Mathematical and Physical Theory of Turbulence

Turbulence arises in practically all flow situations that occurs naturally or in modern technological systems. The turbulence problem poses many formidable intellectual challenges and occupies a central place in modern nonlinear mathematics and statistical physics. As the great physicist Richard Feynman mentioned, it is the last great unsolved problem of classical physics. The American Mathematical Society has listed the turbulence problem as one of the four top unsolved problems of mathematics. It is also one of the seven problems for which the Clay Institute has recently announced a $1 million prize. The powerful notions of scaling and universality, which matured when renormalization group theory was applied to critical phenomena, had been manifested in turbulence previously. The recent dynamical system approach has provided several important insights into the turbulence problem. However, deep problems still remain to challenge conventional methodologies and concepts. There is considerable need and opportunity to advance and apply new physical concepts as well as new mathematical modeling and analysis techniques. There is also an ongoing need to bridge the gap between the grand theories of idealized turbulence and the harsh realities of practical applications. The turbulence problem continues to command the attention of physicists, applied mathematicians, and engineers.

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