Long-term measurements of bottom pressure variations obtained in four experimental campaigns near Sakhalin Island (Cape Svobodny) are analyzed. The statistical characteristics of 20-minute records of sea surface displacements reconstructed in the hydrostatic approximation, as well as individual wave parameters, such as wave height, period, and wave asymmetry, are studied. Records with similar meteorological conditions are sorted according to the significant wave height and the average wave period with the purpose to obtain statistically homogeneous data. The probability distributions of wave heights are constructed and compared with the Rayleigh and Glukhovsky distributions. A significant deviation from the theoretical curves in the range of anomalously high waves is demonstrated, which is associated with the records of intense wave groups in the winter season of 2014–2015.

The research is supported by the Russian Science Foundation (Grant No. 22–17-00153).

How to cite: Didenkulova, I., Kokorina, A., Slunyaev, A., Zaytsev, A., Didenkulova, E., Moskvitin, A., Didenkulov, O., and Pelinovsky, E.: Long-term wave measurements and rogue wave events near Sakhalin Island, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-11024, https://doi.org/10.5194/egusphere-egu23-11024, 2023.

It is known that the modulation instability (MI) is a focusing mechanism responsible for the formation of rogue waves (RWs). Such dynamics are initiated from the injection of sidebands, which translates into an amplitude modulation (AM) of the wave field. The nonlinear stage of unstable wave evolution can be described by exact breather solutions of the nonlinear Schrödinger equation (NLSE). In fact, the amplitude modulation of such coherent RW structures is connected to a particular phase-shift seeded in the carrier wave, i.e. a particular form of localized frequency modulation (FM). By seeding only the local FM information of a deterministic breather to a regular wave train, our experiments show that such an FM localization can indeed trigger pure breather-type RW dynamics. Results of an experimental study on identifying spontaneous RWs in a random wave field by isolating the respective FM and AM dynamics will also be discussed. 

How to cite: He, Y., Trillo, S., Chabchoub, A., Witt, A., and Hoffmann, N.: Extreme waves induced by localized frequency and amplitude modulations in a random sea: an experimental study, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-11963, https://doi.org/10.5194/egusphere-egu23-11963, 2023.

Shoaling surface gravity waves is a process that still calls for a thorough understanding of how it enhances rogue wave formation. Though commonly reduced to water waves passing over a step, the influence of the slope steepness on rogue wave enhancement over a shoal has been demonstrated in numerical simulations. We analytically tackle this with non-equilibrium physics of a spatially varying energy density. While the shoal causes an energy density redistribution and enhances rogue wave occurrence due to a decrease in water depth, the slope effect on the exceedance probability can be interpreted as a second redistribution of the wave statistics. In the presence of a strong departure from a zero-mean water level due to a set-down/set-up the potential energy density is affected by a slope-induced correction. In the case of a shoal, such energy disturbance decreases the total potential energy due to a set-down as compared to linear homogeneous waves, thereby increasing the effect of the energy redistribution. Conversely, a set-up induced by wave-breaking would cause the potential energy density to increase, and so we would observe a decrease in the exceedance probability.

Increasing the slope increases the amplification of rogue wave probability until this amplification saturates at steep slopes. The response of the set-down to the steep slope transition past the saturation point is slower than the depth transition itself, because the effect of lowering the mean water level over the slope balances the pace of the depth transition itself. In contrast, a larger down slope of a subsequent de-shoal zone leads to a stronger decrease in the rogue wave probability. This is because the faster increase of the set-up due to steeper slopes is not balanced by the depth transition, as the mean depth will increase rather than decrease. Thus, a strong asymmetry between shoaling and de-shoaling zones develops. We show that models based on a step can effectively describe the physics of steep finite slopes owing to the saturation of the rogue wave amplification at steep slopes.

Our framework poses a clear unifying picture for wave statistics and energetics transitioning from deep to shallow waters. Waves propagating in deep water will not have their energy affected by the slope and tend to keep a constant rogue wave probability, while in intermediate water the wave energy density will be redistributed due to depth effects on the steepness, vertical asymmetry, and mean water level, ultimately increasing rogue wave likelihoods. Finally, in shallow water the effects on steepness and vertical asymmetry still exist, but the quick divergence of the super-harmonics halts the energy redistribution while the set-up inverts the effect of the latter. Therefore, in the absence of any ocean process besides shoaling, we unify within a single physical mechanism the seemingly contradictory observations of Gaussian statistics in deep water, super-Gaussian (i.e. above) in intermediate water and sub-Gaussian (i.e. below) in shallow waters. 

