Abstract
It is now convenient to reexamine some questions of a fundamental nature with the purpose of analysing the possible consequences of Ruelle’s principle introduced in Sect. 5.7. We shall make frequent reference to the general description of motions given in Chap. 5 in a context in which we imagine that the motions are attracted by some attracting set in phase space, which will have zero volume when energy dissipation occurs in the system. The main purpose of this section and of the following ones is to analyse the consequences of Ruelle’s principle, see Sect. 5.7, with particular attention to fluid motions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Gallavotti, G.: Extension of Onsager’s reciprocity to large fields and the chaotic hypothesis, Physical Review Letters, 77, 4334–4337, 1996.
She, Z.S., Jackson, E.: Constrained Euler system for Navier Stokes tur-bulence, Physical Review Letters, 70, 1255–1258, 1993.
Gallavotti, G.: Ergodicity, ensembles, irreversibility in Boltzmann and beyond, Journal of Statistical Physics. 78, 1571–1589, 1995.
Bonetto, F., Gallavotti, G., Garrido P.: Chaotic principle: an experimental test, Physica D, 105, 226–252, 1997.
Biferale, L., Pierotti, D., Vulpiani, A.: Time-reversible dynamical systems for turbulence, Journal of Physics A, 31, 21–32, 1998.
Rondoni, L., Segre, E.: Fluctuations in two dimensional reversibly damped turbulence, Nonlinearity, 12, 1471–1487, 1999.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Gallavotti, G. (2002). Statistical Properties of Turbulence. In: Foundations of Fluid Dynamics. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04670-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-662-04670-8_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07468-4
Online ISBN: 978-3-662-04670-8
eBook Packages: Springer Book Archive