A Governing Equation for the Small-Scale Turbulence. II. Modified DIA Approach and Kolmogorov’s −5⁄3 Power Low

Abstract

Kolmogorov’s −5⁄3 power law is examined by using the formalism of paper I (J. Phys. Soc. Japan 44 (1978) 1977), which gives an equation for the distortion motion of small eddies. The formalism is combined with the direct-interaction approximation (DIA), and a modified geometrical factor is introduced in order to avoid the infrared divergence of the response integral. It is shown that Kolmogorov’s law may be derived with a good estimate of Kolmogorov’s constant.