Also known as "turbulent diffusion" or "eddy diffusion." In this process, small-scale random fluctuations
accelerate diffusion. In 1926, L. F. Richardson proposed that the average distance between particles grows as
where is the spatial Fourier transform, Eric Weisstein's World of Math is the energy current flowing from large-scale eddies to small-scale eddies, and k is the wavenumber. In 1995, Majda and Elliott (Cipra 1995) computationally confirmed the and hypotheses over orders of magnitude. Critical to Kolmogorov's 1941 theory were the assumption that is roughly constant (with weak fluctuations only) and depends only on forcing on the inertial and integral scales. In his 1964 paper, he argued instead that because of fluctuations, should be a function of space and time capable of varying over many orders of magnitude, producing fluctuations called intermittency. Current theory is unable to decide in favor of either weak fluctuations of intermittency.
Intermittency Factor, Kármán Constant, Kármán-Howarth Equation, Kármán Vortex Street, Lagrangian Turbulence, Kolmogorov Spectrum, Lagrangian Turbulence, Laminar Flow, Mixing Length Theory, Universal Logarithmic Wall Law, Wall Turbulence
References
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Chorin, A. J. Vorticity and Turbulence. New York: Springer-Verlag, 1994.
Cipra, B. "Turbulence Made Universal." Science 267, 795, 1995.
Dracos, T. and Tsinober, A. (Eds.). New Approaches and Concepts in Turbulence. Boston: Birkhäuser, 1992.
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Kolmogorov, A. N. 1941.
Kolmogorov, A. N. 1962.
Landahl, M. and Mollo-Christensen, E. Turbulence and Random Processes in Fluid Mechanics, 2nd ed. Cambridge, England: Cambridge University Press, 1992.
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Leslie, D. C. Developments in the Theory of Turbulence. Oxford, England: Oxford University Press, 1973.
Lumley, J. L. and Panofsky, H. A. The Structure of Atmospheric Turbulence. New York: Interscience Publishers, 1964.
Mathieu, J. and Scott, J. An Introduction to Turbulent Flow. Cambridge, England: Cambridge University Press, 2000.
McComb, W. D. The Physics of Fluid Turbulence. Oxford, England: Oxford University Press, 1991.
Monin, A. S. and Yaglom, A. M. Statistical Fluid Mechanics: Mechanics of Turbulence, English ed. updated, augmented and rev. by the authors, Vol. 1. Cambridge, MA: MIT Press, 1975.
Monin, A. S. and Yaglom, A. M. Statistical Fluid Mechanics: Mechanics of Turbulence, English ed. updated, augmented and rev. by the authors, Vol. 2. Cambridge, MA: MIT Press, 1975.
Piquet, J. Turbulent Flows: Models and Physics. Berlin: Springer-Verlag, 1999.
Sell, G. R.; Foias, C.; and Teman, R. (Eds.). Turbulence in Fluid Flows: A Dynamical Systems Approach. New York: Springer-Verlag, 1993.
Stanisic, M. M. The Mathematical Theory of Turbulence, 2nd ed. New York: Springer-Verlag, 1988.
Tennekes, H. and Lumley, J. L. A First Course in Turbulence. Cambridge, MA: MIT Press, 1972.
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