Skip to main content Accessibility help
×
Home

Convective pattern evolution and secondary instabilities

  • J. P. Gollub (a1), A. R. Mccarriar (a1) and J. F. Steinman (a1)

Abstract

Using an automated laser-Doppler scanning technique, we have performed an extensive study of pattern evolution and instabilities in a large Rayleigh-BBnard cell (20 by 30 times the layer depth) at moderate Prandtl number (2.5). This work differs from earlier experiments in that the Doppler mapping technique permits both the spatial structure and time evolution of the velocity field to be quantitatively studied, and runs lasting up to ten thousand vertical thermal diffusion times are presented. We observe and document the properties of three qualitatively different regimes above the critical Rayeigh number Rc. (i) Below 5Rc, there are a number of simple patterns in which the rolls align perpendicular to all lateral cell boundaries. The patterns are therefore curved and generally contain two boundary-related defects. A change in R induces patterns with many defects, which evolve toward the simple patterns over extraordinarily long times. These features seem to be consistent with theoretical models based on the competition between boundary, curvature and defect contributions to a Liapunov functional. However, stable states are not always reached. (ii) Above 5Rc the skewed-varicose instability of Busse & Clever causes progressively faster broadband time dependence with a spectral tail falling off approximately as the fourth power of the frequency. Doppler imaging shows that the fluctuations are caused by narrowing and pinching off of the rolls. (iii) Above 9Rc both the oscillatory and skewed-varicose instabilities cause local velocity fluctuations. However, substantial mean roll structure persists even over a 40 h period (one horizontal thermal diffusion time) at 1 5Rc. Velocity power spectra with two distinct maxima associated with the two instabilities are still resolved at 50Rc. Finally, we impose thermal inhomogeneities in order to pin the rolls, and show that the fluctuations are suppressed only if the local heat flux is a significant fraction of the convective heat transport per wavelength.

Copyright

References

Hide All
Ahlers, G. & Behringer, R. P. 1978 Evolution of turbulence from the Rayleigh–-Bénard instability. Phys. Rev. Lett. 40, 712716.
Ahlers, G. & Behringer, R. P. 1979 The Rayleigh–-Bénard instability and the evolution of turbulence. Prog. Theor. Phys. Suppl 64, 186201.
Ahlers, G. & Walden, R. W. 1980 Turbulence near onset of convection. Phys. Rev. Lett. 44, 445448.
Behringer, R. P., Agosta, C., Jan, J. S. & Shaumeyer, J. N. 1980 Time-dependent Rayleigh–-Bénard convection and instrumental attenuation. Phys. Lett. 80A, 273–276.
Behringer, R. P., Shaumeyer, J. N., Agosta, C. A. & Clark, C. A. 1982 Onset of turbulence in moderately large aspect ratios. Submitted to Phys. Rev. A.
Bergé, P. 1981 Rayleigh–-Bénard convection in high Prandtl number fluids. In Chaos and Order in Nature (ed. H. Haken). Springer.
Busse, F. H. & Clever, R. M. 1979 Instabilities of convection rolls in a fluid of moderate Prandtl number. J. Fluid Mech. 91, 319355.
Chen, M. M. & Whitehead, J. A. 1968 Evolution of two-dimensional periodic Rayleigh–-Bénard convection cells of arbitrary wave-numbers. J. Fluid Mech. 31, 115.
Clever, R. M. & Busse, F. H. 1974 Transition to time-dependent convection. J. Fluid Mech. 65, 625645.
Cross, M. C. 1982 Ingredients of a theory of convective textures close to onset. Phys. Rev. A 25, 10651076.
Cross, M. C., Daniels, P. G., Hohenberg, P. C. & Siggia, E. D. 1980 Effect of distant sidewalls on wave-number selection in Rayleigh–-Bénard convection. Phys. Rer. Lett. 45, 898901.
Cross, M. C., Daniels, P. G., Hohenberg, P. C. & Siggia, E. D. 1983 Phase-winding solutions in a finite container above the convective threshold. J. Fluid Mech. (in press).
Davis, S. H. 1967 Convection in a box: linear theory. J. Fluid Mech. 30, 465.
Gollub, J. P. 1982 Recent experiments on the transition to turbulent convection. In Nonlinear Dynamics and Turbulence (ed. D. Joseph & G. looss). Pitman.
Gollub, J. P. & Benson, S. V. 1980 Many routes to turbulent convection. J. Fluid Mech. 100, 449470.
Gollub, J. P. & Mccarriar, A. R. 1982 Spatial Fourier analysis of convection patterns. Submitted to Phys. Rev. A.
Gollub, J. P. & Steinman, J. F. 1981 Doppler imaging of the onset of turbulent convection. Phys. Rev. Lett. 47, 505508.
Greenside, H. S., Ahlers, G., Hohenberg, P. C. & Walden, R. W. 1982 A simple stochastic model of the onset of turbulence in Rayleigh–Bénard convection. Bell Labs Preprint.
Kirchartz, K. R., Muller, U., Oertel, H. & Zierep, J. 1981 Axisymmetric and non-axisymmetric convection in a cylindrical container. Acta Mechanica 40, 181194.
Krishnamurti, R. 1970 On the transition to turbulent convection. Part 1. The transition from two- to three-dimensional flow. J. Fluid. Mech. 42, 295307.
Krishnamurti, R. 1973 Some further studies on the transition to turbulent convection. J. Fluid Mech. 60, 285303.
Mclaughlin, J. B. & Orszag, S. A. 1982 Transition from periodic to chaotic thermal convection. J. Fluid Mech. 122, 123142.
Manneville, P. 1981 Numerical simulation of ‘convection’ in cylindrical geometry. CEN Saclay Preprint.
Newell, A. C. & Whitehead, J. A. 1969 Finite bandwidth, finite amplitude convection. J. Fluid Mech. 38, 279303.
Segel, L. A. 1969 Distant sidewalls cause slow amplitude modulation of cellular convection. J. Fluid Mech. 38, 203224.
Siggia, E. D. & Zippelius, A. 1981a Pattern selection in Rayleigh-Bénard convection near threshold. Phys. Rev. Lett. 47, 835838.
Siggia, E. D. & Zippelius, A. 19816 Dynamics aof defects in Rayleigh–-Bénard convection. Phys. Rev. A 24, 10361049.
Stork, K. & Müller, U. 1972 Convection in aboxes: experiments. J. Fluid Mech. 54, 599611.
Willis, G. E. & Deardorff, J. W. 1970 The oscillatory motions of Rayleigh convection. J. Fluid Mech. 44, 661672.
Whitehead, J. A. 1976 The propagation of dislocations in Rayleigh-Bénard rolls and bimodal flow. J. Fluid Mech. 75, 715720.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Convective pattern evolution and secondary instabilities

  • J. P. Gollub (a1), A. R. Mccarriar (a1) and J. F. Steinman (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed