Eddy Viscosity and Diffusivity: Exact Formulas and Approximations
Robert H. Kraichnan
303 Potrillo Drive,
Los Alamos, NM 87544, USA
Abstract
Exact asymptotic expressions for eddy diffusivity and eddy viscosity are obtained as the leading terms of infinite-series representations of integral equations which express the action of turbulence on an infinitesimal mean field. The series are transformed term by term from Eulerian to Lagrangian form. The latter is more suitable for constructing approximations to the exact asymptotic expressions. The analysis is prefaced by some qualitative remarks on possible improvements of eddy transport algorithms in turbulence computations.
