of the above models, the NLSE bi-soliton solutions were used, as well as two single breathers numerically found by the Petviashvili method and placed in a same point of the computational domain. During the evolution calculation the initial structures emitted incoherent waves which were filtered at the boundaries of the domain using the damping procedure. It is shown that after switching off the filtering of radiation, periodically oscillating coherent objects remain on the surface of the liquid, propagate stably during one hundred thousand characteristic wave periods and do not lose energy. The profiles of such structures at different parameters are compared.

This work was supported by RSF grant 19-72-30028 and RFBR grant 20-31-90093.

[1] Kachulin D., Dyachenko A., Dremov S. Multiple Soliton Interactions on the Surface of Deep Water //Fluids. – 2020. – Т. 5. – №. 2. – С. 65.

[2] Dyachenko A. I., Zakharov V. E. On the formation of freak waves on the surface of deep water //JETP letters. – 2008. – Т. 88. – №. 5. – С. 307.

How to cite: Dremov, S., Kachulin, D., and Dyachenko, A.: Bound Coherent Structures Propagating on the Free Surface of Deep Water, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9833, https://doi.org/10.5194/egusphere-egu21-9833, 2021.

Some rock coasts around the world feature very steep slopes immediately adjacent to the shore. If surface waves propagate on such a steep bottom slope, they experience only slight amplification until very close to shore. In this situation, unexpectedly large wave events may occur near the shore. We combine insight from solutions of a simplified mathematical model with statistical analysis and with observations at the Norwegian coast to conclude that even under moderate wave conditions, very large run-up can occur at the shore.

M. Bjørnestad and H. Kalisch, “Extreme wave runup on a steep coastal profile,” AIP Advances 10, 105205 (2020)

How to cite: Kalisch, H., Bjørnestad, M., Roeber, V., and Lagona, F.: Extreme wave run-up on steep rock coasts, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4470, https://doi.org/10.5194/egusphere-egu21-4470, 2021.

Extreme waves events, also referred to as rogue waves, are known to appear in deep-water conditions as well as nearshore zones. The formation of large-amplitude waves in offshore areas has been well-documented and intensively studied in the last decades. On the other hand, wave processes near the coastlines are known to be dominated by wave reflections, which have a significant influence on the incident waves. This experimental study aims to improve understanding of rogue wave formation mechanisms and statistics when waves reflections are at play. To tackle this, several JONSWAP wave trains have been generated in a water wave flume wave while varying the artificial beach inclination to allow several wave reflection conditions. The data collected near the beach confirms an increased formation of extreme waves and attests the decrease of kurtosis with the increase of the beach inclination. Numerical simulations, based on weakly nonlinear wave evolution models, show a very good agreement with the laboratory experiments. 

How to cite: Chabchoub, A., He, Y., Vila-Concejo, A., and Babanin, A.: Experiments and simulations on extreme waves near reflective beaches, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15493, https://doi.org/10.5194/egusphere-egu21-15493, 2021.

Abrupt depth transitions have recently been identified as potential causes of `rogue' or extreme ocean waves. When stationary and (close-to) normally distributed waves travel into shallower water over an abrupt depth transition, distinct spatially localized peaks in the probability of extreme waves occur. These peaks have been predicted numerically, observed experimentally, but not explained theoretically. Providing this theoretical explanation using a leading-order-physics-based statistical model, we show the peaks arise from the interaction between linear free and second-order bound waves, also present in the absence of the abrupt depth transition, and new second-order free waves generated due to the abrupt depth transition.

How to cite: van den Bremer, T., Li, Y., Draycott, S., Zheng, Y., Lin, Z., and Adcock, T.: Why rogue waves occur atop abrupt depth transitions, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10645, https://doi.org/10.5194/egusphere-egu21-10645, 2021.

Non-uniform bathymetry may modify the wave statistics for both surface elevation and velocity field.
Laboratory evidence reported by Trulsen et al. (2012) shows that for a relatively long unidirectional
waves propagating over a sloping bottom, from deep to shallower water, there can be a local maximum
of kurtosis and skewness in surface elevation near the edge of the shallower side of the slope. Recent
laboratory experiments of long-crested irregular waves propagating over a shoal by Trulsen et al. (2020)
reported that the kurtosis of horizontal velocity field have different behaviour from the kurtosis of surface
elevation where the local maximum of kurtosis in surface elevation and horizontal velocity occur at
different location.
In present work, we utilize numerical simulation to study the evolution of skewness and kurtosis for
irregular waves propagating over a three-dimensional varying bathymetry. Numerical simulations are
based on High Order Spectral Method (HOSM) for variable depth as described in Gouin et al. (2017)
for wave evolution and Variational Boussinesq model (VBM) as described in Lawrence et al. (2021) for
velocity field calculation.

