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Convection in heated fluid layers subjected to time-periodic horizontal accelerations

Published online by Cambridge University Press:  17 January 2008

W. PESCH ,
D. PALANIAPPAN ,
J. TAO  and
F. H. BUSSE
W. PESCH
Affiliation:
Institute of Physics, University of Bayreuth, D-95440 Bayreuth, Germany
D. PALANIAPPAN
Affiliation:
Institute of Physics, University of Bayreuth, D-95440 Bayreuth, Germany Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
J. TAO
Affiliation:
Institute of Physics, University of Bayreuth, D-95440 Bayreuth, Germany LTCS and Department of Mechanics and Aerospace Technologies, Peking University, Beijing 100871, China
F. H. BUSSE
Affiliation:
Institute of Physics, University of Bayreuth, D-95440 Bayreuth, Germany
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Abstract

A theoretical study is presented of convection in a horizontal fluid layer heated from below or above which is periodically accelerated in its plane. The analysis is based on Galerkin methods as well as on direct numerical simulations of the underlying Boussinesq equations.

Shaking in a fixed direction breaks the original isotropy of the layer. At onset of convection and at small acceleration, we find longitudinal rolls, where the roll axis aligns parallel to the acceleration direction. With increasing acceleration amplitude, a shear instability takes over and transverse rolls with the axis perpendicular to the shaking direction nucleate at onset. In the nonlinear regime, the longitudinal rolls become unstable against transverse modulations very close to onset which leads to a kind of domain chaos between patches of symmetry degenerated oblique rolls.

In the case of circular shaking, the system is isotropic in the time average sense, however, with a broken chiral symmetry. The onset of convection corresponds to the transverse roll case studied before with the roll axis selected spontaneously. With increasing Rayleigh number, a heteroclinic cycle is observed with the roll changing its orientation periodically in time. At even higher Rayleigh number, this heteroclinic cycle becomes chaotic similarly to the case of the Küppers–Lortz instability.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 596 , 25 January 2008 , pp. 313 - 332
Copyright
Copyright © Cambridge University Press 2008

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References

Assenheimer, K. E. & Steinberg, V. 1997 Rayleigh–Bénard convection near the critical point. Phys. Rev. Lett. 70, 25.Google Scholar
Auer, M. & Busse, F. H. 1994 Wavy rolls and their instabilities in extended fluid layers. In Nonlinear Coherent Structures in Physics and Biology (ed. Spatschek, K. H. & Mertens, F. G.) NATO ASI Series: Physics, vol. 329, pp. 417–422.Google Scholar
Auer, M. & Busse, F. H. 1997 Wavy rolls in the Taylor–Bénard problem. Phys. Fluids 10, 318–320.Google Scholar
Bajaj, K. M, Ahlers, G. & Pesch, W. 2002 Rayleigh–Bénard convection with rotation at small Prandtl numbers. Phys. Rev. E 65, 056309.Google Scholar
Bodenschatz, E., Pesch, W. & Ahlers, G. 2000 Recent developments in Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 32, 709–778.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability Clarendon.Google Scholar
Clever, R. M. & Busse, F. H. 1977 Instabilities of longitudinal convection rolls in an inclined layer. J. Fluid Mech. 81, 107–125.Google Scholar
Clever, R. M. & Busse, F. H. 1979 Nonlinear properties of convection rolls in a horizontal layer rotating about a vertical axis J. Fluid. Mech. 94, 609–627.Google Scholar
Cross, M. C. & Hohenberg, P. C. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys 65, 875.CrossRefGoogle Scholar
Daniels, K. E. & Bodenschatz, E. 2002 Defect turbulence in inclined layer convection. Phys. Rev. Lett. 88, 034501.Google Scholar
Gershuni, G. Z. & Lyubimov, D. V. 1998 Thermal Vibrational Convection. John Wiley.Google Scholar
Gershuni, G. Z., Keller, I. O. & Smorodin, B. L. 1996 Vibrational and convective instability of a plane horizontal fluid layer at finite vibration frequencies. Fluid Dyn. 31, 666–671 (transl. from Izv. R. Akad. Nauk., Mekh. Zhid. i Gaza 5, 41–51, 1996).Google Scholar
Kozlov, A. A., Babushkin, I. A. & Putin, G. F. 2004 The influence of translational vibrations of circular polarization on fluid convective instability and flow pattterns. Proc. 21st Intl Congr. of Theoretical and Applied Mechanics. Warsaw, Poland, 2004.Google Scholar
Küppers, G. & Lortz, D. 1969 Transition from laminar convection to thermal turbulence in a rotating fluid layer. J. Fluid Mech. 35, 609–620.CrossRefGoogle Scholar
Or, A. C. 1997 Finite wavelength instability in a horizontal liquid layer on an oscillating plane. J. Fluid Mech. 335, 213–332CrossRefGoogle Scholar
Pesch, W. 1996 Complex spatiotemporal convection patterns. Chaos 6, 348–357.Google Scholar
Rogers, J. L., Brausch, O., Pesch, W. & Schatz, M. F. 2000 Superlattice patterns in vertically oscillated thermal convection. Phys. Rev. Lett. 85, 4281–4284.Google Scholar
Rogers, J. L., Pesch, W. & Schatz, M. F. 2003 Pattern formation in vertically oscillated convection. Nonlinearity 16, C1–C10.Google Scholar
Rogers, J. L., Pesch, W., Brausch, O. & Schatz, M. F. 2005 Complex-ordered patterns in shaken convection. Phys. Rev. E 71, 066214-1-18.Google Scholar
Schulze, T. P. 1999 A note on subharmonic instabilities. Phys. Fluids 11, 3573–3576.Google Scholar