Drifting Rogue Packets

2018 ◽  
Author(s):  
Amin Chabchoub ◽  
Norbert Hoffmann ◽  
Nail Akhmediev ◽  
Takuji Waseda
Keyword(s):  
Modulation Instability ◽  
Wave Train ◽  
Modulation Frequency ◽  
Phase Speed ◽  
Periodic Wave ◽  
Unstable Wave ◽  
Extreme Waves ◽  
Wave Groups ◽  
The Waves ◽  
Good Agreement

Modulation instability (MI) is one possible mechanism to explain the formation of extreme waves in uni-directional and narrow-banded seas. It can be triggered, when side-bands around the main frequency are excited and subsequently follow an exponential growth. In physical domain this dynamics translates to periodic pulsations of wave groups that can reach heights up to three times the initial amplitude of the wave train. It is well-known that these periodic wave groups propagate with approximately half the waves phase speed in deep-water. We report an experimental study on modulationally unstable wave groups that propagate with a velocity that is higher than the group velocity since the modulation frequency is complex. It is shown that when this additional velocity to the wave groups is small a good agreement with exact nonlinear Schrödinger (NLS) models, that describe the nonlinear stage of MI, is reached. Otherwise a significant deviation is observed that could be compensated when increasing accuracy of the water wave modeling beyond NLS.

scholarly journals Nonlinear dynamics of wave-groups in random seas: unexpected walls of water in the open ocean

2015 ◽  
Vol 471 (2184) ◽  
pp. 20150660 ◽  
Author(s):  
Thomas A. A. Adcock ◽  
Paul H. Taylor ◽  
Scott Draper
Keyword(s):  
Extreme Event ◽  
Open Ocean ◽  
Extreme Waves ◽  
Wave Direction ◽  
Sea State ◽  
Wave Groups ◽  
Large Wave ◽  
Linear Evolution ◽  
Random Seas ◽  
The Waves

This paper investigates the size and structure of large waves on the open ocean. We investigate how nonlinear physics modifies waves relative to those predicted by a linear model. We run linear random simulations and extract extreme waves and the surrounding sea-state. For each extreme event, we propagate the waves back in time under linear evolution before propagating the wave-field forward using a nonlinear model. The differences between large linear and nonlinear wave-groups are then examined. The general trends are that under nonlinear evolution, relative to linear evolution, there is, on average, little or no extra amplitude in the nonlinear simulations; that there is an increase in the width of the crest of the wave-group and a contraction of large wave-groups in the mean wave direction; that large waves tend to move to the front of a wave-packet meaning that the locally largest wave is relatively bigger than the wave preceding it; and that nonlinearity can increase the duration of extreme wave events. In all these trends, there is considerable scatter, although the effects observed are clear. Our simulations show that nonlinearity does play an important part in the formation of extreme waves on deep water.

scholarly journals Oblique wave groups in deep water

1984 ◽  
Vol 146 ◽  
pp. 1-20 ◽  
Author(s):  
P. J. Bryant
Keyword(s):  
Deep Water ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Wave Pattern ◽  
Periodic Wave ◽  
Two Dimensions ◽  
Wave Groups ◽  
Oblique Wave ◽  
Parallel Lines ◽  
The Waves

Oblique wave groups consist of waves whose straight parallel lines of constant phase are oblique to the straight parallel lines of constant group phase. Numerical solutions for periodic oblique wave groups with envelopes of permanent shape are calculated from the equations for irrotational three-dimensional deep-water motion with nonlinear upper free-surface conditions. Two distinct families of periodic wave groups are found, one in which the waves in each group are in phase with those in all other groups, and the other in which there is a phase difference of π between the waves in consecutive groups. It is shown that some analytical solutions for oblique wave groups calculated from the nonlinear Schrödinger equation are in error because they ignore the resonant forcing of certain harmonics in two dimensions. Particular attention is given to oblique wave groups whose group-to-wave angle is in the neighbourhood of the critical angle tan−1√½, corresponding to waves on the boundary wedge of the Kelvin ship-wave pattern.

scholarly journals Periodic waves in the lower thermosphere observed by OI630 nm airglow images

2016 ◽  
Vol 34 (2) ◽  
pp. 293-301 ◽  
Author(s):  
I. Paulino ◽  
A. F. Medeiros ◽  
S. L. Vadas ◽  
C. M. Wrasse ◽  
H. Takahashi ◽  
...  
Keyword(s):  
Lower Thermosphere ◽  
Phase Speed ◽  
Periodic Wave ◽  
Ionospheric Disturbances ◽  
Phase Front ◽  
Spectral Parameters ◽  
Middle Latitudes ◽  
Perkins Instability ◽  
Generation Mechanisms ◽  
The Waves

