scholarly journals Phase Evolution of the Time- and Space-Like Peregrine Breather in a Laboratory

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 308
Author(s):  
Yuchen He ◽  
Pierre Suret ◽  
Amin Chabchoub
Keyword(s):  
Boundary Conditions ◽  
Phase Evolution ◽  
Wave Localization ◽  
Time And Space ◽  
Wave Groups ◽  
Phase Dynamics ◽  
Wave Flume ◽  
Coherent Wave ◽  
Intrinsic Shape ◽  
Peregrine Breather

Coherent wave groups are not only characterized by the intrinsic shape of the wave packet, but also by the underlying phase evolution during the propagation. Exact deterministic formulations of hydrodynamic or electromagnetic coherent wave groups can be obtained by solving the nonlinear Schrödinger equation (NLSE). When considering the NLSE, there are two asymptotically equivalent formulations, which can be used to describe the wave dynamics: the time- or space-like NLSE. These differences have been theoretically elaborated upon in the 2016 work of Chabchoub and Grimshaw. In this paper, we address fundamental characteristic differences beyond the shape of wave envelope, which arise in the phase evolution. We use the Peregrine breather as a referenced wave envelope model, whose dynamics is created and tracked in a wave flume using two boundary conditions, namely as defined by the time- and space-like NLSE. It is shown that whichever of the two boundary conditions is used, the corresponding local shape of wave localization is very close and almost identical during the evolution; however, the respective local phase evolution is different. The phase dynamics follows the prediction from the respective NLSE framework adopted in each case.

Numerical simulation of the Late Jurassic closure of the Vardar Tethys

2021 ◽  
Author(s):  
Nikola Stanković ◽  
Vesna Cvetkov ◽  
Vladica Cvetković
Keyword(s):  
Boundary Conditions ◽  
Numerical Simulations ◽  
Stokes Equations ◽  
Numerical Study ◽  
Phase Evolution ◽  
Staggered Grid ◽  
Second Phase ◽  
Weak Zone ◽  
Ongoing Research ◽  
Magmatic Complex

<p>We report updated results of our ongoing research on constraining geodynamic conditions associated with the final closure of the Vardar branch of the Tethys Ocean by means of application of numerical simulations (previous interim results reported in EGU2020-5919).</p><p>The aim of our numerical study is to test the hypothesis that a single eastward subduction in the Jurassic is a valid explanation for the occurrence of three major, presently observed geological entities that are left behind after the closure of the Vardar Tethys. These include: ophiolite-like igneous rocks of the Sava-Vardar zone and presumably subduction related Timok Magmatic Complex, both Late Cretaceous in age as well as Jurassic ophiolites obducted onto the Adriatic margin. In our simulations we initiate an intraoceanic subduction in the Early/Middle Jurassic, which eventually transitions into an oceanic closure and subsequent continental collision processes.</p><p>In the scope of our study numerical simulations are performed by solving a set of partial differential equations: the continuity equation, the Navier-Stokes equations and the temperature equation. To this end we used I2VIS thermo-mechanical code which utilizes marker in cell approach with finite difference discretization of equations on a staggered grid [Gerya et al., 2000; Gerya&Yuen, 2003].</p><p>The 2D model consists of two continental plates separated by two oceanic slabs connected at a mid-oceanic ridge. Intraoceanic subduction is initiated along the ridge by assigning a weak zone beneath the ridge. Time-dependent boundary conditions for velocity are imposed on the simulation in order to model a transient spreading period. The change of sign in plate velocities is found to be useful for both obtaining obduction / ophiolite emplacement [Duretz et al., 2016] and causing back-arc extension. Changes in velocities are linear in time. Simulations follow a three-phase evolution of velocity boundary conditions consisting of two convergent phases separated by a single divergent phase where spreading regime is dominant. Effect of duration and magnitude of the second phase on model evolution is also explored.</p><p>Our so far obtained simulations were able to reproduce the westward obduction and certain extension processes along the active (European) margin, which match the existing geological relationships. However, the simulations involve an unreasonably short geodynamic event (cca 15-20 My) and we are working on solving this problem with new simulations. </p>

Laboratory Simulation and Analysis of Wave Groups

2006 ◽  
Author(s):  
R. Balaji ◽  
S. A. Sannasiraj ◽  
V. Sundar
Keyword(s):  
Wave Height ◽  
Significant Wave Height ◽  
Region Of Interest ◽  
Offshore Structures ◽  
Laboratory Simulation ◽  
Frequency Of Occurrence ◽  
Wave Groups ◽  
Wave Flume ◽  
The Stability ◽  
Wave Elevations

The coastal and offshore structures are some times exposed to group of waves with successive higher wave elevations exceeding the significant wave height, which is considered to be vulnerable for the stability of the structures. Hence, the knowledge on the existence and frequency of occurrence of ocean wave groups at a particular region of interest is important for the design of the ocean structures. In the present study, the wave groups were simulated theoretically and the same was generated in the laboratory wave flume. The measured wave elevations were analysed through statistical, spectral and wavelet approaches to detect the existence of the groupiness.

