Rayleigh-Bénard problem with imposed weak through-flow: Two coupled Ginzburg-Landau equations

Müller, H. W.; Tveitereid, Morten; Trainoff, Steven P.

doi:10.1103/physreve.48.263

Cited by 37 publications

(24 citation statements)

References 19 publications

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“…A detailed review also had been given by Kelly. 5 Müller et al 6 derived a set of two coupled Ginzburg-Landau equations to describe the dynamics of the amplitudes of both traveling TRs and stationary LRs, and studied the transition between both convection structures. Based on the same set of governing equations, Tveitereid and Müller 7 further examined the preferred pattern at the onset of convection by using the concept of absolute and convective instability.…”

Section: Introductionmentioning

confidence: 99%

Thermal convection in superposed fluid and porous layers subjected to a plane Poiseuille flow

Chang

2006

Physics of Fluids

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Thermal convection in a two-layer system comprised by a fluid layer overlying a layer of porous media saturated with the same fluid has been investigated. The system is heated from below and subjected to a horizontally plane Poiseuille flow. The interaction between both instability mechanisms, the unstably stratification and the shear arising from the plane Poiseuille flow, is studied and a completely linear stability analysis has been carried out by considering both longitudinal rolls ͑LRs͒ and transverse rolls ͑TRs͒. It is found that the neutral curves of both modes may be bimodal, which is dependent on the depth ratio, the ratio of the depth of fluid layer to that of the porous layer. The stability characteristics of LRs are found to be invariant with the Reynolds number based on the horizontal Poiseuille velocity and the Prandtl number of the fluid, and the instability is always dominated by this mode if the Reynolds number is within low or moderate strength. The superimposed Poiseuille flow seems to exert a stabilizing effect on the traveling TRs and the critical transverse mode tends to be within the porous layer with low propagating speed. However, if the Reynolds number is sufficiently large, a shear instability mode appears abruptly with higher propagating speed and then dominates the system instability.

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Section: Introductionmentioning

confidence: 99%

Thermal convection in superposed fluid and porous layers subjected to a plane Poiseuille flow

Chang

2006

Physics of Fluids

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“…In recent experimental work on Rayleigh-Benard convection with throughffow competition between longitudinal and transversal rolls [13,23] has been observed; also a superposition of both structures and more complicated timedependent behavior is possible. This competitive dynamics has been investigated by Brand, Ahlers, and Deissler [24] with a phenomenological model of two coupled amplitude equations for transversal and longitudinal rolls which, however, di6'er from the more rigorously derived equations [25]. Another kind of transversal convection structure has been studied by Pocheau et al [26].…”

Section: Introductionmentioning

confidence: 99%

Transversal convection patterns in horizontal shear flow

1992

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We investigate the influence of a horizontal plane Poiseuille shear flow transversal to the convective roll chain of the Rayleigh-Benard problem. Using a one-dimensional (1D) amplitude equation and a 2D numerical simulation of the basic field equations, we study how different boundary conditions at the inlet and outlet of the channel affect nonlinear convection. If convection is suppressed near the cell apertures, spatially localized traveling-wave states appear with a uniquely selected bulk wavelength. For convectively unstable parameters this pattern is pushed out of the channel; however, the system becomes very sensitive to perturbations, and noise-driven structures occur. Phase-pinning boundary conditions lead for very small flows to stationary roll patterns with a space-dependent wavelength decreasing downstream. Strengthening the throughflow causes local Eckhaus instabilities, which finally generate a transition to propagating rolls.PACS number(s): 47.20. 8p, 47.20.Ky, 47.60.+i

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“…They applied a weakly nonlinear theory for perturbations which modulated both on time and space and obtained a coupled envelope equations. As pointed out by Kato and Fujimura [16], the disagreement between the predictions of [14] and [15] concerning the stability of a mixed mode comes from the difference of the coefficients of nonlinear interaction terms in their respective model. Therefore Kato and Fujimura [16] used the two time-scale analysis and derived rigorously a set of two coupled Landau equations, each of them describing the time evolution of L rolls and T modes respectively.…”

Section: Introductionmentioning

confidence: 93%

“…We recall that while for T modes ω * c = k * c Pe, the L rolls are characterized by ω * c = k * c = 0, whereas (∂ω/∂k) * c = Pe is the group velocity for both patterns. By taking into account the relation (14) together with the fact that (∂ 2 ω/∂k 2 ) * c = O(1), a balance between all terms of (15) …”

Section: Derivation Of Coupled Envelope Equationsmentioning

confidence: 99%

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Weakly nonlinear interaction of mixed convection patterns in porous media heated from below

Delache¹,

Ouarzazi²

2008

International Journal of Thermal Sciences

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Rayleigh-Bénard problem with imposed weak through-flow: Two coupled Ginzburg-Landau equations

Cited by 37 publications

References 19 publications

Thermal convection in superposed fluid and porous layers subjected to a plane Poiseuille flow

Thermal convection in superposed fluid and porous layers subjected to a plane Poiseuille flow

Transversal convection patterns in horizontal shear flow

Weakly nonlinear interaction of mixed convection patterns in porous media heated from below

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