A theory of time-dependent, isotropic turbulence

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Abstract
Second-order equations are derived for the turbulent velocity-field correlation and propagator functions. Is is argued that the concept of the propagator may be more fully exploited as the relationship between eddies at successive times, than as the relationship between the velocity and the arbitrary stirring forces. The resulting equations differ from the direct-interaction approximation of Kraichnan by the presence of additional diffusive-type terms in the equation for the propagator. A generalisation of the diagram technique due to Wyld is used to analyse the approximation procedure to fourth order. It is shown that many higher-order terms in the perturbation series are represented in the truncated equations.

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