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Geometric statistics in turbulence. (English) Zbl 0803.35106

Summary: The author presents results regarding certain average properties of incompressible fluids derived from the equations of motion. He estimates the average dissipation rate, the average dimension of level sets. The role played by the field of direction of vorticity in the three- dimensional Euler and Navier-Stokes equations is discussed and a class of two-dimensional equations that are useful models of incompressible dynamics is described. The author presents results concerning scaling exponents in turbulence.

MSC:

35Q30 Navier-Stokes equations
76B47 Vortex flows for incompressible inviscid fluids
35R60 PDEs with randomness, stochastic partial differential equations
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