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Extra resources for Applied Numerical Analysis - Solutions manual

Example text

ESS stated that the proportionality of Dn (r) to [Dm (r)] n m is often valid over an unexpectedly wide range of scales r extending far beyond the small-scale limit of the inertial range. (In practical applications it is usually assumed that m = 3; then ζm = 1 and within the inertial range the ESS representation is equivalent to that of Eq. ) The use of ✐ ✐ ✐ ✐ ✐ ✐ ✐ 38 “yaglom” 2001/9/26 page 38 ✐ New Trends in Turbulence the ESS method allows to simplify and make more easy the determination of exponents ζn from the experimental data, but in principle values of ζn found by this method may be somewhat aﬀected by the extension of the range of r values considered.

Procaccia, Hydrodynamic Turbulence: A 19th Century Problem with a Challenge for the 21st Century, in Turbulence Modeling and Vortex Dynamics, edited by O. Bortav et al. (Springer, Berlin, 1997) pp. 1-16; V. L’vov and I.

D. ), Nonlinear Dynamics and Turbulence (Pitman, Boston, 1983). [45] P. Berg´e, Y. Pomeau and C. Vidal, L’Ordre dans la Chaos. Vers une Approche D´ eterministe de la Turbulence (Hermann, Paris, 1988). J. A. Lieberman, Regular and Chaotic Dynamics, 2nd Edition (Springer, New York, 1992). P. Kadanoﬀ, From Order to Chaos. Essays: Critical, Chaotic and Otherwise (World Scientiﬁc, Singapore, 1993). C. Hilborn, Chaos and Nonlinear Dynamics. An Introduction for Scientists and Engineers (Oxford University Press, New York, 1994).