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We perform the Borel resummation of the currently known terms of the ɛ-expansion up to order ɛ 4 of the dynamical exponent z in the critical-behavior model A. We obtain the large-order asymptotic approximation of the ɛ-expansion of the dynamical exponent and find a significant discrepancy between the currently calculated orders of the expansion and the obtained asymptotic values. We discuss the influence of this deviation on the accuracy of the resummation results.

Specific problems arising in the use of the method of renormalization group and e expansion in the theory of developed turbulence are discussed: the necessity to take into account the dependence of the model parameters on the expansion parameter e and the large magnitude of the physical value of the expansion parameter. It is shown that quantities independent of the amplitude of the correlation function of the random force possess a uniquely defined e expansion. On the example of the two-loop calculation of the Kolmogorov constant and the turbulent Prandtl number, effectiveness of the improved expansion is demonstrated, which uses an approximate summation of the high-order terms of the e expansion.

The turbulent Prandtl number has been calculated in the two-loop approximation of the $\eps$ expansion of the stochastic theory of turbulence. The strikingly small value obtained for the two-loop correction explains the good agreement of the earlier one-loop result with the experiment. This situation is drastically different from other available nontrivial two-loop results, which exhibit corrections of the magnitude of the one-loop term. The reason is traced to the mutual cancellation of additional divergences appearing in two dimensions which have had a major effect on the results of previous calculations of other quantities., 11 pages, 3 figures