scholarly journals Theoretical and experimental evidence of non-symmetric doubly localized rogue waves

2014 ◽  
Vol 470 (2171) ◽  
pp. 20140318 ◽  
Author(s):  
Jingsong He ◽  
Lijuan Guo ◽  
Yongshuai Zhang ◽  
Amin Chabchoub
Keyword(s):  
Deep Water ◽  
Rogue Waves ◽  
Nls Equation ◽  
Third Order ◽  
Weakly Nonlinear ◽  
Wave Flume ◽  
Symmetric Pattern ◽  
System A ◽  
Special Case ◽  
Good Agreement

We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water.

Experiments and simulations on extreme waves near reflective beaches

2021 ◽  
Author(s):  
Amin Chabchoub ◽  
Yuchen He ◽  
Ana Vila-Concejo ◽  
Alexander Babanin
Keyword(s):  
Rogue Waves ◽  
Formation Mechanisms ◽  
Extreme Waves ◽  
Wave Reflections ◽  
Wave Processes ◽  
Weakly Nonlinear ◽  
Wave Flume ◽  
Wave Trains ◽  
Incident Waves ◽  
Good Agreement

<p>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. </p>

Weakly Nonlinear Mass Transfer in an Internally Soluted and Modulated Porous Layer

2020 ◽  
Vol 12 (5) ◽  
pp. 622-631
Author(s):  
Palle Kiran ◽  
S. H. Manjula
Keyword(s):  
Mass Transfer ◽  
Solvability Condition ◽  
Finite Amplitude ◽  
Amplitude Equation ◽  
Third Order ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Analysis ◽  
System Parameters ◽  
System A ◽  
Rotating Porous Media

The effect of solutal modulation on a rotating porous media is studied. Using solvability condition, the finite amplitude equation is derived at third order of the system. A weakly nonlinear analysis is applied to investigate mass transfer in a porous medium. In this article, the stationary convection is discussed in the presence of solutal Rayleigh number. The amplitude equation (GLE) is solved numerically. Using this GLE the Sherwood number is evaluated in terms of the various system parameters. The effect of individual parameters on mass transport is discussed in detail. It is found that the mass transfer is more for modulated system than un-modulated case. Further, internal solute number Si enhance or diminishes the mass transfer. Finally it is also found that, solutal modulation can be effectively applied in either enhancing or diminishing the mass transfer.

scholarly journals On the kurtosis of deep-water gravity waves

2015 ◽  
Vol 782 ◽  
pp. 25-36 ◽  
Author(s):  
Francesco Fedele
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Rogue Waves ◽  
Angular Frequency ◽  
Quasi Equilibrium ◽  
Weakly Nonlinear ◽  
Excess Kurtosis ◽  
Time Dynamic ◽  
Resonant Interactions ◽  
Type Spectrum

In this paper, we revisit Janssen’s (J. Phys. Oceanogr., vol. 33 (4), 2003, pp. 863–884) formulation for the dynamic excess kurtosis of weakly nonlinear gravity waves in deep water. For narrowband directional spectra, the formulation is given by a sixfold integral that depends upon the Benjamin–Feir index and the parameter $R={\it\sigma}_{{\it\theta}}^{2}/2{\it\nu}^{2}$, a measure of short-crestedness for the dominant waves, with ${\it\nu}$ and ${\it\sigma}_{{\it\theta}}$ denoting spectral bandwidth and angular spreading. Our refinement leads to a new analytical solution for the dynamic kurtosis of narrowband directional waves described with a Gaussian-type spectrum. For multidirectional or short-crested seas initially homogeneous and Gaussian, in a focusing (defocusing) regime dynamic kurtosis grows initially, attaining a positive maximum (negative minimum) at the intrinsic time scale ${\it\tau}_{c}={\it\nu}^{2}{\it\omega}_{0}t_{c}=1/\sqrt{3R}$, or $t_{c}/T_{0}\approx 0.13/{\it\nu}{\it\sigma}_{{\it\theta}}$, where ${\it\omega}_{0}=2{\rm\pi}/T_{0}$ denotes the dominant angular frequency. Eventually the dynamic excess kurtosis tends monotonically to zero as the wave field reaches a quasi-equilibrium state characterized by nonlinearities mainly due to bound harmonics. Quasi-resonant interactions are dominant only in unidirectional or long-crested seas where the longer-time dynamic kurtosis can be larger than that induced by bound harmonics, especially as the Benjamin–Feir index increases. Finally, we discuss the implication of these results for the prediction of rogue waves.

