Dispersion relation for nonlinear waves in a fluid with gas bubbles

1989 ◽  
Vol 29 (5) ◽  
pp. 688-690
Author(s):  
S. I. Plaksin
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Waves ◽  
Gas Bubbles

Stability of strong electromagnetic waves in overdense plasmas against long-wavelength perturbations

1985 ◽  
Vol 33 (2) ◽  
pp. 285-301 ◽  
Author(s):  
F. J. Romeiras ◽  
G. Rowlands
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Waves ◽  
Electromagnetic Waves ◽  
Modulation Depth ◽  
Longitudinal Direction ◽  
Transverse Component ◽  
Ion Density ◽  
Long Wavelength ◽  
The Stability ◽  
Two Parameters

We consider the stability against long-wavelength small parallel perturbations of a class of exact standing wave solutions of the equations that describe an unmagnetized relativistic overdense cold electron plasma. The main feature of these nonlinear waves is a circularly polarized transverse component of the electric field periodically modulated in the longitudinal direction. Using an analytical method developed by Rowlands we obtain a dispersion relation valid for long-wavelength perturbations. This dispersion relation is a biquadratic equation in the phase velocity of the perturbations whose coefficients are very complicated functions of the two parameters used to define the nonlinear waves: the normalized ion density and a quantity related to the modulation depth. This dispersion relation is discussed for the whole range of the two parameters revealing, in particular, the existence of a region in parameter space where the nonlinear waves are stable.

scholarly journals Equation for the three-dimensional nonlinear waves in liquid with gas bubbles

2012 ◽  
Vol 85 (2) ◽  
pp. 025402 ◽  
Author(s):  
Nikolay A Kudryashov ◽  
Dmitry I Sinelshchikov
Keyword(s):  
Nonlinear Waves ◽  
Three Dimensional ◽  
Gas Bubbles

Pressure and Shock Waves in Bubbly Liquids

2015 ◽  
Author(s):  
Shahid Mahmood ◽  
Yungpil Yoo ◽  
Ho-Young Kwak
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Dispersion Relation ◽  
Sound Propagation ◽  
Relaxation Oscillation ◽  
Bubbly Flow ◽  
Gas Bubbles ◽  
Bubbly Liquid ◽  
Bubbly Liquids ◽  
Pressure Profiles

It is well known that sound propagation in liquid media is strongly affected by the presence of gas bubbles that interact with sound and in turn affect the medium. An explicit form of a wave equation in a bubbly liquid medium was obtained in this study. Using the linearized wave equation and the Keller-Miksis equation for bubble wall motion, a dispersion relation for the linear pressure wave propagation in bubbly liquids was obtained. It was found that attenuation of the waves in bubbly liquid occurs due to the viscosity and the heat transfer from/to the bubble. In particular, at the lower frequency region, the thermal diffusion has a considerable affect on the frequency-dependent attenuation coefficients. The phase velocity and the attenuation coefficient obtained from the dispersion relation are in good agreement with the observed values in all sound frequency ranges from kHz to MHz. Shock wave propagation in bubbly mixtures was also considered with the solution of the wave equation, whose particular solution represents the interaction between bubbles. The calculated pressure profiles are in close agreement with those obtained in shock tube experiments for a uniform bubbly flow. Heat exchange between the gas bubbles and the liquid and the interaction between bubbles were found to be very important factor to affect the relaxation oscillation behind the the shock front.

Nonlinear waves in a liquid containing gas bubbles with allowance for phase transition

1989 ◽  
Vol 24 (3) ◽  
pp. 421-426
Author(s):  
A. G. Bondarenko ◽  
N. A. Kudryashov
Keyword(s):  
Phase Transition ◽  
Nonlinear Waves ◽  
Gas Bubbles

The dispersion relation for nonlinear waves in a developing process

1986 ◽  
Vol 4 (3) ◽  
pp. 256-277 ◽  
Author(s):  
Gu Daifang ◽  
Yuan Yeli
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Waves

Propagation and interaction of nonlinear waves in a liquid with gas bubbles

2011 ◽  
Vol 57 (2) ◽  
pp. 224-229
Author(s):  
Yu. P. Bodunova ◽  
S. A. Konoplev ◽  
A. I. Potapov
Keyword(s):  
Nonlinear Waves ◽  
Gas Bubbles

THE ANISOTROPIC CHARACTERS IN TWO-DIMENSIONAL LATTICE

2013 ◽  
Vol 27 (07) ◽  
pp. 1361010
Author(s):  
YANG YANG ◽  
MAI-MAI LIN ◽  
WEN-SHAN DUAN
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Waves ◽  
Particle Displacement ◽  
Transverse Waves ◽  
Compressional Waves ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Special Cases ◽  
Linear And Nonlinear

The anisotropic characters of simple cubic lattice are investigated in this paper. Both the linear and nonlinear wave propagating in this lattice have been studied. The dispersion relation has been studied numerically. It is shown that the dispersion relation strongly depends on the directions of wave propagation. Generally, the direction of waves has the inclination angle α with respect to particle displacement. There are compressional waves α = 0 or transverse waves α = π/2 only for some special cases. The nonlinear waves in this lattice have also been studied. The anisotropic characters of this lattice for the nonlinear waves have also been shown. The compressional and transverse nonlinear solitons have also been studied. The characters of both solitons, such as amplitude and width, have been investigated.

Nonlinear waves in liquids with gas bubbles with account of viscosity and heat transfer

2010 ◽  
Vol 45 (1) ◽  
pp. 96-112 ◽  
Author(s):  
N. A. Kudryashov ◽  
D. I. Sinel’shchikov
Keyword(s):  
Heat Transfer ◽  
Nonlinear Waves ◽  
Gas Bubbles

Quasi-Exact Solutions of the Equation for Description of Nonlinear Waves in a Liquid with Gas Bubbles

2014 ◽  
Vol 74 (3) ◽  
pp. 399-408 ◽  
Author(s):  
Mark B. Kochanov ◽  
Nikolay A. Kudryashov
Keyword(s):  
Exact Solutions ◽  
Nonlinear Waves ◽  
Gas Bubbles

scholarly journals An extended equation for the description of nonlinear waves in a liquid with gas bubbles

Wave Motion ◽  
2013 ◽  
Vol 50 (3) ◽  
pp. 351-362 ◽  
Author(s):  
Nikolai A. Kudryashov ◽  
Dmitry I. Sinelshchikov
Keyword(s):  
Nonlinear Waves ◽  
Gas Bubbles
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