Stability of hexagonal pattern in Rayleigh–Bénard convection for thermodependent shear-thinning fluids

Varé, Thomas; Nouar, Chérif; Métivier, Christel; Bouteraa, Mondher

doi:10.1017/jfm.2020.766

Cited by 4 publications

(11 citation statements)

References 55 publications

(157 reference statements)

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“…Furthermore, the increase of the wavenumber with Ra is all the more significant as non-Boussinesq effects are stronger. These results provide an experimental support to the theoretical study of Vare et al [29] that we have extended here to take into account the variation of the thermal expansion coefficient with temperature in addition to that of viscosity. It is demonstrated theoretically that the band of stable wavenumbers is asymmetric and bent towards large wavenumbers.…”

Section: Discussionsupporting

confidence: 88%

“…The objective of the present work is to provide an experimental support of the theoretical analysis of Vare et al [29] that we have extended here to take into account the variation of the thermal expansion coefficient with temperature. We will show experimentally that the size of the hexagons decreases with increasing the temperature difference.…”

Section: Introductionmentioning

confidence: 74%

“…A multiple scale perturbation theory developed in the vicinity of the onset allows to determine the evolution equation for A p (X, Y, T ). Details can be found in [29] and references therein. Up to third order in perturbation equations, the spatio-temporal evolution of the amplitude A p is described through the equations…”

Section: B Weakly Nonlinear Analysismentioning

confidence: 99%

“…From theoretical point of view, using a weakly nonlinear analysis, Vare et al [29] demonstrated in the case of a a shear-thinning fluid with a thermodependent viscosity that the band of stable wavenumbers of hexagons is open and decentered to the right, i.e. to wavenumbers larger than the critical one.…”

Section: Introductionmentioning

confidence: 99%

“…In Sec. 2, an extension of the theoretical analysis of Vare et al [29] taking into account the temperature-dependence of the thermal expansion coefficient which plays a significant role in the experimental work is given. In Sec.…”

Section: Introductionmentioning

confidence: 99%

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Section: Discussionsupporting

confidence: 88%

Section: Introductionmentioning

confidence: 74%

Section: B Weakly Nonlinear Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Rayleigh–Bénard convection in non-Newtonian fluids: Experimental and theoretical investigations

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Unveiling the competitive role of global modes in the pattern formation of rotating sphere flows

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The wake flow past a streamwise rotating sphere is a canonical model of numerous applications, such as particle-driven flows, sport aerodynamics and freely rising or falling bodies, where the changes in particles’ paths are related to the destabilization of complex flow regimes and associated force distributions. Herein, we examine the spatio-temporal pattern formation, previously investigated by Lorite-Díez & Jiménez-González (J. Fluid Mech., vol. 896, 2020, A18) and Pier (J. Fluids Struct., vol. 41, 2013, pp. 43–50), from a dynamical system perspective. A systematic study of the mode competition between rotating waves, which arise from the linearly unstable modes of the steady-state, exhibits their connection to previously observed helical patterns present within the wake. The organizing centre of the dynamics turns out to be a triple Hopf bifurcation associated with three non-axisymmetric, oscillating modes with respective azimuthal wavenumbers $m=-1,-1$ and $-2$ . The unfolding of the normal form unveils the nonlinear interaction between the rotating waves to engender more complex states. It reveals that for low values of the rotation rate, the flow field exhibits a similar transition to the flow past the static sphere, but accompanied by a rapid variation of the frequencies of the flow with respect to the rotation. The transition from the single helix pattern to the double helix structure within the wake displays several regions with hysteric behaviour. Eventually, the interaction between single and double helix structures within the wake lead towards temporal chaos, which here is attributed to the Ruelle–Takens–Newhouse route. The onset of chaos is detected by the identification of an invariant state of the normal form constituted by three incommensurate frequencies. The evolution of the chaotic attractor is determined using of time-stepping simulations, which were also performed to confirm the existence of bi-stability and to assess the fidelity of the computations performed with the normal form.

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Heat Transport in Rotating Annular Duct: A Short Review

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Heat transport in rotating processes finds a wide range of application in which academic issues in the fluid mechanics and heat transfer areas are here reported. This paper discusses successive works from the seminal paper of Taylor (1923) to recent numerical results established from a broad range of methods such as DNS, LES, RANS or LB methods. The flow regimes identification is thus reported in Taylor–Couette geometry. The role of the axial flow rates in the apparition, stabilization and destruction of the large-scale of the turbulent structures is depicted in the case of Taylor–Couette–Poiseuille geometry. In a non-isothermal condition, a discussion is held on the various exponent values found in the scaling relationships relying on the Nusselt number as a function of the Rayleigh or Reynolds numbers according to the regimes of thermal convection.

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Stability of hexagonal pattern in Rayleigh–Bénard convection for thermodependent shear-thinning fluids

Abstract: Abstract

Cited by 4 publications

References 55 publications

Rayleigh–Bénard convection in non-Newtonian fluids: Experimental and theoretical investigations

Rayleigh–Bénard convection in non-Newtonian fluids: Experimental and theoretical investigations

Unveiling the competitive role of global modes in the pattern formation of rotating sphere flows

Heat Transport in Rotating Annular Duct: A Short Review

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