scholarly journals PAIRWISE INTERACTIONS OF COHERENT STRUCTURES ON THE SURFACE OF DEEP WATER

2019 ◽  
Vol 47 (1) ◽  
pp. 66-68
Author(s):  
D.I. Kachulin ◽  
A.A. Gelash ◽  
A.I. Dyachenko ◽  
V.E. Zakharov
Keyword(s):  
Wave Field ◽  
Deep Water ◽  
Coherent Structures ◽  
Relative Phase ◽  
Field Amplitude ◽  
Energy Losses ◽  
Exact Model ◽  
Pairwise Interactions ◽  
The Moment ◽  
Maximum Amplification

The interactions of coherent structures (different types of solitary wave groups) on the surface of deep water is an important nonlinear wave process, which has been studied both theoretically and experimentally (Dyachenko et al., 2013a, b; Slunyaev et al., 2017). At the moment, a complete theoretical description of such interactions is known only for the simplest model – the nonlinear Schrödinger equation (NSE) where exact multi-soliton solutions are found. In the work (Kachulin, Gelash, 2018), the dynamics of pairwise interactions of coherent structures (breathers) on the surface of deep water were numerically investigated in the framework of the Dyachenko-Zakharov model. Significant differences were found in the collision dynamics of breathers of the compact Dyachenko-Zakharov equation when compared to the behavior of the NLSE solitons. It was found that in a more precise model of gravitational surface waves, in contrast to the NLSE, the maximum amplification of the wave field amplitude during the collision process of coherent structures can exceed the sum of the initial amplitudes of the breathers. In addition, the maximum amplification of the wave field amplitude increases with increasing steepness of the interacting breathers and exceeds unity by 20% at the value of the wave steepness m ≈ 0.2. It was revealed that an important parameter determining the dynamics of pairwise collisions of breathers is the relative phase of these objects at the moment of interaction. The interaction of breathers in the non-integrable Dyachenko-Zakharov model leads to the appearance of small radiation, which was discovered earlier in 2013 (Dyachenko et al., 2013a, b). In the work (Kachulin, Gelash, 2018) we demonstrate that the magnitude of the energy losses of the colliding solitons to radiation also depends on their relative phase. Maximum of the energy losses is observed at the same relative phase, at which the amplitude amplification maximum is observed. In addition, depending on the value of the relative phase, solitons can both gain and lose the energy, which results in increase or decrease of their amplitude after a collision. It was found that, in contrast to the NSE model, the spatial shifts of solitons in a more precise model can be both positive and negative. We use the exact breather solutions of the Dyachenko-Zakharov model and the canonical transformation to physical variables (the free surface profile and the potential on the liquid surface) to find approximate solutions in the form of breathers within the framework of exact nonlinear equations for potential incompressible fluid flows. The preliminary results of our numerical experiments in the exact model demonstrate similar dynamics of the interaction of breathers, which indicates that the theoretical picture of the interaction of coherent structures presented here is universal and can be observed in laboratory experiments. The study of the dynamics of breather interactions in the exact model performed by D.I. Kachulin was supported by the Russian Science Foundation (Grant No. 18-71-00079). The work of V.E. Zakharov and A.I. Dyachenko on the dynamics of breather interactions in approximate models was supported by the state assignment “Dynamics of the complex materials”.

scholarly journals Soliton–Breather Interaction: The Modified Korteweg–de Vries Equation Framework

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1445
Author(s):  
Ekaterina Didenkulova ◽  
Efim Pelinovsky
Keyword(s):  
Optical Fibers ◽  
Water Waves ◽  
Relative Phase ◽  
Vries Equation ◽  
Decisive Role ◽  
Pairwise Interactions ◽  
De Vries ◽  
Series Of Experiments ◽  
Stratified Ocean ◽  
The Moment

Pairwise interactions of particle-like waves (such as solitons and breathers) are important elementary processes that play a key role in the formation of the rarefied soliton gas statistics. Such waves appear in different physical systems such as deep water, shallow water waves, internal waves in the stratified ocean, and optical fibers. We study the features of different regimes of collisions between a soliton and a breather in the framework of the focusing modified Korteweg–de Vries equation, where cubic nonlinearity is essential. The relative phase of these structures is an important parameter determining the dynamics of soliton–breather collisions. Two series of experiments with different values of the breather’s and soliton’s relative phases were conducted. The waves’ amplitudes resulting from the interaction of coherent structures depending on their relative phase at the moment of collision were analyzed. Wave field moments, which play a decisive role in the statistics of soliton gases, were determined.