References

GOUIN, M., DUCROZET, G. & FERRANT, P. 2017 Propagation of 3D nonlinear waves over an elliptical
mound with a High-Order Spectral method. Eur. J. Mech. B Fluids 63, 9–24.
LAWRENCE, C., GRAMSTAD, O. & TRULSEN, K. 2021 Variational Boussinesq model for kinematics
calculation of surface gravity waves over bathymetry. Wave Motion 100, 102665.
TRULSEN, K., RAUSTØL, A., JORDE, S. & RYE, L. 2020 Extreme wave statistics of long-crested
irregular waves over a shoal. J. Fluid Mech. 882, R2.
TRULSEN, K., ZENG, H. & GRAMSTAD, O. 2012 Laboratory evidence of freak waves provoked by
non-uniform bathymetry. Phys. Fluids 24, 097101.

How to cite: Lawrence, C., Trulsen, K., and Gramstad, O.: Extreme wave statistics of random waves propagating over a 3D varying bathymetry, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9261, https://doi.org/10.5194/egusphere-egu21-9261, 2021.

In this study, we investigate the rogue-wave-type phenomena in the physical systems described by the Korteweg-de Vries (KdV)-like equation in the form $ u_t + [u^m \sgn{u}]_x + u_{xxx} = 0 $ with the arbitrary real coefficient $m>0$. The periodic waves (sinusoidal or cnoidal) described by this equation have been shown to suffer from the modulational instability if $m \ge 3$; the modulational growth results in the formation of rogue waves similar to the Peregrine, Kuznetsov-Ma or Akhmediev breathers known for the nonlinear Schrodinger equation. In this work we focus on the rogue wave occurrence in ensembles of soliton-type waves. First of all, the characteristics of the solitary waves are investigated depending on the power $m$. The existence of solitary waves with exponential tails, as well as algebraic solitons and compactons has been shown for different ranges of the parameter $m$ values. Their energetic stability is discussed. Two solitary wave/breathers interactions are studied as elementary acts of the soliton/breather turbulence. It is demonstrated that the property of attracting solitons/breathers is a necessity condition for the formation of rogue waves. Rigorous results are obtained for the integrable versions of the KdV-type equations. Series of numerical simulations of the rogue wave generation has been conducted for different values of $m$. The obtained results are applied to the problems of surface and internal waves in the ocean, and to elastic waves in the solid medium.

The research is supported by the RNF grant 19-12-00253.

How to cite: Pelinovsky, E., Kokorina, A., Slunyaev, A., Talipova, T., Didenkulova, E., Tarasova, T., and Pelinovsky, D.: Rogue waves in the KdV-type models, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1641, https://doi.org/10.5194/egusphere-egu21-1641, 2021.

The propagation of nonlinear waves is well-described by a number of integrable models leading to the concept of the scattering data also known as the nonlinear Fourier spectrum. Here we investigate the fundamental problem of the nonlinear wavefield scattering data corrections in response to a perturbation of initial condition using inverse scattering transform theory. We present a complete theoretical linear perturbation framework to evaluate first-order corrections of the full set of the scattering data within the integrable one-dimensional focusing nonlinear Schrodinger (NLSE) equation, see our recent preprint [1]. The general scattering data portrait reveals nonlinear coherent structures - solitons - playing the key role in the wavefield evolution. Applying the developed theory to a classic box-shaped wavefield we solve the derived equations analytically for a single Fourier mode acting as a perturbation to the initial condition, thus, leading to the sensitivity closed-form expressions for basic soliton characteristics, i.e. the amplitude, velocity, phase and its position. With the appropriate statistical averaging we model the soliton noise-induced effects resulting in compact relations for standard deviations of soliton parameters. Relying on a concept of a virtual soliton eigenvalue we derive the probability of a soliton emergence or the opposite due to noise and illustrate these theoretical predictions with direct numerical simulations of the NLSE evolution. Note that the evolution of the box field within the NLSE model represents a classical so-called dam-break problem. A wide box-shaped field is unstable to long wave perturbations constituting the phenomena of modulation instability. In conclussion we discuss possible applications of the developed theory to these fundamental problems of physics of nonlinear waves.

The work was supported by Russian Science Foundation grant No. 20-71-00022.