How to cite: Mendes, S. and Kasparian, J.: Slope effect on rogue wave occurrence: saturation at steep shoals and unifying picture, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-8408, https://doi.org/10.5194/egusphere-egu23-8408, 2023.

In this talk we consider the impact of viscosity on the stabilization of spatially periodic breathers (SPBs), related rogue wave activity, and permanent downshift in the framework of a higher order nonlinear Schrodinger (HONLS) model. The Floquet spectral theory of the NLS  equation is used to characterize
the perturbed dynamics in terms of nearby solutions of the NLS equation.
Bands of complex spectrum in the Floquet decomposition of the viscous HONLS data shrink almost to complex points indicating the breakup of the SPB into a
soliton-like structure. Rogue waves in the viscous HONLS flow are found to
typically occur when the spectrum is in a one or more soliton-like  configuration. 
Rogue wave activity in the viscous HONLS is compared with  results  on the emergence of soliton-like rogue waves in a nonlinear damped HONLS model.
Although permanent frequency downshift is observed in both the viscous and nonlinear damped HONLS models, there are important differences in their respective impact on the growth of instabilities.

How to cite: Schober, C.: Viscosity, rogue waves, and permanent downshift in nonlinear Schrodinger models, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-10891, https://doi.org/10.5194/egusphere-egu23-10891, 2023.

Winter roads on frozen lakes are an important part of the transportation infrastructure in several Northern countries. Authorities follow various plans for opening and closing roads, maintaining safety by checking ice thickness and instructing drivers. Many of these plans are based on Gold’s formula which relates the thickness of the ice cover to the allowable load based largely on empirical observations of ice failure or non-failure under various loading conditions.

In the case of moving loads such as motorized vehicles, the speed of the load is an important factor in addition to ice strength considerations. Indeed, experience has shown that under certain conditions of speed, ice thickness and water depth, the deflection under a vehicle travelling on a floating ice sheet may be amplified considerably.

Indeed, it was shown in [1] that a decelerating load can lead to constructive interference of waves which could exceed the critical stress for crack formation. Ice roads are particularly treacherous near the shore as the critical speed gets smaller due to decreasing depth. In addition, due to existing blowouts, traffic may have to be rerouted to avoid broken ice. In the present contribution, we consider the waves created by a load moving in a circular path. Following [2], we show that curved paths may also lead to constructive interference which may be more severe than the waves created by a decelerating load.

[1] Dinvay, E., Kalisch, H. & Părău, E.I. Fully dispersive models for moving loads on ice sheets. J. Fluid Mech. 876, 122–149 (2019).

[2] Johnsen, K., Kalisch, H. and Părău, E.I. Ship wave patterns on floating ice sheets. Scientific Reports, 12, 1-10 (2022).

How to cite: Kalisch, H., Johnsen, K., Dinvay, E., and Parau, E.: Safety aspects of floating ice sheets under moving loads, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-6206, https://doi.org/10.5194/egusphere-egu23-6206, 2023.

A mathematical model of Coupled Envelope Evolution Equations (CEEEs) has been derived by Li (2022) for the propagation of nonlinear surface gravity waves. Different from the High-Order Spectral Method (HOSM) (see, e.g., Dommermuth & Yue 1987; West 1987), this newly derived model proposes to use a new pair of canonical variables introduced in the work as the main unknown parameters in the approximate Hamiltonian dynamic equations for surface gravity waves. The canonical conjugates are the envelope of the velocity potential at the free water surface and the surface displacement. They are parameters which are slowly varying in both space and time, similar to the envelope used in a nonlinear Schrödinger equation (NLSE)-based model (see, Li 2021 among others). In the limiting cases of weakly nonlinear monochromatic and irregular waves, it is shown in Li (2022) that the CEEEs can recover the analytical results of the Stokes wave theory (Fenton 1985) and the semi-analytical framework by Li & Li (2021).  Similar to the HOSM, the new model is based on a perturbation expansion and can account for the physics up to arbitrary order in wave steepness. In contrast, it has a semi-analytical feature as it is analytical for the evolution of linear waves but requires additional numerical implementations when wave nonlinearity is accounted for. The new model is especially suitable for the extremely long-term evolution of surface waves in a very large domain in space, which is more so for waves with a narrower bandwidth. In this work, the CEEEs are explored for the nonlinear evolution of gravity-capillary waves on a finite water depth. The finite water waves in the neighborhood of kh ≈ 1.363 are investigated, where k and h denote the characteristic wavenumber and constant water depth, respectively. The roles of the nonlinear forcing of mean flows due to a moderately steep wave group in extremely large wave events are examined.

