Convergents to Infinite Series in Turbulence Theory

Abstract

Padé approximants to the irreducible diagram expansions are proposed as a possible source of convergent sequences of approximations to turbulence correlation functions. The approximants are used to close off infinite-series integral equations, which then must be solved for the correlation functions. Alternatively, they are applied to an explicit expansion about the direct-interaction, or random-coupling, approximation. Good results are obtained for an exactly soluble test problem, the random oscillator, which has served to exhibit inadequacies of some previous approximation schemes for turbulence.