Weakly nonlinear stability analysis of subcritical electrohydrodynamic flow subject to strong unipolar injection

2016 ◽  
Vol 792 ◽  
pp. 328-363 ◽  
Author(s):  
Mengqi Zhang
Keyword(s):  
Electric Field ◽  
Nonlinear Stability ◽  
Landau Equation ◽  
Cross Flow ◽  
Expansion Method ◽  
Nonlinear Stability Analysis ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Ginzburg Landau Equation ◽  
Unipolar Injection

We analyse in detail the weakly nonlinear stability of electrohydrodynamic (EHD) flow of insulating fluids subject to strong unipolar injection, with and without cross-flow. We first consider the hydrostatic electroconvetion induced by a Coulomb force confined between two infinite flat electrodes, taking into account the charge diffusion effect. The effects of various non-dimensionalized parameters are examined in order to depict in detail and to understand better the subcritical bifurcation of hydrostatic electroconvetion. In addition, electrohydrodynamics with low- or high-$Re$cross-flow is also considered for investigating the combined effect of inertia and the electric field. It is found that the base cross-flow is modified by the electric effect and that, even when the inertia is dominating, the electric field can still strengthen effectively the subcritical characteristics of canonical channel flow. In this process, however, the electric field does not contribute directly to the subcriticality of the resultant flow and the intensified subcritical feature of such flow is thus entirely due to the modified hydrodynamic field as a result of the imposed electric field. This finding might be important for flow control strategies involving an electric field. Theoretically, the above results are obtained from a multiple-scale expansion method, which gives rise to the Ginzburg–Landau equation governing the amplitude of the first-order perturbation. The conclusions are deduced by probing the changes of value of the coefficients in this equation. In particular, the sign of the first Landau coefficient indicates the type of bifurcation, being subcritical or supercritical. Moreover, as a quintic-order Ginzburg–Landau equation is derived, the effects of higher-order nonlinear terms in EHD flow are also discussed.

Hydromagnetic Stability of a Thin Viscoelastic Magnetic Fluid on Coating Flow Using Landau Equation

2016 ◽  
Vol 32 (5) ◽  
pp. 643-651 ◽  
Author(s):  
C.-K. Chen ◽  
M.-C. Lin
Keyword(s):  
Viscoelastic Fluid ◽  
Nonlinear Stability ◽  
Film Flow ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Viscoelastic Parameter ◽  
Weakly Nonlinear ◽  
Linear Mode ◽  
Coating Flow ◽  
The One

AbstractThis paper investigates the weakly nonlinear stability of a thin axisymmetric viscoelastic fluid with hydromagnetic effects on coating flow. The governing equation is resolved using long-wave perturbation method as part of an initial value problem for spatial periodic surface waves with the Walter's liquid B type fluid. The most unstable linear mode of a film flow is determined by Ginzburg-Landau equation (GLE). The coefficients of the GLE are calculated numerically from the solution of the corresponding stability problem on coating flow. The effect of a viscoelastic fluid under an applied magnetic field on the nonlinear stability mechanism is studied in terms of the rotation number, Ro, viscoelastic parameter, k, and the Hartmann constant, m. Modeling results indicate that the Ro, k and m parameters strongly affect the film flow. Enhancing the magnetic effects is found to stabilize the film flow when the viscoelastic parameter destabilizes the one in a thin viscoelastic fluid.

Weakly Nonlinear Oscillatory Convection in a Rotating Fluid Layer Under Temperature Modulation

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Palle Kiran ◽  
B. S. Bhadauria
Keyword(s):  
Heat Transport ◽  
Fluid Layer ◽  
Landau Equation ◽  
Complex Form ◽  
Oscillatory Mode ◽  
Temperature Modulation ◽  
Rotating Fluid ◽  
Nonlinear Stability Analysis ◽  
Ginzburg Landau ◽  
Weakly Nonlinear

A study of thermal instability driven by buoyancy force is carried out in an initially quiescent infinitely extended horizontal rotating fluid layer. The temperature at the boundaries has been taken to be time-periodic, governed by the sinusoidal function. A weakly nonlinear stability analysis has been performed for the oscillatory mode of convection, and heat transport in terms of the Nusselt number, which is governed by the complex form of Ginzburg–Landau equation (CGLE), is calculated. The influence of external controlling parameters such as amplitude and frequency of modulation on heat transfer has been investigated. The dual effect of rotation on the system for the oscillatory mode of convection is found either to stabilize or destabilize the system. The study establishes that heat transport can be controlled effectively by a mechanism that is external to the system. Further, the bifurcation analysis also presented and established that CGLE possesses the supercritical bifurcation.

