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Perturbative evaluation of Kolmogorov constant in a self-consistent model of fluid turbulence.

The response integrals of the almost Markovian-Galelian invariant test-field model (TFM) of Kraichnan, generalized to d dimensions, are analyzed. They are found to be both ultraviolet and infrared finite in the range 0<y<6, the force correlation being approximately k(-d+4-y) in the wave-number space. The ultraviolet and infrared poles, occurring, respectively, at y=0 and y=6, are extracted by means of Laurent expansions about these values of y, yielding the Kolmogorov constant both in three and two dimensions: C(3D)=1.64 and C(2D)=8.097. These values are remarkably close to the respective renormalization group (RG) results. However, unlike RG, the perturbative TFM results are found to be (approximately) equally sensitive to both (ultraviolet and infrared) poles in both three and two dimensions.