Localized perturbations in binary fluid convection with and without throughflow

Büchel, P.; Lücke, M.

doi:10.1103/physreve.63.016307

Cited by 11 publications

(10 citation statements)

References 70 publications

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“…The two works Büchel & Lücke (2000b) and Hu et al (2009) show that the numerical simulation results are in very good agreement with the predictions of the linear spatio-temporal stability analysis. Therefore, we expect that the results presented throughout this paper may capture the physical mechanisms of thermal instabilitiy in viscoelastic fluids.…”

Section: Results For Strongly Elastic Fluidssupporting

confidence: 80%

“…Indeed, Jung et al (1996), Büchel & Lücke (2000a) and Hu et al (2007) carried out a spatio-temporal linear stability analysis of RBP flows with binary fluids taking into account the Soret effect. Moreover, the same problem has been addressed by Büchel & Lücke (2000b) and Hu et al (2009) through fully nonlinear two-dimensional numerical simulations initiated by a localized perturbation. In such a problem, the dynamics depend on the sign of the separation ratio, a dimensionless parameter which represents the mass contribution divided by the temperature contribution to buoyancy forces and is proportional to the strength of the Soret effect.…”

Section: Results For Strongly Elastic Fluidsmentioning

confidence: 95%

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Convective and absolute instabilities in Rayleigh–Bénard–Poiseuille mixed convection for viscoelastic fluids

et al. 2015

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The convective and absolute nature of instabilities in Rayleigh-Bénard-Poiseuille (RBP) mixed convection for viscoelastic fluids is examined numerically with a shooting method as well as analytically with a one-mode Galerkin expansion. The viscoelastic fluid is modelled by means of a general constitutive equation that encompasses the Maxwell model and the Oldroyd-B model. In comparison to Newtonian fluids, two more dimensionless parameters are introduced, namely the elasticity number λ 1 and the ratio Γ between retardation and relaxation times. Temporal stability analysis of the basic state showed that the three-dimensional thermoconvective problem can be Squire-transformed. Therefore, one must distinguish mainly between two principal roll orientations: transverse rolls TRs (rolls with axes perpendicular to the Poiseuille flow direction) and longitudinal rolls LRs (rolls with axes parallel to the Poiseuille flow direction). The critical Rayleigh number for the appearance of LRs is found to be independent of the Reynolds number (Re). Depending on λ 1 and Γ , two different regimes can be distinguished. In the weakly elastic regime, the emerging LRs are stationary, while they are oscillatory in the strongly elastic regime. For TRs, it is found that in the weakly elastic regime, the stabilization effect of Re is more important than in Newtonian fluids. Moreover, for sufficiently elastic fluids a jump is observed in the oscillation frequencies and wavenumbers for moderate Re. In the strongly elastic regime, the effect of the imposed throughflow is to promote the appearance of the upstream moving TRs for low values of Re, which are replaced by downstream moving TRs for higher values of Re. Moreover, the results proved that, contrary to the case where Re = 0, the elasticity number λ 1 (the ratio Γ ) has a strongly stabilizing (destabilizing) effect when the throughflow is added. The influence of the rheological parameters on the transition curves from convective to absolute instability in the Reynolds-Rayleigh number plane is also determined. We show that the viscoelastic character of the fluid hastens the transition to absolute instability and even may suppress the convective/absolute transition. Throughout this paper, similarities and differences with the corresponding problem for Newtonian fluids are highlighted.

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Section: Results For Strongly Elastic Fluidssupporting

confidence: 80%

Section: Results For Strongly Elastic Fluidsmentioning

confidence: 95%

Convective and absolute instabilities in Rayleigh–Bénard–Poiseuille mixed convection for viscoelastic fluids

et al. 2015

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“…More recently, the problem of fronts in the Rayleigh-Bénard and Taylor-Couette system has been analyzed in great detail by Lücke and co-workers [68,69,70,210,269,270,271,349,361], both in the case discussed here and in the presence of a throughflow (see section 3.11). In these approaches, the front predictions based on the lowest order amplitude equation are compared in detail with those for pulled fronts obtained by determining the linear spreading point of the full Navier-Stokes equations for this system, and with full numerical simulations.…”

Section: Fronts In Taylor-couette and Rayleigh-bénard Experimentsmentioning

confidence: 99%

“…where the second term on the left hand side is the group velocity term associated with the advection of the pattern, and where z is the fixed coordinate frame along the axis of the cylinders. For an impression of the various types of behavior of the incoherent structures in the CGL equation with an advection term in a finite system with noise we refer to the work by Deissler [115,116,117,119], Deissler and Kaneko 70 [118] and Proctor et al [358]. In the present case, all parameters associated with the terms linear in A in this equation were known directly from the stability analysis [318], while c 3 was determined via the standard method of calculating the nonlinear terms in an amplitude expansion [318] (the parameter g 0 only sets the amplitude scale and hence is not of importance in comparing theory and experiment).…”