scholarly journals Charging of Superconducting Layers in Arrays of Coupled Josephson Junctions for Overcritical Currents

Crystals ◽  
2019 ◽  
Vol 9 (7) ◽  
pp. 327 ◽  
Author(s):  
Marina Cuzminschi ◽  
Alexei Zubarev
Keyword(s):  
Fourier Transform ◽  
Boundary Conditions ◽  
Charge Density Wave ◽  
Josephson Junctions ◽  
Density Wave ◽  
Capacitive Coupling ◽  
Spectral Structure ◽  
Phase Dynamics ◽  
Additional Branch ◽  
Lower Voltage

In this work, we effectuated the numerical simulations of the phase dynamics of an array of Josephson junctions taking into account the capacitive coupling between the neighboring junctions and the diffusion current in the stack. We observed that, if we increase the coupling and the dissipation parameters, the IV characteristic changes qualitatively from the IV characteristics studied before. For currents greater than the critical one, we obtained an additional branch in the IV characteristics. This branch is characterized by a lower voltage than the outermost one. Moreover, we obtained an additional charging of the superconducting layers in the IV region for currents greater than the critical one. We studied the time evolution of this charging by the means of Fast Fourier Transform. We proved that the charge density wave associated with this charging has a complex spectral structure. In addition, we analyzed the behavior of the system for different boundary conditions, appropriate to different experimental setups.

The physical simulation of wave groups and their variations in a wave flume

2013 ◽  
Vol 32 (11) ◽  
pp. 68-73 ◽  
Author(s):  
Si Liu ◽  
Yongliang Zhang ◽  
Shuxue Liu ◽  
Jinxuan Li ◽  
Zhisheng Xia
Keyword(s):  
Physical Simulation ◽  
Wave Groups ◽  
Wave Flume

Confined states in phase dynamics: The influence of boundary conditions and transient behavior

1990 ◽  
Vol 42 (4) ◽  
pp. 2101-2113 ◽  
Author(s):  
Robert J. Deissler ◽  
Y. C. Lee ◽  
Helmut R. Brand
Keyword(s):  
Boundary Conditions ◽  
Transient Behavior ◽  
Phase Dynamics

scholarly journals Introduction: Active Margins in Transition—Magmatism and Tectonics through Time: An Issue in Honor of Arthur W. Snoke

Geosphere ◽  
2021 ◽  
Author(s):  
Allen J. McGrew ◽  
Joshua J. Schwartz
Keyword(s):  
Boundary Conditions ◽  
Plate Tectonics ◽  
Time And Space ◽  
Active Margin ◽  
Broad Scope ◽  
Active Margins

The evolution of active margins through time is the record of plate tectonics as inscribed on the continents. This themed issue honors the eclectic contributions of Arthur W. Snoke (Fig. 1) to the study of active margins with a series of papers that amply demonstrate the broad scope of active margin tectonics and the diverse methods that tectonic geologists employ to decipher their histories. Taken together, this set of papers illustrates the diversity of boundary conditions that guide the development of active margins and the key parameters that regulate their evolution in time and space.

scholarly journals Emergence of coherent wave groups in deep-water random sea

2013 ◽  
Vol 87 (6) ◽  
Author(s):  
C. Viotti ◽  
D. Dutykh ◽  
J. M. Dudley ◽  
F. Dias
Keyword(s):  
Deep Water ◽  
Wave Groups ◽  
Coherent Wave

A SPH numerical wave flume with non-reflective open boundary conditions

2018 ◽  
Vol 163 ◽  
pp. 483-501 ◽  
Author(s):  
Xingye Ni ◽  
Weibing Feng ◽  
Shichang Huang ◽  
Yu Zhang ◽  
Xi Feng
Keyword(s):  
Boundary Conditions ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Numerical Wave Flume ◽  
Wave Flume ◽  
Numerical Wave

scholarly journals The Peregrine Breather on the Zero-Background Limit as the Two-Soliton Degenerate Solution: An Experimental Study

2021 ◽  
Vol 9 ◽  
Author(s):  
Amin Chabchoub ◽  
Alexey Slunyaev ◽  
Norbert Hoffmann ◽  
Frederic Dias ◽  
Bertrand Kibler ◽  
...  
Keyword(s):  
Free Water ◽  
High Amplitude ◽  
Finite Amplitude ◽  
Surface Boundary ◽  
Wave Amplification ◽  
Wave Flume ◽  
Degenerate Solution ◽  
Surface Boundary Conditions ◽  
Bose Einstein ◽  
Peregrine Breather

Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known as the degenerate two-soliton which also leads to high amplitude maxima. In this study, we report several observations of such multi-soliton with doubly-localized peaks in a water wave flume. The data collected in this experiment confirm the distinctive attainment of wave amplification by a factor of two in good agreement with the dynamics of the nonlinear Schrödinger equation solution. Advanced numerical simulations solving the problem of nonlinear free water surface boundary conditions of an ideal fluid quantify the physical limitations of the degenerate two-soliton in hydrodynamics.

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