Isotropic Turbulence and Spectra

Abstract

The knowledge gained from similarity theory is applied in many fields of natural and engineering science, among others, in fluid mechanics. In this field, similarity considerations are often used for providing insight into the flow phenomenon and for generalization of results. The importance of similarity theory rests on the recognition that it is possible to gain important new insights into flows from the similarity of conditions and processes without having to seek direct solutions for posed problems.

Further Reading

1.1 Hydrodynamics and Scaling

• G.I. Barenblatt, Scaling Phenomena in Fluid Mechanics (Cambridge University Press, Cambridge, 1994)

• G.K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1973)

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

• C.R. Doering, J.D. Gibbon, Applied Analysis of the Navier–Stokes Equations (Cambridge University Press, Cambridge, 1995)

• G.S. Golitsyn, Selected Papers (Moscow, Nauka, 2008)

• J. Katz, Introductory Fluid Mechanics (Cambridge University Press, Cambridge, 2010)

• J.-L. Lagrange, Mecanique Analytique (Cambridge University Press, Cambridge, 2009)

• A.J. Majda, A.L. Bertozzi, Vorticity and Incompressible Flow (Cambridge University Press, Cambridge, 2002)

• P. Mueller, The Equations of Oceanic Motions (Cambridge University Press, Cambridge, 2006)

• L. Prandtl, O.G. Tietjens, Applied Hydro- and Aeromechanics (McGraw Hill, London, 1953)

• M. Samimy et al., A Gallery of Fluid Motion (Cambridge University Press, Cambridge, 2003)

• P. Taberling, O. Cardoso, Turbulence A Tentative Dictionary (Plenum, New York, 1994)

• M. Van-Dyke, An Album of Fluid Motion (Parabolic, Stanford, CA, 1982)

1.2 Turbulence

• G.K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, 1959)

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

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

• J.R. Herring, J.C. McWilliams, Lecture Notes on Turbulence (World Scientific, Singapore, 1987)

• M. Lesieur, Turbulence in Fluids (Springer, Berlin, 2008)

• D.C. Leslie, Developments in the Theory of Turbulence (Clarendon, Oxford, 1973)

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

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

• K.R. Sreenivasan, Rev. Mod. Phys. 71, S 383 (1999)

1.3 Statistical Aspects of Turbulence

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

• M. Lesieur et al. (eds.), New Trends in Turbulence (Springer, Berlin, 2001)

• J.L. Lumley (ed.), Fluid Mechanics and the Environment. Dynamical Approaches (Springer, Berlin, 2001)

• M. Oberlack, F.H. Busse (eds.), Theories of Turbulence (Springer, New York, 2002)

• J. Peinke, A. Kittel, S. Barth, M. Oberlack (eds.), Progress in Turbulence (Springer, Berlin, 2005)

• S.B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, 2000)

• Y. Zhou, Phys. Rep. 488, 1 (2010)

1.4 Simulation of Turbulent Flows

• P.S. Bernard, J.M. Wallace, Turbulent Flow. Analysis, Measurement, and Prediction (Wiley, New York, 2002)

• H.A. Dijkstra, Nonlinear Physical Oceanology (Springer, Berlin, 2006)

• P. Durbin, B. Pettersson-Reif, Statistical Theory and Modeling for Turbulent Flows (Wiley, New York, 2010)

• J. Hoffman, C. Johnson, Computational Turbulent Incompressible Flow (Springer, Berlin, 2007)

• M.Z. Jacobson, Fundamentals of Atmospheric Modeling (Cambridge University Press, Cambridge, 2005)

• P. Lynch, The Emergence of Numerical Weather Prediction (Cambridge University Press, Cambridge, 2006)

• R. Schiestel, Modeling and Simulation of Turbulent Flows (Wiley, New York, 2008)