Key words: waves/free-surface flow, gravity-capillary waves

References

Dommermuth, D. G & Yue, D. K. P. 1987 A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech. 184, 267–288.

Fenton, J.D. 1985 A fifth-order Stokes theory for steady waves. J. Waterway, Port, Coast. & Ocean Eng. 111 (2), 216–234.

Li, Y. 2022 On coupled envelope evolution equations in the Hamiltonian theory of nonlinear surface gravity waves. submitted to J. Fluid Mech (under review).

Li, Y. & Li, X. 2021 Weakly nonlinear broadband and multidirectional surface waves on an arbitrary depth: A framework, Stokes drift, and particle trajectories. Phys. Fluids 33 (7), 076609.

Li, Y. 2021 Three-dimensional surface gravity waves of a broad bandwidth on deep water. J. Fluid Mech. 926, 1–43.

West, B. J., Brueckner, K A, Janda, R. S., Milder, D M & Milton, R. L. 1987 A new numerical method for surface hydrodynamics. J. Geophys. Res.: Oceans 92 (C11), 11803–11824.

How to cite: Li, Y.: A mathematical model for nonlinear gravity-capillary waves in a large temporal-spatial domain, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-13972, https://doi.org/10.5194/egusphere-egu23-13972, 2023.

We consider measurement data from a surface-following wave buoy in the southern North Sea. The data were collected in a water depth that lies within the range of applicability of the Korteweg-de Vries (KdV) equation. We intend to increase the understanding of nonlinear processes that might be responsible for the increased rogue wave occurrence observed at this site (Teutsch et al., 2020). More specifically, we investigate the role of (potentially “spectral”) solitons identified by the nonlinear Fourier transform (NLFT) for the KdV equation for the occurrence of rogue waves. In a previous study, we identified a connection between the spectral solitons and rogue waves at the considered station. Teutsch et al. (2022) showed that KdV-NLFT spectra containing one exceptionally large outstanding soliton often corresponded to measured time series including a rogue wave. Some of the time series with a large outstanding soliton however did not contain rogue waves. In this study, we investigate if these outliers might correspond to rogue waves at a different location. This is motivated by the fact that the NLFT soliton spectrum does not change under the KdV equation. We therefore propagate the time series without rogue waves, but with an outstanding soliton in the KdV-NLFT spectrum, according to the KdV equation, to investigate the occurrence of rogue waves shortly upstream or downstream of the recorded time series.

References:

Teutsch, I., Weisse, R., Moeller, J., and Krueger, O. (2020): A statistical analysis of rogue waves in the southern North Sea, Natural Hazards and Earth System Sciences, 20, 2665–2680.

Teutsch, I., Brühl, M., Weisse, R., and Wahls, S (2022): Contribution of solitons to enhanced rogue wave occurrence in shallow water: a case study in the southern North Sea. Natural Hazards and Earth System Sciences Discussions, under review.

How to cite: Teutsch, I., Wahls, S., and Weisse, R.: Investigation of Measured Non-Rogue Wave Time Series With Large Outstanding Spectral Solitons, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-12796, https://doi.org/10.5194/egusphere-egu23-12796, 2023.

Using a recently developed second-order theory of  irregular waves on a current varying arbitrarily with depth [1], we study dispersive focussing of wave groups and their dependence on the current profile.  Long-crested wave groups are presumed to propagate obliquely on a flow with non-linear dependence on depth. We investigate the wave surface elevation and wave kinematics of a focused wave group. Nonlinear wave surface elevations vary with the angle between the wave propagation and flow, and it is found that they increase to a maximum where the current increases adversely for larger depth. For wave kinematics, the horizontal wave-induced velocity shows significantly different behaviours due to the presence of shear current.