[1] R. Mullyadzhanov and A. Gelash. Solitons in a box-shaped wavefield with noise: perturbation theory and statistics. arXiv preprint arXiv:2008.08874, 2020.

How to cite: Gelash, A. and Mullyadzhanov, R.: Solitons in a box-shaped wavefield with noise: perturbation theory and statistics, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13742, https://doi.org/10.5194/egusphere-egu21-13742, 2021.

The one-dimensional nonlinear Schrodinger equation (NLSE) serves as a universal model of nonlinear wave propagation appearing in different areas of physics. In particular it describes weakly nonlinear wave trains on the surface of deep water and captures up to certain extent the phenomenon of rogue waves formation. The NLSE can be completely integrated using the inverse scattering transform method that allows transformation of the wave field to the so-called scattering data representing a nonlinear analogue of conventional Fourier harmonics. The scattering data for the NLSE can be calculated by solving an auxiliary linear system with the wave field playing the role of potential – the so-called Zakharov-Shabat problem. Here we present a novel efficient approach for numerical computation of scattering data for spatially periodic nonlinear wave fields governed by focusing version of the NLSE. The developed algorithm is based on Fourier-collocation method and provides one an access to full scattering data, that is main eigenvalue spectrum (eigenvalue bands and gaps) and auxiliary spectrum (specific phase parameters of the nonlinear harmonics) of Zakharov-Shabat problem. We verify the developed algorithm using a simple analytic plane wave solution and then demonstrate its efficiency with various examples of large complex nonlinear wave fields exhibiting intricate structure of bands and gaps. Special attention is paid to the case when the wave field is strongly nonlinear and contains solitons which correspond to narrow gaps in the eigenvalue spectrum, see e.g. [1], when numerical computations may become unstable [2]. Finally we discuss applications of the developed approach for analysis of numerical and experimental nonlinear wave fields data.

The work was supported by Russian Science Foundation grant No. 20-71-00022.

[1] A. A. Gelash and D. S. Agafontsev, Physical Review E 98, 042210 (2018).

[2] A. Gelash and R. Mullyadzhanov, Physical Review E 101, 052206 (2020).

How to cite: Mullyadzhanov, I., Mullyadzhanov, R., and Gelash, A.: Efficient Fourier-collocation method for full scattering data of Zakharov-Shabat periodic problem, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1720, https://doi.org/10.5194/egusphere-egu21-1720, 2021.

Similar to the theory of direct scattering transform for nonlinear wave fields containing solitons within the focusing one-dimensional nonlinear Schrödinger equation [1], we revisit the theory associated with the Korteweg–De Vries equation. We study a crucial fundamental property of the scattering problem for multisoliton potentials demonstrating that in many cases position parameters of solitons cannot be identified with standard machine precision arithmetics making solitons in some sense “uncatchable”. Using the dressing method we find the landscape of soliton scattering coefficients in the plane of the complex spectral parameter for multisoliton wave fields truncated within a finite domain, allowing us to capture the nature of such anomalous numerical errors. They depend on the size of the computational domain L leading to a counterintuitive exponential divergence when increasing L in the presence of a small uncertainty in soliton eigenvalues. Then we demonstrate how one of the scattering coefficients loses its analytical properties due to the lack of the wave-field compact support in case of L→∞. Finally, we show that despite this inherent direct scattering transform feature, the wave fields of arbitrary complexity can be reliably analyzed using high-precision arithmetics and high-order algorithms based on the Magnus expansion [2, 3] providing accurate information about soliton amplitudes, velocities, positions and intensity of the radiation. This procedure is robust even in the presence of noise opening broad perspectives in analyzing experimental data on propagation of surface waves on shallow water.

The work is partially funded by Russian Science Foundation grant No 19-79-30075.

[1] Gelash A., Mullyadzhanov R. Anomalous errors of direct scattering transform // Physical Review E 101 (5), 052206, 2020.

[2] Mullyadzhanov R., Gelash A. Direct scattering transform of large wave packets // Optics Letters 44 (21), 5298-5301, 2019.

[3] Gudko A., Gelash A., Mullyadzhanov R. High-order numerical method for scattering data of the Korteweg—De Vries equation // Journal of Physics: Conference Series 1677 (1), 012011, 2020.

How to cite: Gudko, A., Gelash, A., and Mullyadzhanov, R.: High-orders methods and high-precision arithmetics make direct scattering transform for the Korteweg-De Vries equation robust., EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1730, https://doi.org/10.5194/egusphere-egu21-1730, 2021.