Phenomena on Rogue Waves and Rational Solution of Korteweg-de Vries Equation

2013 ◽  
Author(s):  
Ni Song ◽  
Wei Zhang ◽  
Qian Wang
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Kdv Equation ◽  
Rational Solution ◽  
Rogue Waves ◽  
Nls Equation ◽  
Engineering Structures ◽  
Weakly Nonlinear ◽  
Nonlinear Mechanism ◽  
De Vries

An appropriate nonlinear mechanism may create the rogue waves. Perhaps the simplest mechanism, which is able to create considerate changes in the wave amplitude, is the nonlinear interaction of shallow-water solitons. The most well-known examples of such structure are Korteweg-de Vries (KdV) solitons. The Korteweg-de Vries (KdV) equation, which describes the shallow water waves, is a basic weakly dispersive and weakly nonlinear model. Basing on the homogeneous balanced method, we achieve the general rational solution of a classical KdV equation. Numerical simulations of the solution allow us to explain rare and unexpected appearance of the rogue waves. We compare the rogue waves with the ones generated by the nonlinear Schrödinger (NLS) equation which can describe deep water wave trains. The numerical results illustrate that the amplitude of the KdV equation is higher than the one of the NLS equation, which may causes more serious damage of engineering structures in the ocean. This nonlinear mechanism will provide a theoretical guidance in the ocean and physics.

Soliton, Breather, and Rogue Wave for a (2+1)-Dimensional Nonlinear Schrödinger Equation

2016 ◽  
Vol 71 (2) ◽  
pp. 95-101 ◽  
Author(s):  
Hai-Qiang Zhang ◽  
Xiao-Li Liu ◽  
Li-Li Wen
Keyword(s):  
Rogue Wave ◽  
Dimensional Space ◽  
Rogue Waves ◽  
Space Structures ◽  
Nls Equation ◽  
Third Order ◽  
Nonlinear Schrödinger ◽  
Circular Pattern ◽  
Bright Line ◽  
Fundamental Pattern

AbstractIn this paper, a (2+1)-dimensional nonlinear Schrödinger (NLS) equation, which is a generalisation of the NLS equation, is under investigation. The classical and generalised N-fold Darboux transformations are constructed in terms of determinant representations. With the non-vanishing background and iterated formula, a family of the analytical solutions of the (2+1)-dimensional NLS equation are systematically generated, including the bright-line solitons, breathers, and rogue waves. The interaction mechanisms between two bright-line solitons and among three bright-line solitons are both elastic. Several patterns for first-, second, and higher-order rogue wave solutions fixed at space are displayed, namely, the fundamental pattern, triangular pattern, and circular pattern. The two-dimensional space structures of first-, second-, and third-order rogue waves fixed at time are also demonstrated.

Numerical Simulation on Nonlinear Evolution of Rogue Waves on Currents Based on the NLS Equation

2011 ◽  
Author(s):  
Hanhong Hu ◽  
Ning Ma
Keyword(s):  
Numerical Simulation ◽  
Deep Water ◽  
Water Waves ◽  
Rogue Waves ◽  
Domain Model ◽  
Energy Concentration ◽  
Current Field ◽  
Nls Equation ◽  
Steady Current ◽  
Deep Water Wave

