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.

Comment on ‘Propagation of solitary waves and shock wavelength in the pair plasma (J. Plasma Phys. 78, 525–529, 2012)’

2014 ◽  
Vol 80 (3) ◽  
pp. 513-516
Author(s):  
Frank Verheest
Keyword(s):  
Shock Wave ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Plasma Phys ◽  
Theoretical Underpinning ◽  
Pair Plasma ◽  
Electrons And Positrons ◽  
Small Dissipation ◽  
Pseudopotential Approach ◽  
Wave Properties

In a recent paper ‘Propagation of solitary waves and shock wavelength in the pair plasma (J. Plasma Phys. 78, 525–529, 2012)’, Malekolkalami and Mohammadi investigate nonlinear electrostatic solitary waves in a plasma comprising adiabatic electrons and positrons, and a stationary ion background. The paper contains two parts: First, the solitary wave properties are discussed through a pseudopotential approach, and then the influence of a small dissipation is intuitively sketched without theoretical underpinning. Small dissipation is claimed to lead to a shock wave whose wavelength is determined by linear oscillator analysis. Unfortunately, there are errors and inconsistencies in both the parts, and their combination is incoherent.

Parametrically excited solitary waves

1984 ◽  
Vol 148 ◽  
pp. 451-460 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Complex Amplitude ◽  
Clean Water ◽  
Vertical Oscillation ◽  
Capillary Length ◽  
Cubic Schrödinger Equation ◽  
Limiting Case ◽  
Long Channel ◽  
Weak Damping

A modulated cross-wave of resonant frequencyω1, carrier frequencyω =ω1 {1 + O(ε)}, slowly varying complex amplitude O(ε½b), longitudinal scale b/ε½ and timescale 1/εω is induced in a long channel of breadth b that contains water of depth d and is subjected to a vertical oscillation of amplitude O(εb) and frequency 2ω, where 0 < ε [Lt ] 1. The complex amplitude satisfies a cubic Schrödinger equation, generalized to incorporate weak damping and the parametric excitation. A solution is obtained that describes the standing solitary wave observed by Wu, Keolian & Rudnick (1984). The results depend on both d/b and l*/b, where l* is the capillary length (l* = 2.7 mm for clean water), and solitary waves are impossible if d/b < 0.325 for l*/b = 0 or if l*/b > 0.045 for d/b [gsim ] 1. The corresponding cnoidal waves (of which the solitary wave is a limiting case) are considered in an appendix.

scholarly journals Transverse instability of gravity–capillary solitary waves on deep water in the presence of constant vorticity

2019 ◽  
Vol 871 ◽  
pp. 1028-1043
Author(s):  
M. Abid ◽  
C. Kharif ◽  
H.-C. Hsu ◽  
Y.-Y. Chen
Keyword(s):  
Growth Rate ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Deep Water ◽  
Capillary Waves ◽  
Two Dimensional ◽  
Transverse Instability ◽  
Constant Vorticity ◽  
Dimensional Gravity ◽  
Wave Properties

The bifurcation of two-dimensional gravity–capillary waves into solitary waves when the phase velocity and group velocity are nearly equal is investigated in the presence of constant vorticity. We found that gravity–capillary solitary waves with decaying oscillatory tails exist in deep water in the presence of vorticity. Furthermore we found that the presence of vorticity influences strongly (i) the solitary wave properties and (ii) the growth rate of unstable transverse perturbations. The growth rate and bandwidth instability are given numerically and analytically as a function of the vorticity.

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.

Extreme solitary waves on falling liquid films

2014 ◽  
Vol 745 ◽  
pp. 564-591 ◽  
Author(s):  
S. Chakraborty ◽  
P.-K. Nguyen ◽  
C. Ruyer-Quil ◽  
V. Bontozoglou
Keyword(s):  
Solitary Waves ◽  
Detailed Comparison ◽  
Liquid Films ◽  
Equation Model ◽  
Local Flow ◽  
Liquid Film Flow ◽  
Wave Models ◽  
Low Dimensional ◽  
Falling Liquid Films ◽  
Wave Properties

AbstractDirect numerical simulation (DNS) of liquid film flow is used to compute fully developed solitary waves and to compare their characteristics with the predictions of low-dimensional models. Emphasis is placed on the regime of high inertia, where available models provide widely differing results. It is found that the parametric dependence of wave properties on inertia is highly non-trivial, and is satisfactorily approximated only by the four-equation model of Ruyer-Quil & Manneville (Eur. Phys. J. B, vol. 15, 2000, pp. 357–369). Detailed comparison of the asymptotic shapes of upstream and downstream tails is performed, and inherent limitations of all long-wave models are revealed. Local flow reversal in front of the main hump, which has been previously discussed in the literature, is shown to occur for an inertia range bounded from below and from above, and the boundaries are interpreted in terms of the capillary origin of the phenomenon. Computational results are reported for the entire range of Froude numbers, providing benchmark data for all wall inclinations.

Forced solitary waves over complex topography

2021 ◽  
Author(s):  
Nikolay Makarenko ◽  
Danila Denisenko
Keyword(s):  
Solitary Waves ◽  
Stationary Flow ◽  
Free Surface Flows ◽  
Specific Class ◽  
Complex Topography ◽  
Wave Trapping ◽  
Small Height ◽  
Forced Waves ◽  
A Chain ◽  
Von Mises

&lt;p&gt;In present paper we consider the problem on solitary waves forced by a chain of gently sloped obstacles of small height. Steady two-dimensional free-surface flows over a complex topography are studied analytically in the case when the far upstream flow is slightly supercritical. Small height- and steepness restrictions are important here since these circumstances provide the balance between nonlinear dispersion and hydraulic effects both affecting nearly hydrostatic non-uniform flow. Fully non-linear irrotational Euler equations are formulated via the von Mises transformation that parametrizes the family of streamlines in a curvilinear flow domain. It is well known that the critical value of the Froude number is the bifurcation point providing non-uniqueness of stationary flow. In present work, we construct and analyze approximate solitary-wave solutions by using long-wave expansion procedure with two small parameters.&amp;#160; In addition, we apply the Lyapunov - Schmidt method which ensures an analytical condition of the wave-trapping formulated in terms of the Melnikov function. A specific class of multi-bumped topographies is considered in order to demonstrate multiplicity of forced waves. The amount of different wave regimes depends on the number of bumps and pits, as well as on their location and size in relation to each other.&lt;/p&gt;

Dynamical behavior of parametrically excited solitary waves in Faraday's water trough experiment

1996 ◽  
Vol 219 (1-2) ◽  
pp. 74-78 ◽  
Author(s):  
Wei Wang ◽  
Xinlong Wang ◽  
Junyi Wang ◽  
Rongjue Wei
Keyword(s):  
Solitary Waves ◽  
Dynamical Behavior ◽  
Parametrically Excited ◽  
Water Trough
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