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Prog. Theor. Phys. Supplement No.64 (1978) pp. 425-435
Fluctuation Theories for Non-Linear Hydrodynamics
Ronald Forrest Fox
School of Physics, Georgia Institute of Technology, Atlanta, Georgia
Abstract:
The Landau-Lifshitz theory of fluctuations in a viscous fluid is reviewed. The derivation of the near equilibrium, linear behavior is shown to be based upon a flawed, loose analogy with the Onsager-Machlup theory of irreversible processes. A proper derivation, as originally given by Fox and Uhlenbeck is sketched. Consequently, the application of the Landau-Lifshitz theory to the non-linear regime is questioned. Such an application is shown to lead to divergencies in any case. An alternative formulation, due to Keizer, and structured in parallel with the macrovariable fluctuation theory of van Kampen and Kubo is shown to lead to a consistent theory without divergencies and in agreement with the near equilibrium theory.
URL :
http://ptp.ipap.jp/link?PTPS/64/425/
DOI : 10.1143/PTPS.64.425
References:
- L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, London, 1959), Chap. 17.
- N. G. van Kampen, Can. J. Phys. 39 (1961), 551.
- N. G. van Kampen, Adv. Chem. Phys. 34 (1976), 245.
-
R. Kubo, K. Matsuo and K. Kitahara, J. Stat. Phys. 9 (1973), 51[CrossRef].
-
J. Keizer, Phys. Fluids 21 (1978), 198[AIP Scitation].
-
L. Onsager and S. Machlup, Phys. Rev. 91 (1953), 1505[APS].
-
S. Machlup and L. Onsager, Phys. Rev. 91 (1953), 1512[APS].
- S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics (North-Holland, Amsterdam, 1962).
-
R. F. Fox and G. E. Uhlenbeck, Phys. Fluids 13 (1970), 1893[AIP Scitation];
ibid. 13 (1970), 2881[AIP Scitation].
-
M. Bixon and R. Zwanzig, Phys. Rev. 187 (1969), 267[APS].
- S. J. Putterman, Superfluid Hydrodynamics (North-Holland, Amsterdam, 1974), Chap. 4.
-
S. J. Putterman, Phys. Rev. Lett. 39 (1977), 585[APS].
- K. T. Mashiyama and H. Mori, to appear in J. Stat. Phys. (1978).
- R. F. Fox, to appear in Phys. Rep. (1979).
- L. Arnold, Stochastic Differential Equations (Wiley-Interscience, New York, 1974).
-
R. F. Fox, J. Math. Phys. 13 (1972), 1196[CrossRef].
-
R. F. Fox, J. Math. Phys. 19 (1978), 1993[CrossRef].