Abstract. Periodic wave structures in the thermosphere have been observed at São João do Cariri (geographic coordinates: 36.5° W, 7.4° S; geomagnetic coordinates based on IGRF model to 2015: 35.8° E, 0.48° N) from September 2000 to November 2010 using OI630.0 nm airglow images. During this period, which corresponds to almost one solar cycle, characteristics of 98 waves were studied. Similarities between the characteristics of these events and observations at other places around the world were noted, primarily the spectral parameters. The observed periods were mostly found between 10 and 35 min; horizontal wavelengths ranged from 100 to 200 km, and phase speed from 30 to 180 m s−1. These parameters indicated that some of the waves, presented here, are slightly faster than those observed previously at low and middle latitudes (Indonesia, Carib and Japan), indicating that the characteristics of these waves may change at different places. Most of observed waves have appeared during magnetically quiet nights, and the occurrence of those waves followed the solar activity. Another important characteristic is the quasi-monochromatic periodicity that distinguish them from the single-front medium-scale traveling ionospheric disturbances (MSTIDs) that have been observed previously over the Brazilian region. Moreover, most of the observed waves did not present a phase front parallel to the northeast–southwest direction, which is predicted by the Perkins instability process. It strongly suggests that most of these waves must have had different generation mechanisms from the Perkins instability, which have been pointed out as being a very important mechanism for the generation of MSTIDs in the lower thermosphere.

scholarly journals Singular solutions of the BBM equation: analytical and numerical study

Nonlinearity ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 388-410
Author(s):  
Sergey Gavrilyuk ◽  
Keh-Ming Shyue
Keyword(s):  
Phase Velocity ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Wave Train ◽  
Wave Length ◽  
Periodic Wave ◽  
Travelling Wave ◽  
Constant State ◽  
Bbm Equation ◽  
Good Agreement

Abstract We show that the Benjamin–Bona–Mahony (BBM) equation admits stable travelling wave solutions representing a sharp transition from a constant state to a periodic wave train. The constant state is determined by the parameters of the periodic wave train: the wave length, amplitude and phase velocity, and satisfies both the generalized Rankine–Hugoniot conditions for the exact BBM equation and for its wave averaged counterpart. Such stable shock-like travelling structures exist if the phase velocity of the periodic wave train is not less than the solution wave averaged. To validate the accuracy of the numerical method, we derive the (singular) solitary limit of the Whitham system for the BBM equation and compare the corresponding numerical and analytical solutions. We find good agreement between analytical results and numerical solutions.

Quasi-wave trains in a cold collisionless plasma

1971 ◽  
Vol 6 (3) ◽  
pp. 513-526 ◽  
Author(s):  
Yoshinori Inoue
Keyword(s):  
Wave Train ◽  
Geometric Mean ◽  
Collisionless Plasma ◽  
Periodic Wave ◽  
Larmor Radius ◽  
Special Cases ◽  
Computer Calculations ◽  
Wave Trains ◽  
Hydromagnetic Waves ◽  
The Waves

Non-linear hydromagnetic waves in a cold collisionless plasma are investigated by numerical and analytic methods. For this problem, Saffman has already implied that there may exist a non-periodic wave different from the well-known solitary wave (or wave train). His analysis is based on the assumption that the quasi-ergodic theorem can be applied to the present problem. However, the propriety of the assumption has not been discussed.It is seen from the computer calculations that in general the waves do not have periodicity, as Saffman pointed out. Furthermore, some concrete examples show the behaviour of these ergodic waves more clearly. The width of the waves is of the order of ion Larmor radius. These waves are here called quasi-wave trains. In some special cases, the waves reduce to wave trains (with periodicity). Some of them have a length scale of the geometric mean between the Larmor radii of the electron and of the ion.

Peristaltic pumping of rigid objects in an elastic tube

2011 ◽  
Vol 672 ◽  
pp. 219-244 ◽  
Author(s):  
D. TAKAGI ◽  
N. J. BALMFORTH
Keyword(s):  
Solitary Wave ◽  
Wave Train ◽  
Periodic Wave ◽  
Radial Force ◽  
Elastic Tube ◽  
Left Behind ◽  
Rigid Objects ◽  
Peristaltic Pumping ◽  
Long Rod ◽  
The Waves

A mathematical model is developed for long peristaltic waves propelling a suspended rigid object down a fluid-filled axisymmetric tube. The fluid flow is described using lubrication theory and the deformation of the tube using linear elasticity. The object is taken to be either an infinitely long rod of constant radius or a parabolic-shaped lozenge of finite length. The system is driven by a radial force imposed on the tube wall that translates at constant speed down the tube axis and with a form chosen to generate a periodic wave train or a solitary wave. These waves exert a traction on the enclosed object, forcing it into motion. Periodic waves drive the infinite rod at a speed that attains a maximum at a moderate forcing amplitude and approaches approximately one quarter of the wave speed in the large-amplitude limit. The finite lozenge can be entrained and driven at the same speed as a solitary wave or periodic wave train if the forcing is sufficiently strong. For weaker forcing, the lozenge is either left behind the solitary wave or interacts repeatedly with the waves in the periodic train to generate stuttering forward progress. The threshold forcing amplitude for entrainment increases weakly with the radial span of the enclosed object, but strongly with the axial length, with entrainment becoming impossible if the object is too long.