Section: Fronts and Noise-sustained Structures In Convective Systems ...mentioning

confidence: 99%

Front propagation into unstable states

2003

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This paper is an introductory review of the problem of front propagation into unstable states. Our presentation is centered around the concept of the asymptotic linear spreading velocity v*, the asymptotic rate with which initially localized perturbations spread into an unstable state according to the linear dynamical equations obtained by linearizing the fully nonlinear equations about the unstable state. This allows us to give a precise definition of pulled fronts, nonlinear fronts whose asymptotic propagation speed equals v*, and pushed fronts, nonlinear fronts whose asymptotic speed v^dagger is larger than v*. In addition, this approach allows us to clarify many aspects of the front selection problem, the question whether for a given dynamical equation the front is pulled or pushed. It also is the basis for the universal expressions for the power law rate of approach of the transient velocity v(t) of a pulled front as it converges toward its asymptotic value v*. Almost half of the paper is devoted to reviewing many experimental and theoretical examples of front propagation into unstable states from this unified perspective. The paper also includes short sections on the derivation of the universal power law relaxation behavior of v(t), on the absence of a moving boundary approximation for pulled fronts, on the relation between so-called global modes and front propagation, and on stochastic fronts.Comment: final version with some added references; a single pdf file of the published version is available at http://www.lorentz.leidenuniv.nl/~saarloo

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“…Concerning the characterization of the absolute or convective nature of the instabilities in such flows, the boundary curves separating these two types of instabilities for both negative separation factors (corresponding to the two TW solutions) and positive separation factors (corresponding to the SOC solution) are first plotted as a function of the throughflow rate in the paper of Jung et al (1996). Büchel & Lücke (2000b) then studied the linear spatiotemporal properties of spatially localized convective perturbations for heated binary fluid layers, with or without throughflow. Fronts and pulse-like wave packets formed out of the three relevant perturbations (two oscillatory ones and a stationary one) are analysed after evaluating the appropriate saddle points of the three respective dispersion relations of the linear stability equations over the complex wavenumber plane.…”

Section: Introductionmentioning

confidence: 99%

Linear biglobal analysis of Rayleigh–Bénard instabilities in binary fluids with and without throughflow

Henry

Yin

et al. 2012

J. Fluid Mech.

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Three-dimensional Rayleigh–Bénard instabilities in binary fluids with Soret effect are studied by linear biglobal stability analysis. The fluid is confined transversally in a duct and a longitudinal throughflow may exist or not. A negative separation factor $\psi = \ensuremath{-} 0. 01$, giving rise to oscillatory transitions, has been considered. The numerical dispersion relation associated with this stability problem is obtained with a two-dimensional Chebyshev collocation method. Symmetry considerations are used in the analysis of the results, which allow the classification of the perturbation modes as ${S}_{l} $ modes (those which keep the left–right symmetry) or ${R}_{x} $ modes (those which keep the symmetry of rotation of $\lrm{\pi} $ about the longitudinal mid-axis). Without throughflow, four dominant pairs of travelling transverse modes with finite wavenumbers $k$ have been found. Each pair corresponds to two symmetry degenerate left and right travelling modes which have the same critical Rayleigh number ${\mathit{Ra}}_{c} $. With the increase of the duct aspect ratio $A$, the critical Rayleigh numbers for these four pairs of modes decrease and closely approach the critical value ${\mathit{Ra}}_{c} = 1743. 894$ obtained in a two-dimensional situation, one of the mode (a ${S}_{l} $ mode called mode A) always remaining the dominant mode. Oscillatory longitudinal instabilities ($k\approx 0$) corresponding to either ${S}_{l} $ or ${R}_{x} $ modes have also been found. Their critical curves, globally decreasing, present oscillatory variations when the duct aspect ratio $A$ is increased, associated with an increasing number of longitudinal rolls. When a throughflow is applied, the symmetry degeneracy of the pairs of travelling transverse modes is broken, giving distinct upstream and downstream modes. For small and moderate aspect ratios $A$, the overall critical Rayleigh number in the small Reynolds number range studied is only determined by the upstream transverse mode A. In contrast, for larger aspect ratios as $A= 7$, different modes are successively dominant as the Reynolds number is increased, involving both upstream and downstream transverse modes A and even the longitudinal mode.

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Localized perturbations in binary fluid convection with and without throughflow

Cited by 11 publications

References 70 publications

Convective and absolute instabilities in Rayleigh–Bénard–Poiseuille mixed convection for viscoelastic fluids

Convective and absolute instabilities in Rayleigh–Bénard–Poiseuille mixed convection for viscoelastic fluids

Front propagation into unstable states

Linear biglobal analysis of Rayleigh–Bénard instabilities in binary fluids with and without throughflow

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