Nonlinear Kelvin–Helmholtz instability of magnetized surface waves on a subsonic gas–viscous potential liquid interface

Sirwah, Magdy A.

doi:10.1016/j.physa.2006.09.029

Cited by 16 publications

(19 citation statements)

References 30 publications

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“…The case when S(2, 2k) = 0 for where 2 , ⌽ 2 ͑ j͒ , and ⌿ 2 ͑ j͒ , (j = 1, 2) become infinite, corresponds to the case of second harmonic resonance, which can be dealt with along the same lines outlined by Singla et al [37]; we have assumed this quantity to be different from zero in (25)- (27). (2) = 0.689 g/cm 3 , U (1) = 5 cm/s, U (2) = 7 cm/s, (1) = 0.8 cm 2 /s, (2) = 0.9 cm 2 /s, = (1) = 0.6, = (2) = 0.7, g = 981 cm/s 2 , and k y = 0 (normal curves) and 2 (curves with *).…”

Section: The Second-order Problemmentioning

confidence: 99%

“…Awasthi and Agrawal [21] have studied the viscous potential flow analysis of Kelvin-Helmholtz instability of a cylindrical interface and observed that the viscosity has a stabilizing effect. The viscous potential flow theory has been widely used in recent years, and attracts many researchers to study various linear and nonlinear stability problems of physical interest (Joseph and Liao [22], Joseph et al [23], Wang et al [24], Elcoot [25,26], Sirwah [27], Zakaria [28], Obied Allah [29], Awasthi and Agrawal [30], Awasthi et al [31], Moatimid and Hassan [32], and Asthana et al [33], among others).…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear electroviscoelastic potential flow instability theory of two superposed streaming dielectric fluids

et al. 2014

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The nonlinear electrohydrodynamic Kelvin-Helmholtz instability of two superposed viscoelastic Walters B= dielectric fluids in the presence of a tangential electric field is investigated in three dimensions using the potential flow analysis. The method of multiple scales is used to obtain a dispersion relation for the linear problem, and a nonlinear Ginzburg-Landau equation with complex coefficients for the nonlinear problem. The linear and nonlinear stability conditions are obtained and discussed both analytically and numerically. In the linear stability analysis, we found that the fluid velocities and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities, and surface tension have stabilizing effects; and that the system in the three-dimensional disturbances is more stable than in the corresponding case of twodimensional disturbances. While in the nonlinear analysis, for both two-and three-dimensional disturbances, we found that the fluid velocities, surface tension, and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities have stabilizing effects, and that the system in the three-dimensional disturbances is more unstable than its behavior in the two-dimensional disturbances for most physical parameters except the kinematic viscosities.Résumé : La méthode d'analyse du potentiel d'écoulement nous permet d'étudier l'instabilité électrodynamique non linéaire de type Kelvin-Helmholtz, de deux fluides diélectriques viscoélastiques de type Walter B= superposés, en présence d'un champ électrique tangentiel. Nous utilisons la méthode à échelles multiples pour obtenir la relation de dispersion du problème linéaire, alors que l'équation non linéaire de Ginzburg-Landau avec coefficients complexes pour le problème non linéaire. Nous obtenons et discutons les conditions de stabilité pour les cas linéaire et non linéaire, analytiquement et numériquement. Dans l'analyse de stabilité linéaire, nous trouvons que les vitesses de fluide et les viscosités cinématiques ont des effets déstabilisants, alors que le champ électrique, les viscoélasticités cinématiques et la tension superficielle sont stabilisants. Le système est plus stable contre les perturbations tridimensionnelles que contre les perturbations bidimensionnelles. Dans le cas non linéaire, pour des perturbations en deux et trois dimensions, nous trouvons que les vitesses de fluide, la tension superficielle et les viscosités cinématiques sont déstabilisants, alors que le champ électrique, les viscoélasticités cinématiques sont stabilisants. De plus, le système est plus instable dans son comportement sous perturbations en trois dimensions qu'en deux dimensions pour la plupart des paramètres physiques, sauf les viscosités cinématiques. [Traduit par la Rédaction]

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Section: The Second-order Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear electroviscoelastic potential flow instability theory of two superposed streaming dielectric fluids

et al. 2014

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“…Meanwhile, the viscosity occurred only at the interface. Sirwah studied the interface instability between two fluids, utilizing the viscous potential theory in his approach. Furthermore, he gave numerous examples to indicate the effects of the various parameters on the stability configuration.…”

Section: Introductionmentioning

confidence: 99%

The effect of a periodic tangential magnetic field on the stability of a horizontal magnetic fluid sheet

Moatimid

Eldabe

Sayed

2019

Heat Trans. Asian Res.

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The current article aims at investigating the effect of a periodic tangential magnetic field on the stability of a horizontal flat sheet. The media were considered porous, the three viscous-fluid layers were initially streaming with uniform velocities, and the magnetic field admitted the presence of free-surface currents. Furthermore, the transfer of mass and heat phenomenon was taken into account. The analysis, in this paper, was followed by the viscous potential theory. Moreover, the stability of the boundary-value problem resulted in coupled secondorder linear differential equations with damping and complex coefficients. In regard to the uniform and periodic magnetic field, the standard normal mode approach was applied to deduce a general dispersion relation and judge the stability criteria. In addition, several unfamiliar cases were reported, according to appropriate data choices. The stability conditions were theoretically analyzed, and the influences of the various parameters in the stability profile were identified through a set of diagrams. In accordance wth the oscillating field, the coupled dispersion equations were combined to give the established Mathieu equation. Therefore, the governed transition curves were, theoretically, obtained. Finally, the results were numerically confirmed. K E Y W O R D S magnetic field, mass and heat transfer, porous media, stability analysis, viscous potential flow

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“…Sirwah [23] applied viscous potential flow theory to study the Kelvin-Helmholtz instability in the presence of tangential magnetic field and observed that the tangential magnetic field plays a stabilizing role in the stability analysis. Sirwah [24] investigated the nonlinear stability analysis of magnetic fluids in the presence of constant normal magnetic field and observed that normal magnetic field has destabilizing effect on the stability of the system.…”

Section: Introductionmentioning

confidence: 99%

Viscous potential flow analysis of magnetohydrodynamic capillary instability with heat and mass transfer

Tiwari

Awasthi

Agrawal

2015

Ain Shams Engineering Journal

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A linear analysis of capillary instability of a cylindrical interface in the presence of axial magnetic field has been carried out when there is heat and mass transfer across the interface. Both fluids are taken as incompressible, viscous and magnetic with different kinematic viscosities and different magnetic permeabilities. Viscous potential flow theory is used for the investigation and a dispersion relation that accounts for the growth of axisymmetric waves is derived. Stability criterion is given by critical value of applied magnetic field as well as critical wave number and stability is discussed theoretically as well as numerically. Various graphs are drawn showing the effect of various physical parameters such as magnetic field strength, heat transfer capillary number, and permeability ratio, on the stability of the system. It has been observed that the axial magnetic field and heat and mass transfer both have stabilizing effect on the stability of the system. Ó 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Nonlinear Kelvin–Helmholtz instability of magnetized surface waves on a subsonic gas–viscous potential liquid interface

Cited by 16 publications

References 30 publications

Nonlinear electroviscoelastic potential flow instability theory of two superposed streaming dielectric fluids

Nonlinear electroviscoelastic potential flow instability theory of two superposed streaming dielectric fluids

The effect of a periodic tangential magnetic field on the stability of a horizontal magnetic fluid sheet

Viscous potential flow analysis of magnetohydrodynamic capillary instability with heat and mass transfer

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