The Role of Equatorial Rossby Waves in Tropical Cyclogenesis. Part I: Idealized Numerical Simulations in an Initially Quiescent Background Environment

2010 ◽  
Vol 138 (4) ◽  
pp. 1368-1382 ◽  
Author(s):  
Jeffrey S. Gall ◽  
William M. Frank ◽  
Matthew C. Wheeler
Keyword(s):  
Tropical Cyclone ◽  
Large Scale ◽  
Phase Speed ◽  
Tropical Cyclogenesis ◽  
Initial Amplitude ◽  
Low Level ◽  
Wave Simulation ◽  
Horizontal Momentum ◽  
Good Agreement

Abstract This two-part series of papers examines the role of equatorial Rossby (ER) waves in tropical cyclone (TC) genesis. To do this, a unique initialization procedure is utilized to insert n = 1 ER waves into a numerical model that is able to faithfully produce TCs. In this first paper, experiments are carried out under the idealized condition of an initially quiescent background environment. Experiments are performed with varying initial wave amplitudes and with and without diabatic effects. This is done to both investigate how the properties of the simulated ER waves compare to the properties of observed ER waves and explore the role of the initial perturbation strength of the ER wave on genesis. In the dry, frictionless ER wave simulation the phase speed is slightly slower than the phase speed predicted from linear theory. Large-scale ascent develops in the region of low-level poleward flow, which is in good agreement with the theoretical structure of an n = 1 ER wave. The structures and phase speeds of the simulated full-physics ER waves are in good agreement with recent observational studies of ER waves that utilize wavenumber–frequency filtering techniques. Convection occurs primarily in the eastern half of the cyclonic gyre, as do the most favorable conditions for TC genesis. This region features sufficient midlevel moisture, anomalously strong low-level cyclonic vorticity, enhanced convection, and minimal vertical shear. Tropical cyclogenesis occurs only in the largest initial-amplitude ER wave simulation. The formation of the initial tropical disturbance that ultimately develops into a tropical cyclone is shown to be sensitive to the nonlinear horizontal momentum advection terms. When the largest initial-amplitude simulation is rerun with the nonlinear horizontal momentum advection terms turned off, tropical cyclogenesis does not occur, but the convectively coupled ER wave retains the properties of the ER wave observed in the smaller initial-amplitude simulations. It is shown that this isolated wave-only genesis process only occurs for strong ER waves in which the nonlinear advection is large. Part II will look at the more realistic case of ER wave–related genesis in which a sufficiently intense ER wave interacts with favorable large-scale flow features.

Steepness effect on modulation instability of the nonlinear wave train

2007 ◽  
Vol 19 (1) ◽  
pp. 014105 ◽  
Author(s):  
Wen-Son Chiang ◽  
Hwung-Hweng Hwung
Keyword(s):  
Nonlinear Wave ◽  
Modulation Instability ◽  
Wave Train

scholarly journals Statistics of Simulated Storm Waves over Bathymetry

2021 ◽  
Vol 9 (7) ◽  
pp. 784
Author(s):  
Arnida Lailatul Latifah ◽  
Durra Handri ◽  
Ayu Shabrina ◽  
Henokh Hariyanto ◽  
E. van Groesen
Keyword(s):  
Water Waves ◽  
Open Water ◽  
Storm Events ◽  
Extreme Waves ◽  
Marine Structures ◽  
Wave Statistics ◽  
Storm Waves ◽  
Different Types ◽  
Run Up ◽  
Good Agreement

This paper shows simulations of high waves over different bathymetries to collect statistical information, particularly kurtosis and crest exceedance, that quantifies the occurrence of exceptionally extreme waves. This knowledge is especially pertinent for the design and operation of marine structures, safe ship trafficking, and mooring strategies for ships near the coast. Taking advantage of the flexibility to perform numerical simulations with HAWASSI software, with the aim of investigating the physical and statistical properties for these cases, this paper investigates the change in wave statistics related to changes in depth, breaking and differences between long- and short-crested waves. Three different types of bathymetry are considered: run-up to the coast with slope 1/20, waves over a shoal, and deep open-water waves. Simulations show good agreement in the examined cases compared with the available experimental data and simulations. Then predictive simulations for cases with a higher significant wave height illustrate the changes that may occur during storm events.

Periodic wave solution of the Kundu-Mukherjee-Naskar equation in birefringent fibers via the Hamiltonian-based algorithm

2021 ◽  
Author(s):  
Kang-Jia Wang ◽  
Hong-Wei Zhu
Keyword(s):  
Wave Solution ◽  
Bright Light ◽  
Periodic Wave ◽  
Optical Soliton ◽  
Numerical Results ◽  
Periodic Wave Solution ◽  
Soliton Dynamics ◽  
Good Agreement

Abstract The Kundu-Mukherjee-Naskar equation can be used to address certain optical soliton dynamics in the (2+1) dimensions. In this paper, we aim to find its periodic wave solution by the Hamiltonian-based algorithm. Compared with the existing results, they have a good agreement, which strongly proves the correctness of the proposed method. Finally, the numerical results are presented in the form of 3-D and 2-D plots. The results in this work are expected to shed a bright light on the study of the periodic wave solution in physics.

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