Abstract
Three recent applications of maximal entropy procedures to models of turbulence in plasmas are described. They are (1) the calculation of “most probable” states in guiding-center plasmas and vortex fluids, (2) the calculation of “most probable” magnetohydrodynamic equilibrium profiles, and (3) the prediction of absolute equilibrium Gibbs ensemble spectra for Navier-Stokes fluids. Further conjectures on the role of entropies in turbulence theories are offered.
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References
C. C. Lin (1943) On the Motion of Vortices in Two Dimensions ( Toronto: University of Toronto Press).
L. Onsager (1949) Nuovo Cimento Suppl. 6, 279.
J. B. Taylor and B. McNamara (1971) Phys. Fluids 14, 1492.
D. Montgomery, 1975, in C. de Witt and J. Peyraud, eds., Plasma Physics: Les Houches 1972 ( New York: Gordon and Breach ), pp. 425–535.
C. E. Seyler (1976) Phys. Fluids 19, 1336.
R. H. Kraichnan and D. Montgomery (1980) Rep. Prog. Phys. 43, 547.
G. Joyce and D. Montgomery (1973) J. Plasma Phys. 10, 107.
D. Montgomery and G. Joyce (1974) Phys. Fluids 17, 1139.
N. G. Van Kampen (1964) Phys. Rev. A135, 362.
D. Lynden-Bell (1967) Mon. Not. R. Astron. Soc. 136, 101.
D. L. Book, B. E. McDonald, and S. Fisher (1975) Phys. Rev. Lett. 34, 4.
B. E. McDonald (1974) J. Comput. Phys. 16, 360.
G. A. Kriegsmann and E. L. Reiss (1978) Phys. Fluids 21, 258.
A term in S was omitted in Ref. [11], where this conclusion was reached. It has since been put in and the entropy recomputed, but the conclusion did not change (B. E. McDonald, private communication).
See, for example, G. Batemann (1978) MHD Instabilities ( Cambridge, Mass.: MIT Press).
D. Montgomery, L. Turner, and G. Vahala (1979) J. Plasma Phys. 21, 239.
J. Ambrosiano and G. Vahala (1981) Phys. Fluids 24, 2253.
T. D. Lee (1952) Q. Appl. Math. 10, 69.
R. H. Kraichnan (1967) Phys. Fluids 10, 1417.
D. Montgomery (1976) Phys. Fluids 19, 802.
See, for example, D. C. Leslie (1973) Development in the Theory of Turbulence (Oxford: Oxford University Press) or R. H. Kraichnan (1975) Adv. Math. 16, 305.
G. Carnevale (1979) Ph.D. Thesis (Harvard), and (1982) J. Fluid Mech. 122, 143; G. Carnevale and G. Holloway (1981) Information decay and the predictability of turbulent flows, NCAR Preprint; G. Carnevale, U. Frisch, and R. Salmon (1981) J. Ph.s. A 14, 1701.
That Eq. (26) is a good prediction for the time averages of the solutions to Eq. (25) with y = 0 had been previously established by C. E. Seyler, Y. Salu, D. Montgomery, and G. Knorr (1975) Phys. Fluids 18, 803.
E. T. Jaynes (1957) Phys. Rev. 106, 620, and 108, 171.
E. T. Jaynes (1963) in K. W. Ford, ed., Statistical Physics, Vol. III (New York: W. A. Benjamin ), pp. 181–218.
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Montgomery, D. (1985). Maximal Entropy in Fluid and Plasma Turbulence: A Review. In: Smith, C.R., Grandy, W.T. (eds) Maximum-Entropy and Bayesian Methods in Inverse Problems. Fundamental Theories of Physics, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2221-6_23
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DOI: https://doi.org/10.1007/978-94-017-2221-6_23
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