Large volume limit of the distribution of characteristic exponents in turbulence (Q798140)

The author considers a turbulent viscous flow and obtains rigorous upper bounds on the distribution of characteristic exponents in terms of dissipation. Despite the phenomenon of intermittancy for such flows, the bounds have a good large volume behavior as a characteristic exponent density should exist for spatially extended conservation or dissipative physical system. For two-dimensional fluids the result shows that the total information creation is bounded above by a fixed multiple of the total energy dissipation at fixed viscosity. For an intermittent model of turbulence the distribution of the characteristic exponents is estimated. A change in behavior is found to occur at the value of 2.6 of the self-similarity dimension.