Weakly nonlinear evolution of pressure waves in a polydisperse bubbly liquid

2021 ◽  
Vol 149 (4) ◽  
pp. A30-A30
Author(s):  
Takuma Kawame ◽  
Tetsuya Kanagawa
Keyword(s):  
Nonlinear Evolution ◽  
Bubbly Liquid ◽  
Pressure Waves ◽  
Weakly Nonlinear

scholarly journals Models for strongly-nonlinear evolution of long internal waves in a two-layer stratification

2007 ◽  
Vol 14 (1) ◽  
pp. 31-47 ◽  
Author(s):  
T. Sakai ◽  
L. G. Redekopp
Keyword(s):  
Internal Waves ◽  
Nonlinear Evolution ◽  
Phase Speed ◽  
Environmental Parameters ◽  
Exact Expression ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Polynomial Fit ◽  
Nonlinear Relation ◽  
Nonlinear Extensions

Abstract. Models describing the evolution of long internal waves are proposed that are based on different polynomial approximations of the exact expression for the phase speed of uni-directional, fully-nonlinear, infinitely-long waves in the two-layer model of a density stratified environment. It is argued that a quartic KdV model, one that employs a cubic polynomial fit of the separately-derived, nonlinear relation for the phase speed, is capable of describing the evolution of strongly-nonlinear waves with a high degree of fidelity. The marginal gains obtained by generating higher-order, weakly-nonlinear extensions to describe strongly-nonlinear evolution are clearly demonstrated, and the limitations of the quite widely-used quadratic-cubic KdV evolution model obtained via a second-order, weakly-nonlinear analysis are assessed. Data are presented allowing a discriminating comparison of evolution characteristics as a function of wave amplitude and environmental parameters for several evolution models.

W-shape bright and several other solutions to the (3+1)-dimensional nonlinear evolution equations

2021 ◽  
pp. 2150468
Author(s):  
Youssoufa Saliou ◽  
Souleymanou Abbagari ◽  
Alphonse Houwe ◽  
M. S. Osman ◽  
Doka Serge Yamigno ◽  
...  
Keyword(s):  
Acoustic Waves ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Singular Function ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Quantum Electron ◽  
Ion Acoustic ◽  
Trigonometric Function Solutions

By employing the Modified Sardar Sub-Equation Method (MSEM), several solitons such as W-shape bright, dark solitons, trigonometric function solutions and singular function solutions have been obtained in two famous nonlinear evolution equations which are used to describe waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in a plasma. These models are the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation and the (3+1)-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation, respectively. Comparing the obtained results with Refs. 32–34 and Refs. 43–46, additional soliton-like solutions have been retrieved and will be useful in future to explain the interaction between lower nonlinear ion-acoustic waves and the parameters of the MSEM and the obtained figures will have more physical explanation.

Nonlinear dynamics of the elliptic instability

2010 ◽  
Vol 646 ◽  
pp. 471-480 ◽  
Author(s):  
NATHANAËL SCHAEFFER ◽  
STÉPHANE LE DIZÈS
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulations ◽  
Shear Layer ◽  
Rapid Growth ◽  
Vortex Core ◽  
Nonlinear Evolution ◽  
Core Size ◽  
Layer Formation ◽  
Vortex Loop ◽  
Weakly Nonlinear

In this paper, we analyse by numerical simulations the nonlinear dynamics of the elliptic instability in the configurations of a single strained vortex and a system of two counter-rotating vortices. We show that although a weakly nonlinear regime associated with a limit cycle is possible, the nonlinear evolution far from the instability threshold is, in general, much more catastrophic for the vortex. In both configurations, we put forward some evidence of a universal nonlinear transition involving shear layer formation and vortex loop ejection, leading to a strong alteration and attenuation of the vortex, and a rapid growth of the vortex core size.

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