Throughflow and G-Jitter Effects on Oscillatory Convection in a Rotating Porous Medium

2020 ◽  
Vol 12 (6) ◽  
pp. 781-791
Author(s):  
S. H. Manjula ◽  
Palle Kiran ◽  
B. S. Bhadauria
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Heat Transport ◽  
Landau Equation ◽  
Nonlinear Stability Analysis ◽  
Periodic Mode ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Analysis ◽  
The Impact

The impact of vertical throughflow and g-jitter effect on rotating porous medium is investigated. A feeble nonlinear stability analysis associate to complex Ginzburg-Landau equation (CGLE) has been studied. This weakly nonlinear analysis performed for a periodic mode of convection and quantified heat transport in terms of the Nusselt number, which is governed by the non-autonomous advanced CGLE. Each idea, rotation and throughflow is used as an external mechanism to the system either to extend or decrease the heat transfer. The results of amplitude and frequency of modulation on heat transport are analyzed and portrayed graphically. Throughflow has dual impact on heat transfer either to increase or decrease heat transfer in the system. Particularly the outflow enhances and inflow diminishes the heat transfer. High centrifugal rates promote heat transfer and low centrifugal rates diminish heat transfer. The streamlines and isotherms area portrayed graphically, the results of rotation and throughflow on isotherms shows convective development.

scholarly journals New Exact Traveling Wave Solutions of the Time Fractional Complex Ginzburg-Landau Equation via the Conformable Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhao Li ◽  
Tianyong Han
Keyword(s):  
Traveling Wave ◽  
Landau Equation ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Ginzburg Landau ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Ginzburg Landau Equation

In this study, the exact traveling wave solutions of the time fractional complex Ginzburg-Landau equation with the Kerr law and dual-power law nonlinearity are studied. The nonlinear fractional partial differential equations are converted to a nonlinear ordinary differential equation via a traveling wave transformation in the sense of conformable fractional derivatives. A range of solutions, which include hyperbolic function solutions, trigonometric function solutions, and rational function solutions, is derived by utilizing the new extended G ′ / G -expansion method. By selecting appropriate parameters of the solutions, numerical simulations are presented to explain further the propagation of optical pulses in optic fibers.

JACOBI ELLIPTIC FUNCTION SOLUTION OF GINZBURG–LAUDAU EQUATION BASED ON BCS THEORY

2011 ◽  
Vol 25 (28) ◽  
pp. 2203-2208
Author(s):  
CHUNHUAN XIANG
Keyword(s):  
Elliptic Function ◽  
Landau Equation ◽  
Expansion Method ◽  
Phase Factor ◽  
Bcs Theory ◽  
Jacobi Elliptic Function ◽  
Ginzburg Landau ◽  
Function Solution ◽  
Ginzburg Landau Equation

The GL (Ginzburg–Landau) equation is a very important equation in superconductivity, which can be employed to explain many phenomena. In the present work, by using the expanded F-expansion method, some new exact Jacobi elliptic function solutions of the equation are obtained. More important is the phase factor of the solutions.

scholarly journals Study of Weakly nonlinear Mass transport in Newtonian Fluid with Applied Magnetic Field under Concentration/Gravity modulation

2019 ◽  
Vol 8 (1) ◽  
pp. 513-522 ◽  
Author(s):  
Om Prakash Keshri ◽  
Vinod K. Gupta ◽  
Anand Kumar
Keyword(s):  
Mass Transport ◽  
Fluid Layer ◽  
Landau Equation ◽  
Periodic Part ◽  
Gravity Modulation ◽  
Nonlinear Stability Analysis ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Mass Transfer Effect ◽  
Time Periodic

Abstract In the present paper, a weakly nonlinear stability analysis is used to analyze the effect of time-periodic concentration/gravity modulation on mass transport. We have considered an infinite horizontal fluid layer with constant appliedmagnetic flux salted from above, subjected to an imposed time-periodic boundary concentration (ITBC) or gravity modulation (ITGM). In the case of ITBC, the concentration gradient between the plates of the fluid layer consists of a steady part and a time-dependent oscillatory part. The concentration of both walls is modulated. In the case of ITGM, the gravity fleld consists of two parts: a constant part and an externally imposed time periodic part, which can be realized by oscillating the fluid layer. We have expanded the infinitesimal disturbances in terms of power series of an amplitude of modulation, which is assumed to be small. Ginzburg-Landau equation is derived for dinding the rate of mass transfer. Effect of various parameters on the mass transport is also discussed. It is found that the mass transport can be controlled by suitably adjusting the frequency and amplitude of modulation.

Application of bifurcation method and rational sine-Gordon expansion method for solving 2D complex Ginzburg–Landau equation

2020 ◽  
Vol 34 (09) ◽  
pp. 2050079
Author(s):  
Temesgen Desta Leta ◽  
Abdelfattah El Achab ◽  
Wenjun Liu ◽  
Jian Ding
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Landau Equation ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Long Distance ◽  
Ginzburg Landau ◽  
Bifurcation Method ◽  
Wave Solutions ◽  
Ginzburg Landau Equation

This paper implements bifurcation method and the rational sine-Gordon expansion method to investigate the dynamical behavior of traveling wave solutions of a 2D complex Ginzburg–Landau equation. By varying the parameters, we obtained traveling wave solutions including the periodic wave solutions, solitary wave solution, kink and anti-kink wave solution and in addition by using the rational sine-Gordon expansion method, we determined bright and dark soliton which have a great contribution in the long distance telecommunication system.

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