Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-15T19:18:14.998Z Has data issue: false hasContentIssue false
  • English
  • Français

The scattering of light by a chaotically convecting fluid

Published online by Cambridge University Press:  21 April 2006

Susan C. Ryrie
Susan C. Ryrie
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

The way in which light, scattered by a thin layer of fluid, may be used to obtain quantitative information about the temperature field in the fluid is investigated. Expressions for the phase shift imposed by the fluid, and the intensity of the scattered light are derived in terms of the Fourier representation of the temperature field, under the assumption of small variations in the refractive index. The method is applied to the particular case of chaotic convection, with a view to studying the connection between strange attractors and turbulence. Two simple mathematical models of chaotic convection are studied; particular emphasis is attached to the statistical properties of the flow and of the scattered light field, which are calculated numerically.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 174 , January 1987 , pp. 155 - 185
Copyright
© 1987 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benettin, G., Casartelli, M., Galgani, L., Giorgilli, A. & Strelcyn, J. M. 1978 On the reliability of numerical studies of stochasticity. I. Existence of time averages. Nuovo Cim. 44B, 183–195.Google Scholar
Berry, M. V. 1977 Focusing and twinkling: critical exponents from catastrophes in non-Gaussian random short waves. J. Phys. A 10 (12), 2061–2081.Google Scholar
Bleistein, N. & Handelsman, R. A. 1975 Asymptotic Expansion of Integrals. pp. 340–353. Holt, Rinehart & Winston.
Croquette, V., Mory, M. & Schosseler, F. 1983 Rayleigh-Bénard convective structures in a cylindrical container. J. Physique 44, 293–301.Google Scholar
Curry, J. H., Herring, J. R., Loncaric, J. & Orszag, S. A. 1984 Order and disorder in two-and three-dimensional Bénard convection. J. Fluid Mech. 147, 1–38.Google Scholar
Drazin, P. G. & Reid, W. H. 1982 Hydrodynamic Stability. Cambridge University Press.
Foias, C. & Temam, R. 1983 Asymptotic numerical analysis for the Navier-Stokes equations. In Nonlinear Dynamics and Turbulence (ed. G. I. Barenblatt, G. Iooss & D. D. Joseph), ch. 8, pp. 139–155. Pitman.
Grebogi, C., Ott, E. & Yorke, J. A. 1983 Fractal basin boundaries, long-lived chaotic transients, and unstable-unstable pair bifurcation. Phys. Rev. Lett. 50, 935–938.Google Scholar
Grossmann, S. & Sonneborn-Schmick, B. 1982 Correlation decay in the Lorenz model as a statistical physics problem. Phys. Rev. A 25, 2371–2384.Google Scholar
Hawkins, S. C. 1984 The scattering of light by a chaotically convecting fluid. Ph.D. thesis, University of Bristol.
Jones, D. S. 1964 The Theory of Electromagnetism, p. 343. Pergamon.
Knobloch, E. 1978 On the statistical dynamics of the Lorenz model. J. Stat. Phys. 20, 695–708.Google Scholar
Lanford, O. E. 1981 Strange attractors and turbulence. In Hydrodynamic Instabilities and the Transition to Turbulence (ed. H. L. Swinney & J. P. Gollub), Topics in applied physics, vol. 45. Springer.
Lorenz, E. N. 1963 Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141.Google Scholar
Lücke, M. 1976 Statistical dynamics of the Lorenz model. J. Stat. Phys. 15, 455–475.Google Scholar
McLaughlin, J. B. & Martin, P. C. 1975 Transition to turbulence in a statically stressed fluid system. Phys. Rev. A 12, 186–203.Google Scholar
Ruelle, D. & Takens, F. 1971 On the nature of turbulence. Comm. Math. Phys. 20, 167–192.Google Scholar
Smith, H. 1977 The validity of statistical results from. N-body calculations. Astron. Astrophys. 61, 305–312.Google Scholar
Sparrow, C. 1982 The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. Springer.