Nonlinear Fourier Analysis Algorithm and Models for Water Waves in Terms of Surface Elevation, Amplitude Modulations

2019 ◽  
Author(s):  
Alfred R. Osborne
Keyword(s):  
Synthetic Aperture Radar ◽  
Surface Waves ◽  
Shallow Water ◽  
Wave Field ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Surface Elevation ◽  
Synthetic Aperture ◽  
Wave Measurements

Abstract This paper addresses two issues with regard to nonlinear ocean waves. (1) The first issue relates to the often-confused differences between the coordinates used for the measurement and characterization of ocean surface waves: The surface elevation and the complex modulation of a wave field. (2) The second issue relates to the very different kinds of physical wave behavior that occur in shallow and deep water. Both issues come from the known, very different behaviors of deep and shallow water waves. In shallow water one often uses the Korteweg-deVries that describes the wave surface elevation in terms of cnoidal waves and solitons. In deep water one uses the nonlinear Schrödinger equation whose solutions correspond to the complex envelope of a wave field that has Stokes wave and breather solutions. Here I make clear the relationships between the two ways of characterizing surface waves. Furthermore, and more importantly, I address the issues of matching the two types of wave behavior as the wave motion passes from deep to shallow water, or vice versa. For wave measurements we normally obtain the surface elevation with a wave staff, resistance gauge or pressure recorder for getting time series. Remote sensing applications relate to the use of lidar, radar or synthetic aperture radar for obtaining space series. The two types of wave behavior can therefore crucially depend on where the instrument is placed on the “ground track” or “field” over which the lidar or radar measurements are made. Thus the matching problem from deep to shallow water is not only important for wave measurements, but also for wave modeling. Modern wave models [Osborne, 2010, 2018, 2019a, 2019b] that maintain the coherent structures of wave dynamics (solitons, Stokes waves, breathers, superbreathers, vortices, etc.) must naturally pass from deep to shallow water where the nature of the nonlinear physics, and the form of the coherent structures, change. I address these issues and more herein. This paper is directed towards the development of methods for the real time measurement of waves by shipboard radar and for wave measurements by airplane and helicopter using lidar and synthetic aperture radar. Wave modeling efforts are also underway.

Statistics of Coherent Structures Collisions and their Dynamics on the Surface of Deep Water

2020 ◽  
Author(s):  
Sergey Dremov ◽  
Dmitriy Kachulin ◽  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Incompressible Fluid ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Energy Exchange ◽  
Relative Phase ◽  
Collision Probability ◽  
Statistical Characteristics ◽  
Potential Flows

<p>        The present work is devoted to the study of coherent structures collisions dynamics in the models of deep water waves equations: the model of a supercompact equation for deep water unidirectional waves (SCEq) and the model of Dyachenko equations for potential flows of incompressible fluid with free surface. In these models there are special solutions in the form of coherent wave structures called breathers. They can be found numerically by using the Petviashvili method. One can consider the combination of such breathers as a model of rarefied soliton gas, and their paired collisions in this case are a key feature in forming of dynamics and statistics in the model. To describe statistical characteristics of breathers collision Probability Density Function (PDF) is used. PDF of breathers wave amplitudes during their collision was calculated and compared with the known results in the model of Nonlinear Schrodinger equation (NLS). In contrast to the NLS model there is a number of interesting features in the model of SCEq. For instance, the amplitude maximum of wave arising during the collision can exceed the sum of interacting breathers amplitudes, what cannot happen in NLS model. Moreover, it depends on the initial breathers steepness. In addition, it is shown that the breathers acquire phase and space shifts after each collision, and thus their velocity also changes. Depending on the relative phase breathers can give their energy or take it, and as a result their amplitude can be decreased or increased respectively. The same situation can be seen in the model of equations for potential flows of incompressible fluid with free surface. In addition to the dependence on relative phase the duration of the collision also affects the energy exchange. Breathers collisions are accompanied by appearance of little radiation, and its value is relatively less than the value of energy exchange. The results of statistics calculating and dynamics studying in the rarefied gas of coherent structures will be shown in the present work.</p><p>           The work was supported by Russian Science Foundation grant № 18-71-00079.</p>

scholarly journals Bound Coherent Structures Propagating on the Free Surface of Deep Water

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 115
Author(s):  
Dmitry Kachulin ◽  
Sergey Dremov ◽  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Nonlinear Models ◽  
Ideal Incompressible Fluid ◽  
Equation Model ◽  
System Of Nonlinear Equations ◽  
Potential Flows ◽  
Deep Water Waves

This article presents a study of bound periodically oscillating coherent structures arising on the free surface of deep water. Such structures resemble the well known bi-soliton solution of the nonlinear Schrödinger equation. The research was carried out in the super-compact Dyachenko-Zakharov equation model for unidirectional deep water waves and the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. The special numerical algorithm that includes a damping procedure of radiation and velocity adjusting was used for obtaining such bound structures. The results showed that in both nonlinear models for deep water waves after the damping is turned off, a periodically oscillating bound structure remains on the fluid surface and propagates stably over hundreds of thousands of characteristic wave periods without losing energy.

scholarly journals Branching processes with interactions: subcritical cooperative regime

2021 ◽  
Vol 53 (1) ◽  
pp. 251-278
Author(s):  
Adrián González Casanova ◽  
Juan Carlos Pardo ◽  
José Luis Pérez
Keyword(s):  
Population Genetics ◽  
Branching Processes ◽  
Jump Diffusion ◽  
Pairwise Interaction ◽  
Pairwise Interactions ◽  
Different Types ◽  
Interesting Object ◽  
The Moment ◽  
Dynamics Of Populations

AbstractIn this paper, we introduce a family of processes with values on the nonnegative integers that describes the dynamics of populations where individuals are allowed to have different types of interactions. The types of interactions that we consider include pairwise interactions, such as competition, annihilation, and cooperation; and interactions among several individuals that can be viewed as catastrophes. We call such families of processes branching processes with interactions. Our aim is to study their long-term behaviour under a specific regime of the pairwise interaction parameters that we introduce as the subcritical cooperative regime. Under such a regime, we prove that a process in this class comes down from infinity and has a moment dual which turns out to be a jump-diffusion that can be thought as the evolution of the frequency of a trait or phenotype, and whose parameters have a classical interpretation in terms of population genetics. The moment dual is an important tool for characterizing the stationary distribution of branching processes with interactions whenever such a distribution exists; it is also an interesting object in its own right.

Quelques aspects des conditions de depot du flysch

1962 ◽  
Vol S7-IV (1) ◽  
pp. 41-48 ◽  
Author(s):  
Marguerite Rech-Frollo
Keyword(s):  
Shallow Water ◽  
Deep Water ◽  
Organic Material ◽  
Detrital Material ◽  
Water Origin ◽  
The Moment ◽  
Bird Tracks ◽  
Marine Basin

Abstract Analysis of the Niesen flysch between Le Sepey and Mosses lake does not confirm the deep-water bathymetry commonly attributed to flysch deposits. The juxtaposition of organic material over continental alluvium--a typical flysch characteristic--was observed only at shallow depths. The muddy sands, source of the flysch deposits, are actually formed at shallow depths. Bird tracks reported from certain flysch beds also suggest shallow-water origin for the deposits. Cross currents produced after periodic disruption of tectonic and climatic equilibria in parts of a marine basin corresponding to the continental platforms explain the mechanical sorting of the organisms and detrital material as well as the granoclastic structure of the flysch. After deposition of the flysch and before its compaction orogenic mobility at the bottom of the basin affected the petrography of the flysch causing corrosion of the quartz and feldspars at the moment of consolidation. Evidence presented by proponents of a deep-water origin for the flysch deposits--based on foraminifera and the petrographic and paleo-oceanographic characters of the deep-water sands--is reviewed.

Loading History Effects for Deep-Water S-Lay of Pipelines

2004 ◽  
Vol 126 (2) ◽  
pp. 156-163 ◽  
Author(s):  
Heedo D. Yun ◽  
Ralf R. Peek ◽  
Paul R. Paslay ◽  
Frans F. Kopp
Keyword(s):  
Deep Water ◽  
Numerical Solutions ◽  
Pipe Material ◽  
Loading History ◽  
Material Models ◽  
Plastic Deformations ◽  
History Effects ◽  
Departure Angle ◽  
Numerical Finite Element ◽  
The Moment

