Abstract
Starting from an extension of the Direct Interaction Approximation to weakly compressible turbulence previously proposed by Marion et al., a one-time two-point closure is derived. This model differs from the standard Eddy Damped Quasi-Normal Markovian theory by the assumptions introduced when expressing the two-time correlations. It is stressed that both the new model and the EDQNM closure lead to a closed set of equations whose structure is essentially unaffected. Only the characteristic times differ. Both closures lead to very similar results in the case of incompressible turbulence, whereas in the case of compressible turbulence it will be shown in a future note that the results are strongly affected.
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