Article ID Journal Published Year Pages File Type
9877488 Physica D: Nonlinear Phenomena 2005 26 Pages PDF
Abstract
Several relations from the Kolmogorov theory of fully-developed three-dimensional turbulence are rigorously established for finite-time averages over Leray-Hopf weak solutions of the Navier-Stokes equations. The Navier-Stokes equations are considered with periodic boundary conditions and an external forcing term. The main parameter is the Grashof number associated with the forcing term. The relations rigorously proved in this article include estimates for the energy dissipation rate, the Kolmogorov wavenumber, the Taylor wavenumber, the Reynolds number, and the energy cascade process. For some estimates the averaging time depends on the macroscale wavenumber and the kinematic viscosity alone, while for others such as the Kolmogorov energy dissipation law and the energy cascade, the estimates depend also on the Grashof number. As compared with earlier works by some of the authors the more physical concept of finite-time average is replacing the concept of infinite-time average used before.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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