By Tsinober, A. (1937-)

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Extra resources for An informal introduction to turbulence

Example text

For this reason and some more specific reasons explained later these issues are discussed only briefly in this volume. Basic information on scales and scaling and related matters in turbulence can be found in appendix C. Two notes are in order. First, the most accepted division of turbulent flows on large and small scales is to a large extent artificial and in some sense even unphysical due to strong coupling between the two and due to an ambiguity of the very term ’scale’ (see chapter 5 and appendix C).

However, it is important to stress that transition to turbulent regime may be quite sudden. For example, this may l T h e literature on fluid flow instabilities and transition is vast. Comprehensive reviews and lists of references can be found in Drazin and Reid (1981), Huerre and Rossi (1998), and Monin and Yaglom (1997, 1998), and also Monin (1986). For recent developments, see Fasel and Saric (2000). 1). From the mathematical point of view the transitions from one flow regime to another with increasing Reynolds number – as we observe them in physical space – are believed to be a manifestation of generic structural changes of the mathematical objects called phase flow and attractors in the phase space through bifurcations in a given flow geometry (Hopf, 1948).

205, 593). It is now recognized that despite the considerable successes of the present studies of the application of modern ideas on chaos to well-controlled fluid flows, they appear to have little relevance when applied to the more general 6 Provided that the corresponding three-dimensional problem for the Navier-Stokes equations does have a unique solution. 7 Though some authors hold an opposite opinion, Bohr et al. (1998), Ruelle (1990). METHODS OF DESCRIBING TURBULENT FLOWS 41 problem of fluid turbulence (Mullin, 1993, p.

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