Anomalous Waves Triggered by Abrupt Depth Changes: Laboratory Experiments and Truncated KdV Statistical Mechanics

Moore, Nicholas J.; Bolles, C. Tyler; Majda, Andrew J.; Qi, Di

doi:10.1007/s00332-020-09649-2

Cited by 23 publications

(20 citation statements)

References 49 publications

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“…Moreover, instead of bound super-harmonics in our model, one could investigate the effect of the nonlinear evolution of interacting free modes. For instance, similar experimental results were interpreted using a statistical matching of Korteweg-De Vries equilibrium states at the depth transition point (Majda et al 2019;Moore et al 2020).…”

Section: Discussionmentioning

confidence: 96%

“…2019; Moore et al. 2020). In retrospect to the ideas in Onorato & Suret (2016), these works obtained a connection between variance and skeweness with the dynamics.…”

Section: Discussionmentioning

confidence: 99%

“…For a step, these bathymetry effects have been described by nonlinear evolution of interacting free modes with a truncation of the Korteweg–De Vries equation (Majda, Moore & Qi 2019; Moore et al. 2020) and as travelling wave packets subject to second-order effects in steepness (Li et al. 2021 a , c ).…”

Section: Introductionmentioning

confidence: 99%

“…Nonlinearities and abrupt depth change lead waves out of equilibrium, deviating from Gaussian statistics. For a step, these bathymetry effects have been described by nonlinear evolution of interacting free modes with a truncation of the Korteweg-De Vries equation (Majda, Moore & Qi 2019;Moore et al 2020) and as travelling wave packets subject to second-order effects in steepness (Li et al 2021a,c). However, wave height probability distributions able to describe the laboratory results of Trulsen et al (2020) are still lacking.…”

Section: Introductionmentioning

confidence: 99%

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Non-homogeneous analysis of rogue wave probability evolution over a shoal

et al. 2022

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Non-equilibrium evolution of wave fields, as occurring over sudden bathymetry variations, can produce rogue seas with anomalous wave statistics. We handle this process by modifying the Rayleigh distribution through the energetics of second-order theory and a non-homogeneous reformulation of the Khintchine theorem. The resulting probability model reproduces the enhanced tail of the probability distribution of unidirectional wave tank experiments. It also describes why the peak of rogue wave probability appears atop the shoal, and explains the influence of depth on variations in peak intensity. Furthermore, we interpret rogue wave likelihoods in finite depth through the $H$ – $\sigma$ diagram, allowing a quick prediction for the effects of rapid depth change apart from the probability distribution.

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Section: Discussionmentioning

confidence: 96%

“…2019; Moore et al. 2020). In retrospect to the ideas in Onorato & Suret (2016), these works obtained a connection between variance and skeweness with the dynamics.…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Non-homogeneous analysis of rogue wave probability evolution over a shoal

et al. 2022

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“…Majda, Moore, and Qi 17 developed a statistical model based on truncated KdV-equation and also confirmed the experimental results in Bolles, Speer, and Moore 14 . Motivated by the statistical model of Majda, Moore, and Qi 17 , Moore et al 18 conducted new experimental measurements and compared with the truncated KdV model in shallow water with abrupt depth changes.…”

Section: Introductionmentioning

confidence: 99%

Statistical properties of wave kinematics in long-crested irregular waves propagating over non-uniform bathymetry

2021

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Experimental and numerical evidence have shown that non-uniform bathymetry may alter significantly the statistical properties of surface elevation in irregular wave fields. The probability of 'rogue' waves is increased near the edge of the upslope as long-crested irregular waves propagate into shallower water. The present paper studies the statistics of wave kinematics in long-crested irregular waves propagating over a shoal with a Monte-Carlo approach. High Order Spectral Method is employed as wave propagation model and Variational Boussinesq Model is employed to calculate wave kinematics. The statistics of horizontal fluid velocity can be different from statistics in surface elevation as the waves propagate over uneven bathymetry. We notice strongly non-Gaussian statistics when the depth changes abruptly in sufficiently shallow water. We find an increase of kurtosis in the horizontal velocity around the downslope area. Furthermore, the effects of the bottom slope with different incoming waves are discussed in terms of kurtosis and skewness. Finally, we investigate the evolution of kurtosis and skewness of the horizontal velocity over a sloping bottom in a deeper regime. The vertical variation of these statistical quantities is also presented.

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Hamilton's principle with phase changes and conservation principles for moist potential vorticity

Kooloth

Smith

Stechmann

2023

Quart J Royal Meteoro Soc

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Many definitions of moist potential vorticity (PV) have been proposed to extend the dry theory of Ertel PV. None of the moist PV definitions seem to have all of the desirable properties of the dry Ertel PV. For instance, dry PV is not only a globally conserved quantity, but also a material invariant that is conserved along fluid parcel trajectories. Therefore, an open question remains: Is there a moist PV that is a material invariant, if clouds and phase changes of water are present? In prior studies, definitions of moist PV have been proposed based on physical and mathematical intuition. Here, a systematic approach is used. In particular, a particle relabeling symmetry is devised for a moist atmosphere and then Noether's theorem is employed to arrive at the associated conservation laws for a moist PV. A priori, it is not clear whether this systematic approach will be viable, since it relies on variational derivatives in Hamilton's principle, and phase changes introduce singularities that could potentially prevent derivatives at the cloud edge. However, it is shown that the energy and the Lagrangian density are sufficiently smooth to allow variational derivatives, in a moist Boussinesq system with reversible phase transitions between water vapor and liquid cloud water. From the particle relabeling symmetry, a moist Kelvin circulation theorem is found, along with a moist PV conservation law that applies not for each individual parcel but for parcel‐integrated PV, integrated over certain local volumes.

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Anomalous Waves Triggered by Abrupt Depth Changes: Laboratory Experiments and Truncated KdV Statistical Mechanics

Cited by 23 publications

References 49 publications

Non-homogeneous analysis of rogue wave probability evolution over a shoal

Non-homogeneous analysis of rogue wave probability evolution over a shoal

Statistical properties of wave kinematics in long-crested irregular waves propagating over non-uniform bathymetry

Hamilton's principle with phase changes and conservation principles for moist potential vorticity

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