scholarly journals Measurement of the velocity field in parametrically excited solitary waves

2014 ◽  
Vol 754 ◽  
pp. 590-604 ◽  
Author(s):  
Leonardo Gordillo ◽  
Nicolás Mujica
Keyword(s):  
Velocity Field ◽  
Solitary Waves ◽  
Current Theory ◽  
Parametrically Excited ◽  
Localized Structures ◽  
Hamiltonian Models ◽  
Oscillating Boundary ◽  
Vorticity Equations ◽  
Streaming Velocity ◽  
Vertical Vibrations

AbstractParametrically excited solitary waves emerge as localized structures in high-aspect-ratio free surfaces subject to vertical vibrations. Herein, we provide the first experimental characterization of the hydrodynamics of these waves using particle image velocimetry. We show that the underlying velocity field of parametrically excited solitary waves is primarily composed of a subharmonic oscillatory component. Our results confirm the accuracy of Hamiltonian models with added dissipation in describing this field. Remarkably, our measurements also uncover the onset of a streaming velocity field which we show to be as important as other crucial nonlinear terms in the current theory. Using vorticity equations, we show that the streaming pattern arises from the coupling of the potential bulk flow with the oscillating boundary layers on the vertical walls. Numerical simulations provide good agreement between this model and experiments.

Observation of a standing kink cross wave parametrically excited

1991 ◽  
Vol 434 (1891) ◽  
pp. 435-440 ◽  
Keyword(s):  
Solitary Waves ◽  
Theoretical Explanation ◽  
Vertical Oscillation ◽  
Cylindrical Tank ◽  
Hyperbolic Tangent ◽  
Parametrically Excited ◽  
Short Side ◽  
Kink Wave ◽  
Forced Waves ◽  
Wave Properties

A layer of water in a cylindrical tank is known to be capable of sustaining standing solitary waves within a certain parametric domain when the tank is excited under vertical oscillation. A new mode of forced waves is discovered to exist in a different parametric domain for rectangular tanks with the wave sloshing across the short side of the tank and with its profile modulated by one or more hyperbolic-tangent, or kink-wave-like envelopes. A theoretical explanation for the kink wave properties is provided. Experiments were performed to confirm their existence.

Folded Solitary Waves and Foldons in the (2+1)-Dimensional Long Dispersive Wave Equation

2003 ◽  
Vol 58 (5-6) ◽  
pp. 280-284
Author(s):  
J.-F. Zhang ◽  
Z.-M. Lu ◽  
Y.-L. Liu
Keyword(s):  
Wave Equation ◽  
Solitary Waves ◽  
Coherent Structures ◽  
Bäcklund Transformation ◽  
Dispersive Wave ◽  
Variable Separation ◽  
New Class ◽  
Localized Structures ◽  
Dispersive Wave Equation ◽  
03.65 Ge

By means of the Bäcklund transformation, a quite general variable separation solution of the (2+1)- dimensional long dispersive wave equation: λqt + qxx − 2q ∫ (qr)xdy = 0, λrt − rxx + 2r ∫ (qr)xdy= 0, is derived. In addition to some types of the usual localized structures such as dromion, lumps, ring soliton and oscillated dromion, breathers soliton, fractal-dromion, peakon, compacton, fractal and chaotic soliton structures can be constructed by selecting the arbitrary single valued functions appropriately, a new class of localized coherent structures, that is the folded solitary waves and foldons, in this system are found by selecting appropriate multi-valuded functions. These structures exhibit interesting novel features not found in one-dimensions. - PACS: 03.40.Kf., 02.30.Jr, 03.65.Ge.

