Lagrangian Description of Chaotic Flows

Abstract

In the previous consideration, the scalar diffusion was discussed in terms of Eulerian (laboratory) coordinate frame. In modern studies in fluid dynamics, it is quite common to describe the velocity and pressure fields in the Eulerian way, with these quantities being measured and defined at a given point in space.

Further Reading

1.1 Correlation and Diffusion

• J.-P. Bouchaund, A. Georges, Phys. Rep. 195, 127 (1990)

• H.L. Pecseli, Fluctuations in Physical Systems (Cambridge University Press, Cambridge, 2006)

• L.E. Reichl, A Modern Course in Statistical Physics (Wiley-Interscience, New York, 1998)

• D. Sornette, Critical Phenomena in Natural Sciences (Springer, Berlin, 2006)

1.2 Lagrangian Correlation Function and Turbulence

• G.K. Batchelor, The Scientific Papers of Sir G.I. Taylor. Meteorology, Oceanology, Turbulent Flow, vol. 2 (Cambridge University Press, Cambridge, 1960)

• G.K. Batchelor, H.K. Moffat, M.G. Worster, Perspectives in Fluid Dynamics (Cambridge University Press, Cambridge, 2000)

• P. Bernand, J.M. Wallace, Turbulent Flow (Wiley, New York, 2002)

• T. Cebeci, Analysis of Turbulent Flows (Elsevier, Amsterdam, 2004)

• O. Darrigol, Words of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl (Oxford University press, New York, 2009)

• P.A. Davidson, Turbulence, An Introduction for Scientists and Engineers (Oxford University Press, Oxford, 2004)

• U. Frisch, Turbulence: The Legacy of A.N. N. Kolmogorov (Cambridge University Press, Cambridge, 1995)

• W. Frost, T.H. Moulden (eds.), Handbook of Turbulence (Plenum Press, New York, 1977)

• S. Heinz, Statistical Mechanics of Turbulent Flows (Springer, Berlin, 2003)

• M. Lesieur, Turbulence in Fluids (Kluwer, Dordrecht, 1997)

• W.D. McComb, The Physics of Fluid Turbulence (Clarendon Press, Oxford, 1994)

• A.S. Monin, A.M. Yaglom, Statistical Fluid Mechanics (MIT, Cambridge, 1975)

• H. Tennekes, J.L. Lumley, A First Course in Turbulence (MIT, New York, 1970)

• A. Tsinober, An informal Introduction to Turbulence (Kluwer, Dordrecht, 2004)

1.3 Correlation Functions and Geophysical Turbulence

• G.T. Csanady, Turbulent Diffusion in the Environment (D. Reidel, Dordrecht, 1972)

• N.F. Frenkiel (ed.), Atmospheric Diffusion and Air Pollution (Academic, New York, 1959)

• F.T.M. Nieuwstadt, H. Van Dop (eds.), Atmospheric Turbulence and Air Pollution Modeling (D. Reidel, Dordrecht, 1981)

• H.A. Panofsky, I.A. Dutton, Atmospheric Turbulence, Models and Methods for Engineering Applications (Wiley Interscience, New York, 1970)

• F. Pasquill, F.B. Smith, Atmospheric Diffusion (Ellis Horwood Limited, New York, 1983)

• J.C. Wyngaard, Turbulence in the Atmosphere (Cambridge University Press, Cambridge, 2000)

1.4 Seed Diffusion Effects

• M.P. Brenner, Classical Physics Through the Work of GI Taylor (MIT, Cambridge, 2000)

• R.M. Mazo, Brownian motion, Fluctuations, Dynamics and Applications (Clarendon Press, Oxford, 2002)

• T. Squires, S. Quake, Rev. Mod. Phys. 77, 986 (2005)

• G.H. Weiss, Aspects and Applications of the Random Walk (Elsevier, Amsterdam, 1994)

• Ya B. Zeldovich, A.A. Ruzmaikin, D.D. Sokoloff, The Almighty Chance (World Scientific, Singapore, 1990)