Solitary waves on a free surface of a heated Maxwell fluid

2008 ◽  
Vol 465 (2101) ◽  
pp. 109-121 ◽  
Author(s):  
D Comissiong ◽  
R.A Kraenkel ◽  
M.A Manna
Keyword(s):  
Free Surface ◽  
Temperature Gradient ◽  
Solitary Waves ◽  
Vries Equation ◽  
Maxwell Fluid ◽  
Oscillatory Instability ◽  
Thermal Gradients ◽  
Nonlinear Structures ◽  
Long Wave ◽  
Specific Influence

The existence of an oscillatory instability in the Bénard–Marangoni phenomenon for a viscoelastic Maxwell's fluid is explored. We consider a fluid that is bounded above by a free deformable surface and below by an impermeable bottom. The fluid is subject to a temperature gradient, inducing instabilities. We show that due to balance between viscous dissipation and energy injection from thermal gradients, a long-wave oscillatory instability develops. In the weak nonlinear regime, it is governed by the Korteweg–de Vries equation. Stable nonlinear structures such as solitons are thus predicted. The specific influence of viscoelasticity on the dynamics is discussed and shown to affect the amplitude of the soliton, pointing out the possible existence of depression waves in this case. Experimental feasibility is examined leading to the conclusion that for realistic fluids, depression waves should be more easily seen in the Bénard–Marangoni system.

scholarly journals Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface

2002 ◽  
Vol 9 (3/4) ◽  
pp. 221-235 ◽  
Author(s):  
R. Grimshaw ◽  
E. Pelinovsky ◽  
O. Poloukhina
Keyword(s):  
Free Surface ◽  
Shear Flow ◽  
Solitary Waves ◽  
Vries Equation ◽  
Wave Theory ◽  
Higher Order ◽  
Internal Solitary Waves ◽  
Long Wave ◽  
De Vries ◽  
Stratified Shear Flow

Abstract. A higher-order extension of the familiar Korteweg-de Vries equation is derived for internal solitary waves in a density- and current-stratified shear flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed in terms of integrals of the modal function for the linear long-wave theory. An illustrative example of a two-layer shear flow is considered, for which we discuss the parameter dependence of the coefficients in the extended Korteweg-de Vries equation.

A reformulation and applications of interfacial fluids with a free surface

2009 ◽  
Vol 631 ◽  
pp. 375-396 ◽  
Author(s):  
T. S. HAUT ◽  
M. J. ABLOWITZ
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Solitary Waves ◽  
Wave Equations ◽  
Computational Studies ◽  
Free Interface ◽  
Long Wave ◽  
Ideal Fluids ◽  
Non Local ◽  
Two Fluid

A non-local formulation, depending on a free spectral parameter, is presented governing two ideal fluids separated by a free interface and bounded above either by a free surface or by a rigid lid. This formulation is shown to be related to the Dirichlet–Neumann operators associated with the two-fluid equations. As an application, long wave equations are obtained; these include generalizations of the Benney–Luke and intermediate long wave equations, as well as their higher order perturbations. Computational studies reveal that both equations possess lump-type solutions, which indicate the possible existence of fully localized solitary waves in interfacial fluids with sufficient surface tension.

Solitary waves in a dusty adiabatic electronegative plasma

2010 ◽  
Vol 76 (3-4) ◽  
pp. 409-418 ◽  
Author(s):  
A. A. MAMUN ◽  
K. S. ASHRAFI ◽  
M. G. M. ANOWAR
Keyword(s):  
Solitary Waves ◽  
Vries Equation ◽  
Negative Ions ◽  
Finite Amplitude ◽  
Reductive Perturbation Method ◽  
Charged Dust ◽  
Electronegative Plasma ◽  
Ion Acoustic ◽  
Basic Features ◽  
Electronegative Plasmas

AbstractThe dust ion-acoustic solitary waves (SWs) in an unmagnetized dusty adiabatic electronegative plasma containing inertialess adiabatic electrons, inertial single charged adiabatic positive and negative ions, and stationary arbitrarily (positively and negatively) charged dust have been theoretically studied. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation which admits an SW solution. The combined effects of the adiabaticity of plasma particles, inertia of positive or negative ions, and presence of positively or negatively charged dust, which are found to significantly modify the basic features of small but finite-amplitude dust-ion-acoustic SWs, are explicitly examined. The implications of our results in space and laboratory dusty electronegative plasmas are briefly discussed.