The development of the highest crest as a function of propagation time is studied for a wave group which linearly focusses at a particular position and time in the absence of shear. The adverse shear causes an increase in maximum height. Exponential and linear depth dependence is compared, and a real, measured shear current [2] is used showing the practical importance of the results.

The results complement our recent study of weakly nonlinear wave statistics in the presence of arbitrary vertical shear, which showed among other observations, a strongly increased probability of rogue waves in the presence of an adverse vertical shear, in accordance with field observations by Zippel and Thomson [2].

[1] Zheng, Z, Li, Y and Ellingsen, S Å 2023 “Statistics of weakly nonlinear waves on currents with strong vertical shear” Phys. Rev. Fluids (accepted, in press)
[2] Zippel, S and Thomson, J 2017 “Surface wave breaking over sheared currents: Observations from the Mouth of the Columbia River J. Geophys. Res.: Oceans 24 127102.

How to cite: Zheng, Z., Li, Y., and Ellingsen, S.: Weakly nonlinear focused wave group on arbitrary shear based on second-order theory, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-13773, https://doi.org/10.5194/egusphere-egu23-13773, 2023.

Fluid motion under water waves includes an Eulerian return flow in the direction opposite to wave propagation that is of importance for accurately modelling the transport of tracers in the ocean like sediments, plastic pollution, oil, etc. The return flow is related to the mean flow, that is to the derivative in space of the zero-harmonic component of the velocity potential φ₀. It turns out that this component is not consistently taken into account in some derivations of the high-order nonlinear Schrödinger equation (HONLS) using the multiscale development at arbitrary depth, which therefore do not correctly reproduce experimental results in the deep-water limit.

We show how to formulate a Neumann problem for φ₀ that can be solved at fourth order in steepness for arbitrary depth. The derivative of such term is thus included in the HONLS in both cases of propagation in time and in space. We compare the results of the simulations obtained using our model to those obtained with previously published fourth-order models without the mean-flow term, to observations and to accurate simulations performed with the high-order spectral method. While our model is equivalent to alternative formulations in intermediate water, it is more accurate in deep water.  Our model therefore provides the first fourth-order NLS relevant for depths ranging from intermediate to deep water.

How to cite: Gomel, A., Montessuit, C., Armaroli, A., Eeltink, D., Chabchoub, A., Kasparian, J., and Brunetti, M.: Mean flow in high-order wave evolution equations at arbitrary depth, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-9054, https://doi.org/10.5194/egusphere-egu23-9054, 2023.

Quantitative assessments of wave-driven run-up and inundation scenarios have been of high interest to coastal residents, engineers, emergency managers, and scientists. Though it is possible to obtain general estimates of wave run-up based on empirical formulae, such approximations are often of limited applicability, especially in areas with complex shorelines and bathymetries. Due to the substantial increase in computing power, numerical models have emerged as reliable and cost-effective tools for nearshore wave assessment. Accurate computation of wave run-up requires the numerical models to account for phase-dependent processes that can pose challenges to the quality and computational complexity of the numerical solution. 

We present the strategic development of a new Boussinesq-type model with the objective of building a reliable tool for operational run-up forecasting systems.  The effort has led to a computer code where multiple fundamental features are optimized for both computational efficiency and accuracy to achieve fast and reliable solutions of nearshore waves. This requires the model to answer several challenges including wave breaking, numerical diffusion, moving boundaries, and computational complexity. To solve for these contradicting requirements, the model relies on a lean numerical structure that supports mass and momentum conservation across discontinuities and long-distance propagation of irregular waves. An eddy viscosity closure approach based on temporally and spatially varying turbulent kinetic energy alleviates the chronic limitation of depth-integrated dispersive solutions to wave breaking. In an attempt to achieve real-time run-up computations over large domains, the new model efficiently uses commodity graphics cards hardware, and targeted grid refinement through locally nested domains.

Finally, the new model has been verified and validated with standard benchmark tests for problems involving commonly encountered nearshore wave processes that are crucial for accurate run-up computations.

How to cite: Mihami, F.-Z. and Roeber, V.: Development of a phase-resolving nearshore wave model for run-up assessment, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-7460, https://doi.org/10.5194/egusphere-egu23-7460, 2023.