Intermittency and the slow approach to Kolmogorov scaling

From a simple path integral involving a variable volatility in the velocity differences, we obtain velocity probability density functions with exponential tails, resembling those observed in fully developed turbulence. The model yields realistic scaling exponents and structure functions satisfying extended self-similarity. But there is an additional small-scale dependence for quantities in the inertial range, which is linked to a slow approach to Kolmogorov [Dokl. Akad. Nauk 30, 9 (1941)] scaling occurring in the large-distance limit.