scholarly journals Numerical Study on Weakly Nonlinear Evolution of Pressure Waves in Water Flows Containing Many Translational Bubbles Acting a Drag Force

2021 ◽  
Vol 35 (2) ◽  
pp. 356-364
Author(s):  
Takahiro YATABE ◽  
Tetsuya KANAGAWA ◽  
Takahiro AYUKAI
Keyword(s):  
Drag Force ◽  
Nonlinear Evolution ◽  
Numerical Study ◽  
Pressure Waves ◽  
Weakly Nonlinear ◽  
Water Flows

Weakly nonlinear propagation of pressure waves in liquids containing translational bubbles acting a drag force

2019 ◽  
Vol 146 (4) ◽  
pp. 3078-3078
Author(s):  
Takahiro Yatabe ◽  
Takahiro Ayukai ◽  
Tetsuya Kanagawa
Keyword(s):  
Drag Force ◽  
Nonlinear Propagation ◽  
Pressure Waves ◽  
Weakly Nonlinear

scholarly journals Theoretical elucidation of effect of drag force and translation of bubble on weakly nonlinear pressure waves in bubbly flows

2021 ◽  
Vol 33 (3) ◽  
pp. 033315
Author(s):  
Takahiro Yatabe ◽  
Tetsuya Kanagawa ◽  
Takahiro Ayukai
Keyword(s):  
Drag Force ◽  
Bubbly Flows ◽  
Pressure Waves ◽  
Weakly Nonlinear

scholarly journals Electrodynamics of a magnet moving through a conducting pipe

2006 ◽  
Vol 84 (4) ◽  
pp. 253-271 ◽  
Author(s):  
M Hossein Partovi ◽  
Eliza J Morris
Keyword(s):  
Drag Force ◽  
Eddy Currents ◽  
Numerical Study ◽  
Full Range ◽  
Magnetic Behavior ◽  
Integral Form ◽  
Asymptotic Formulas ◽  
Pipe Material ◽  
Point Dipole ◽  
Axially Symmetric

The popular demonstration involving a permanent magnet falling through a conducting pipe is treated as an axially symmetric boundary-value problem. Specifically, Maxwell's equations are solved for an axially symmetric magnet moving coaxially inside an infinitely long, conducting cylindrical shell of arbitrary thickness at nonrelativistic speeds. Analytic solutions for the fields are developed and used to derive the resulting drag force acting on the magnet in integral form. This treatment represents a significant improvement over existing models, which idealize the problem as a point dipole moving slowly inside a pipe of negligible thickness. It also provides a rigorous study of eddy currents under a broad range of conditions, and can be used for magnetic braking applications. The case of a uniformly magnetized cylindrical magnet is considered in detail, and a comprehensive analytical and numerical study of the properties of the drag force is presented for this geometry. Various limiting cases of interest involving the shape and speed of the magnet and the full range of conductivity and magnetic behavior of the pipe material are investigated and corresponding asymptotic formulas are developed.PACS Nos.: 81.70.Ex, 41.20.–q, 41.20.Gz

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.

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