For economic reasons S-Lay is often preferred to J-Lay. However in very deep water S-Lay requires a high curvature of the stinger to achieve the required close-to-vertical departure angle (or a large, low curvature stinger). Choosing the high curvature stinger can lead to plastic deformations of the pipe. The high top tension increases the plastic deformations in two ways: firstly it adds an overall tensile component to the strains, thereby increasing the strains at the 12 o’clock position. Secondly, it increases the strain concentrations, which arise due to discontinuous support of the pipe on the stinger. Typically, the pipe is guided over a series of roller beds. The high top tension tends to straighten the spans between the rollerbeds. To accommodate this (so that the pipe can still follow the stinger), higher curvatures occur at the roller beds. Analytical and numerical solutions are provided to quantify this effect. The analytical solution is fully developed for an arbitrary pipe material models, provided that: (i) the moment-curvature relation for the pipe under tension is known, and (ii) no cyclic plastic ratchetting occurs due to repeated bending of the pipe over the roller beds and straightening in the spans between roller beds. Agreement between the analytical and numerical (finite element) results is excellent. Proper loading history must be used in the numerical simulation, otherwise the level of strain concentration can be overpredicted.

scholarly journals Estimating marine engine efficiency in dynamic processes

2021 ◽  
Vol 2021 (3) ◽  
pp. 74-81
Author(s):  
Andrei Aleksandrovich Panasenko
Keyword(s):  
Transient Process ◽  
Rotation Speed ◽  
Transient Processes ◽  
Dynamic Processes ◽  
Energy Losses ◽  
Sharp Change ◽  
Additional Energy ◽  
Transport Ship ◽  
The Moment ◽  
Moment Of Resistance

The article considers the problem of efficiency of energy objects, which is mainly estimated on the basis of their static characteristics. If dynamic processes take up a significant part of the object's time and budget, then there is a need for additional account of energy losses in transient processes. Using the analysis results it is necessary to select the settings of the object regulators. The problem hasn’t been thrown much light on in the publications. An attempt has been made to estimate the additional energy losses of the main engine operating on the propeller of a transport ship. To analyze the transient process of the dependence of the rotation speed on time, it is assumed that this process is caused by a sharp change in the moment of resistance by a given value. The Excel program was proposed to assess the dependence of the rotation speed on time. 10% of the nominal value of the setting or disturbing influences was chosen as the change leading out of the static equilibrium. To compare various transient processes it is proposed to use the value of the length of the transient process in time. Assessing energy losses was carried out by using the coefficient of increasing power consumption during the transient process. The additional energy losses were proved to make more than 1.0 - 1.5% of the nominal power of the controlled object due to the presence of transient processes at 10% disturbance. By changing the settings of the automatic control system (ACS) these losses can be reduced. It has been found that adjusting the ACS settings to reduce energy losses under disturbing influences leads to the higher energy losses during reference influences.

scholarly journals Mechanisms of control in hope jumping as a function of task constraint

2007 ◽  
Vol 2 (1) ◽  
pp. 31-39
Author(s):  
Luiz H. da Silva ◽  
Ana M. Pellegrini
Keyword(s):  
Relative Phase ◽  
Beat Frequency ◽  
Motor Task ◽  
Jump Height ◽  
Upper Limbs ◽  
Haptic Information ◽  
Task Constraint ◽  
Continuous Relative Phase ◽  
The Moment ◽  
Male University Students

Hope jumping is a motor task that can be performed in different ways and with ropes with different physical characteristics (weight, texture, and size). When the rope jump is performed with the rope being self controlled, relevant haptic information is available for the action control. In order to examine the adjustments made by the performer in rope jumping with ropes of different weight, eight male university students performed a sequence of 30 rope-jumping with ropes of 180, 255, and 330g. The rope was turn by the participant in a selfpaced mode. Such sequences were registered in video and the following variables were obtained: continuous relative phase, rope beat frequency, jump height, rope height, and temporal interval between the moment of the loss of the feet contact with the floor and the crossing of the rope under the feet. The results showed that only the rope frequency changed as a function of the rope weight, suggesting that the upper limbs when turning the rope are responsible for the adjustments in order to maintain the same level of performance.

Bound Coherent Structures Propagating on the Free Surface of Deep Water

2021 ◽  
Author(s):  
Sergey Dremov ◽  
Dmitry Kachulin ◽  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Incompressible Fluid ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Initial Conditions ◽  
Soliton Solutions ◽  
Ideal Incompressible Fluid ◽  
System Of Nonlinear Equations ◽  
Computational Domain

<p><span>               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. </span><span>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.</span></p><p><span>This work was supported by RSF grant </span><span>19-72-30028</span><span> and </span><span>RFBR grant </span><span>20-31-90093</span><span>.</span></p><p><span>[1] Kachulin D., Dyachenko A., Dremov S. Multiple Soliton Interactions on the Surface of Deep Water //Fluids. – 2020. – Т. 5. – №. 2. – С. 65.</span></p><p><span>[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.</span></p>

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