Nonlinear, Nonlocal and Fractional Turbulence (eBook)

Experts of fluid dynamics agree that turbulence is nonlinear and nonlocal. Because of a direct correspondence, nonlocality also implies fractionality. Fractional dynamics is the physics related to fractal (geometrical) systems and is described by fractional calculus. Up-to-present, numerous criticisms of linear and local theories of turbulence have been published. Nonlinearity has established itself quite well, but so far only a very small number of general nonlocal concepts and no concrete nonlocal turbulent flow solutions were available.

 

This book presents the first analytical and numerical solutions of elementary turbulent flow problems, mainly based on a nonlocal closure. Considerations involve anomalous diffusion (Lévy flights), fractal geometry (fractal-?, bi-fractal and multi-fractal model) and fractional dynamics. Examples include a new 'law of the wall' and a generalization of Kraichnan's energy-enstrophy spectrum that is in harmony with non-extensive and non-equilibrium thermodynamics (Tsallis thermodynamics) and experiments. Furthermore, the presented theories of turbulence reveal critical and cooperative phenomena in analogy with phase transitions in other physical systems, e.g., binary fluids, para-ferromagnetic materials, etc.; the two phases of turbulence identifying the laminar streaks and coherent vorticity-rich structures.

 

This book is intended, apart from fluids specialists, for researchers in physics, as well as applied and numerical mathematics, who would like to acquire knowledge about alternative approaches involved in the analytical and numerical treatment of turbulence.

Peter W. Egolf made an apprenticeship as a heating designer and studied at the University of Applied Sciences of Central Switzerland heating and air conditioning. After working in an industrial R&D laboratory, he studied physics at the Swiss Federal Institute of Technology (ETH Zurich). In 1984 he obtained his diploma in Dynamical Meteorology. Then he entered a R&D division at Gebrüder Sulzer AG in Winterthur, where he invented and investigated industrial air conditioning systems. At an advanced age he had the opportunity to make a PhD in a Noble Laureate 'family' in low-temperature physics (superfluidity). In 1989 Egolf introduced the Lagrange-Hamilton description of the free surface of quantum fluid He II. In 1990 he obtained his PhD at ETHZ with an innovation award. In the late 1980's he invented the Difference-Quotient Turbulence Model (DQTM). From 1990 on a ten years' employment at the Swiss Federal Institute for Materials Testing and Research followed in the field of energy and buildings. In 1994 he entered the field of research on ice slurries. In 1998 Egolf created the International Working Party on Ice Slurries of the International Institute of Refrigeration (IIR) and was its first President. From 2000-2018 he was the head of the Theory and Numerics Division (SIT) of the Thermal Sciences Institute at the University of Applied Sciences of Western Switzerland. He initiated a second International Working Party of the IIR (on Magnetic Refrigeration), and for ten years he was serving as its President. Furthermore, he was awarded the first prices of the Swiss Technology Awards 1996 and 2006. Today, Peter W. Egolf is retired, however, he is still involved in the study of fundamental research on fractional turbulence and nonextensive thermodynamics of turbulence. He was a main organizer of eight international conferences. Egolf invented or co-invented a new melting/freezing model, an innovative storage device for ice slurries, a translucent solar thermal wall, an innovative decentralized air-conditioning system, a high-frequency magnetic refrigerator, a new hyper-thermia cancer treatment method with rotating nanowires, etc. You will find more information on his biography in numerous editions of Who'sWho in the World, Who's Who in Science and Engineering and Who'sWho in America.