Turbulence: The Legacy of A. N. Kolmogorov

Written five centuries after the first studies of Leonardo da Vinci and half a century after A.N. Kolmogorov's first attempt to predict the properties of flow, this textbook presents a modern account of turbulence, one of the greatest challenges in physics. "Fully developed turbulence" is ubiquitous in both cosmic and natural environments, in engineering applications and in everyday life. Elementary presentations of dynamical systems ideas, probabilistic methods (including the theory of large deviations) and fractal geometry make this a self-contained textbook. This is the first book on turbulence to use modern ideas from chaos and symmetry breaking. The book will appeal to first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, as well as professional scientists and engineers. This Textbook Presents A Modern Account Of Turbulence, One Of The Greatest Challenges In Physics. The State-of-the-art Is Put Into Historical Perspective Five Centuries After The First Studies Of Leonardo And Half A Century After The First Attempt By A.n. Kolmogorov To Predict The Properties Of Flow At Very High Reynolds Numbers. Such Fully Developed Turbulence Is Ubiquitous In Both Cosmical And Natural Environments, In Engineering Applications And In Everyday Life. First, A Qualitative Introduction Is Given To Bring Out The Need For A Probabilistic Description Of What Is In Essence A Deterministic System. Kolmogorov's 1941 Theory Is Presented In A Novel Fashion With Emphasis On Symmetries (including Scaling Transformations) Which Are Broken By The Mechanisms Producing The Turbulence And Restored By The Chaotic Character Of The Cascade To Small Scales. Considerable Material Is Devoted To Intermittency, The Clumpiness Of Small-scale Activity, Which Has Led To The Development Of Fractal And Multifractal Models. Such Models, Pioneered By B. Mandelbrot, Have Applications In Numerous Fields Besides Turbulence (diffusion Limited Aggregation, Solid-earth Geophysics, Attractors Of Dynamical Systems, Etc). The Final Chapter Contains An Introduction To Analytic Theories Of The Sort Pioneered By R. Kraichnan, To The Modern Theory Of Eddy Transport And Renormalization And To Recent Developments In The Statistical Theory Of Two-dimensional Turbulence. The Book Concludes With A Guide To Further Reading. The Intended Readership For The Book Ranges From First-year Graduate Students In Mathematics, Physics, Astrophysics, Geosciences And Engineering, To Professional Scientists And Engineers.--book Jacket. Uriel Frisch. Includes Bibliographical References (p. 255-282) And Indexes. "Keratinocytes, as the main cellular component of the organism/environment interface, perform a vast range of functions in protection, secretion, sensation and self-repair by virtue of their great plasticity of form and development. Indeed recent medical advances in laboratory culture of these cells for use as skin grafts in cases of severe burns or ulceration owe much of their success to this very plasticity. This very practical handbook draws upon a wide range of international expertise making a collection of methods suitable for keratinocyte manipulation for use by new and old hands alike. Together with its companion volume The Keratinocyte Handbook it provides a comprehensive dossier of the keratinocyte which will prove an invaluable reference resource for all encountering keratinocytes in both laboratory and clinic, including dermatologists, molecular and cell biologists and biochemists."--Pub. desc This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such 'fully developed turbulence' is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers. Elementary presentations of dynamical systems ideas, of probabilistic methods (including the theory of large deviations) and of fractal geometry make this a self-contained textbook In Chapter 41 of his Lectures on Physics, devoted to hydrodynamics and turbulence, Richard Feynman (1964) observes this: Often, people in some unjustified fear of physics say you can't write an equation for life.