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Chapter 7 - Hydrodynamic fluctuations

Published online by Cambridge University Press:  13 October 2009

J.-P. Rivet
Affiliation:
Observatoire de la Cote d'Azur
J. P. Boon
Affiliation:
Université Libre de Bruxelles
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Summary

The object of the present chapter is small deviations from local equilibrium which are triggered by spontaneous fluctuations. In real fluids these fluctuations which temporarily disturb the system from local equilibrium are such that a fluid at global equilibrium can be viewed as a reservoir of excitations extending over a broad range of wavelengths and frequencies from the hydrodynamic scale down to the range of the intermolecular potential. Non-intrusive scattering techniques are used to probe these fluctuations at the molecular level (neutron scattering spectroscopy) and at the level of collective excitations (light scattering spectroscopy) (Boon and Yip, 1980). The quantity measured by these scattering methods is the power spectrum of density fluctuations, i.e. the dynamic structure factor S(k, ω) which is the space- and time-Fourier transform of the correlation function of the density fluctuations. The spectral function S(k, ω) is important because it provides insight into the dynamical behavior of spontaneous fluctuations (or forced fluctuations in non-equilibrium systems). Whereas the fluctuations extend continuously from the molecular level to the hydrodynamic scale, there are experimental and theoretical limitations to the ranges where they can be probed and computed. Indeed, no theory provides a fully explicit analytical description of space-time dynamics establishing the bridge between kinetic theory and hydrodynamic theory. Scattering techniques have limited ranges of wavelengths over which fluctuation correlations can be probed.

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Publisher: Cambridge University Press
Print publication year: 2001

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  • Hydrodynamic fluctuations
  • J.-P. Rivet, Observatoire de la Cote d'Azur, J. P. Boon, Université Libre de Bruxelles
  • Book: Lattice Gas Hydrodynamics
  • Online publication: 13 October 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511524707.008
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  • Hydrodynamic fluctuations
  • J.-P. Rivet, Observatoire de la Cote d'Azur, J. P. Boon, Université Libre de Bruxelles
  • Book: Lattice Gas Hydrodynamics
  • Online publication: 13 October 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511524707.008
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Hydrodynamic fluctuations
  • J.-P. Rivet, Observatoire de la Cote d'Azur, J. P. Boon, Université Libre de Bruxelles
  • Book: Lattice Gas Hydrodynamics
  • Online publication: 13 October 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511524707.008
Available formats
×