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

On periodic water-waves and their convergence to solitary waves in the long-wave limit

1981 ◽  
Vol 303 (1481) ◽  
pp. 633-669 ◽  
Keyword(s):  
Integral Equation ◽  
Solitary Waves ◽  
Water Waves ◽  
Periodic Problem ◽  
Existence Theory ◽  
Periodic Waves ◽  
Equation Formulation ◽  
Long Wave ◽  
Integral Equation Formulation ◽  
Wave Limit

A detailed discussion of Nekrasov’s approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of Amick & Toland (1981) to show the convergence of periodic waves to solitary waves in the long-wave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasov leads, via the Maximum Principle, to new results about qualitative features of periodic waves for which there has long been a global existence theory (Krasovskii 1961, Keady & Norbury 1978).

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

A Theoretical Study of the Temperature Gradient Effect on the Soret Coefficient in n-Pentane/n-Decane Mixtures Using Non-Equilibrium Molecular Dynamics

2020 ◽  
Vol 45 (4) ◽  
pp. 319-332
Author(s):  
Xiaoyu Chen ◽  
Ruquan Liang ◽  
Yong Wang ◽  
Ziqi Xia ◽  
Lichun Wu ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Temperature Gradient ◽  
Thermal Gradient ◽  
Linear Response ◽  
Theoretical Study ◽  
Soret Coefficient ◽  
Thermal Gradients ◽  
Gradient Effect ◽  
Non Equilibrium Molecular Dynamics ◽  
Non Equilibrium

AbstractThe effect of the temperature gradient on the Soret coefficient in n-pentane/n-decane (n-C5/n-C10) mixtures was investigated using non-equilibrium molecular dynamics (NEMD) with the heat exchange (eHEX) algorithm. n-Pentane/n-decane mixtures with three different compositions (0.25, 0.5, and 0.75 mole fractions, respectively) and the TraPPE-UA force field were used in computing the Soret coefficient ({S_{T}}) at 300 K and 1 atm. Added/removed heat quantities (ΔQ) of 0.002, 0.004, 0.006, 0.008, and 0.01 kcal/mol were employed in eHEX processes in order to study the effect of different thermal gradients on the Soret coefficient. Moreover, a phenomenological description was applied to discuss the mechanism of this effect. Present results show that the Soret coefficient values firstly fluctuate violently and then become increasingly stable with increasing ΔQ (especially in the mixture with a mole fraction of 0.75), which means that ΔQ has a smaller effect on the Soret coefficient when the temperature gradient is higher than a certain thermal gradient. Thus, a high temperature gradient is recommended for calculating the Soret coefficient under the conditions that a linear response and constant phase are ensured in the system. In addition, the simulated Soret coefficient obtained at the highest ΔQ within three different compositions is in great agreement with experimental data.

scholarly journals Effect of temperature gradient on heavy quark anti-quark potential using gravity dual model

2020 ◽  
Author(s):  
S Ganesh ◽  
M Mishra
Keyword(s):  
Temperature Gradient ◽  
Gluon Plasma ◽  
Effect Of Temperature ◽  
Dual Model ◽  
Thermal Gradients ◽  
Imaginary Time ◽  
Thermal Systems ◽  
Naturally Occurring ◽  
Quark Potential ◽  
Stationary Approximation

Abstract Thermal systems have traditionally been modeled via Euclideanized space by analytical continuation of time to an imaginary time. We extend the concept to static thermal gradients by recasting the temperature variation as a variation in the Euclidean metric. We apply this prescription to determine the Quark anti-Quark potential in a system with thermal gradient. A naturally occurring QCD medium with thermal gradients is a Quark Gluon Plasma (QGP). However, the QGP evolves in time. Hence, we use a quasi-stationary approximation, which is applicable only if the rate of time evolution is slow. Hence the application of our proposal to a Quark anti-Quark potential in QGP can be seen as a step towards a more exact theory which would incorporate time varying thermal gradients. The effect of a static temperature gradient on the Quark anti-Quark potential is analyzed using a gravity dual model. A non-uniform black string metric is developed, by perturbing the Schwarzchild metric, which allows to incorporate the temperature gradient in the dual AdS space. Finally, an expression for the Quark anti-Quark potential, in the presence of a static temperature gradient, is derived.

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