A New Class of (2+1)-Dimensional Combined Structures with Completely Elastic and Non-Elastic Interactive Properties

2006 ◽  
Vol 61 (1-2) ◽  
pp. 53-59 ◽  
Author(s):  
Cheng-Lin Bai ◽  
Cheng-Jie Bai ◽  
Hong Zhao
Keyword(s):  
Solitary Waves ◽  
Balance Method ◽  
Physical Models ◽  
Variable Separation ◽  
New Class ◽  
Localized Structures ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

Taking the new (2+1)-dimensional generalized Broer-Kaup system as an example, we obtain an exact variable separation excitation which can describe some quite universal (2+1)-dimensional physical models, with the help of the extended homogeneous balance method. Based on the derived excitation, a new class of combined structures, i. e., semifolded solitary waves and semifoldons, is defined and studied. The interactions of the semifolded localized structures are illustrated both analytically and graphically. - PACS numbers: 05.45.Yv, 02.30.Jr, 02.30.Ik

Interaction dynamics of solitary waves on a falling film

1995 ◽  
Vol 294 ◽  
pp. 123-154 ◽  
Author(s):  
H.-C. Chang ◽  
E. Demekhin ◽  
E. Kalaidin
Keyword(s):  
Solitary Waves ◽  
Structure Theory ◽  
Binary Interaction ◽  
Falling Film ◽  
Wave Dynamics ◽  
Localized Structures ◽  
Physical Experiments ◽  
Solitary Pulse ◽  
Short Transition ◽  
Simple Dynamical System

Beyond a short transition region near the inlet, waves on a falling film evolve into distinct pulse-like solitary waves that dominate all subsequent interfacial dynamics. Numerical and physical experiments indicate that these localized structures can attract and repel each other. Attractive interaction through the capillary ripples of the pulses causes two pulses to coalesce into a bigger pulse which accelerates and precipitates further coalescence. This binary interaction between an ‘excited’ pulse after coalescence and its smaller front neighbour is the key mechanism that drives the observed wave dynamics. From symmetry arguments, two dominant modes for a solitary pulse are obtained and used to develop an inelastic coherent structure theory for binary interaction between an excited pulse and its front neighbour. The theory offers a simple dynamical system that quantitatively describes the binary interaction and promises to elucidate the complex wave dynamics on a falling film.

Small-amplitude analysis of a non-thermal variable charge dust soliton

2008 ◽  
Vol 74 (4) ◽  
pp. 555-568
Author(s):  
MOULOUD TRIBECHE
Keyword(s):  
Solitary Waves ◽  
Vlasov Equation ◽  
Small Amplitude ◽  
Dusty Plasmas ◽  
Physical Parameters ◽  
Amplitude Analysis ◽  
Variable Charge ◽  
Localized Structures ◽  
Self Consistent ◽  
Solitary Structures

AbstractSmall-amplitude electrostatic solitary waves are investigated in an unmagnetized dusty plasma with hot variable charge non-thermal dust grains. These nonlinear localized structures are small-amplitude self-consistent solutions of the Vlasov equation in which the dust response is non-Maxwellian. Localized solitary structures that may possibly occur are discussed and the dependence of their characteristics on physical parameters is traced. Our investigation may be taken as a prerequisite for the understanding of the electrostatic solitary waves that may occur in space dusty plasmas.

SOLITARY WAVES, SOLITON BOUND STATES AND CHAOS IN A DISSIPATIVE KORTEWEG-DE VRIES EQUATION

1994 ◽  
Vol 04 (05) ◽  
pp. 1135-1146 ◽  
Author(s):  
VLADIMIR I. NEKORKIN ◽  
MANUEL G. VELARDE
Keyword(s):  
Internal Waves ◽  
Solitary Waves ◽  
Liquid Layer ◽  
Bound States ◽  
Vries Equation ◽  
Stratified Fluid ◽  
Localized Structures ◽  
Fluid Layers ◽  
De Vries ◽  
Wave Trains

Propagating dissipative (localized) structures like solitary waves, pulses or “solitons,” “bound solitons,” and “chaotic” wave trains are shown to be solutions of a dissipation-modified Korteweg-de Vries equation that in particular appears in Marangoni-Bénard convection when a liquid layer is heated from the air side and in the description of internal waves in sheared, stably stratified fluid layers.

Steady solution of the velocity field of steep solitary waves

2018 ◽  
Vol 73 ◽  
pp. 70-79 ◽  
Author(s):  
W.Y. Duan ◽  
Z. Wang ◽  
B.B. Zhao ◽  
R.C. Ertekin ◽  
J.W. Kim
Keyword(s):  
Velocity Field ◽  
Solitary Waves ◽  
Steady Solution
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