In this paper, nonlinear instability and evolution of deep-water rogue waves on following and opposing currents were described by numerical simulation for laboratory investigation. The generation of rogue waves in a numerical tank by means of wave focusing technique had been studied. Here a spatial domain model of current modified nonlinear Schro¨dinger (NLSC) equations in one horizontal dimension (1D) was established for describing the deep-water wave trains in a prescribed stationary current field. The transient water waves (TWW) was adopted as the initial condition of the NLSC equation. The steady current was added to see the effect of wave-current interaction on the energy concentration of gravity waves. The influence of current as well as other terms in the NLSC equations on wave height, inclination, particle velocity and acceleration are shown. Meanwhile, the focusing time/position of TWW influenced by the current field is investigated, which is of course a very important factor in experimental research when we generate rogue waves in the laboratory.

scholarly journals Multi-rogue waves solutions to the focusing NLS equation and the KP-I equation

2011 ◽  
Vol 11 (3) ◽  
pp. 667-672 ◽  
Author(s):  
P. Dubard ◽  
V. B. Matveev
Keyword(s):  
Fiber Optics ◽  
Deep Water ◽  
Acoustic Waves ◽  
Liquid Surface ◽  
Large Family ◽  
Rogue Waves ◽  
Point Of View ◽  
Rational Solutions ◽  
Nls Equation ◽  
Physical Importance

Abstract. We construct a multi-parametric family of quasi-rational solutions to the focusing NLS equation, presenting a profile of multiple rogue waves. These solutions have also been used by us to construct a large family of smooth, real localized rational solutions of the KP-I equation quite different from the multi-lumps solutions first constructed in Bordag et al. (1977). The physical relevance of both equations is very large. From the point of view of geosciences,the focusing NLS equation is relevant to the description of surface waves in deep water, and the KP-I equation occurs in the description of capillary gravitational waves on a liquid surface, but also when one considers magneto-acoustic waves in plasma (Zhdanov, 1984) etc. In addition, there are plenty of equations of physical importance, having their origin in fiber optics, hydrodynamics, plasma physics and many other areas, which are gauge equivalent to the NLS equation or to the KP-I equation. Therefore our results can be easily extended to a large number of systems of physical interest to be discussed in separate publications.

Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huanhuan Lu ◽  
Yufeng Zhang
Keyword(s):  
Vries Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
Wave Solutions ◽  
De Vries ◽  
Rogue Wave Solutions ◽  
Bilinear Formulation ◽  
Hirota Bilinear

AbstractIn this paper, we analyse two types of rogue wave solutions generated from two improved ansatzs, to the (2 + 1)-dimensional generalized Korteweg–de Vries equation. With symbolic computation, the first-order rogue waves, second-order rogue waves, third-order rogue waves are generated directly from the first ansatz. Based on the Hirota bilinear formulation, another type of one-rogue waves and two-rogue waves can be obtained from the second ansatz. In addition, the dynamic behaviours of obtained rogue wave solutions are illustrated graphically.

scholarly journals On the physical constraints for the exceeding probability of deep water rogue waves

2021 ◽  
Vol 108 ◽  
pp. 102402
Author(s):  
S. Mendes ◽  
A. Scotti ◽  
P. Stansell
Keyword(s):  
Deep Water ◽  
Rogue Waves ◽  
Physical Constraints

scholarly journals Efficient Numerical Evaluation of Thermodynamic Quantities on Infinite (Semi-)classical Chains

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Christian B. Mendl ◽  
Folkmar Bornemann
Keyword(s):  
Transfer Operator ◽  
Classical System ◽  
Free Energy Density ◽  
Classical Particle ◽  
Thermodynamic Quantities ◽  
Nls Equation ◽  
Classical Systems ◽  
Particle Chain ◽  
Dynamics Simulations ◽  
Good Agreement

AbstractThis work presents an efficient numerical method to evaluate the free energy density and associated thermodynamic quantities of (quasi) one-dimensional classical systems, by combining the transfer operator approach with a numerical discretization of integral kernels using quadrature rules. For analytic kernels, the technique exhibits exponential convergence in the number of quadrature points. As demonstration, we apply the method to a classical particle chain, to the semiclassical nonlinear Schrödinger (NLS) equation and to a classical system on a cylindrical lattice. A comparison with molecular dynamics simulations performed for the NLS model shows very good agreement.

Sign in / Sign up

Export Citation Format

Share Document