EXACT RESUMMATIONS IN THE THEORY OF HYDRODYNAMIC TURBULENCE .3. SCENARIOS FOR ANOMALOUS SCALING AND INTERMITTENCY

Elements of the analytic structure of anomalous scaling and intermitte ncy in fully developed hydrodynamic turbulence are described. We focus here on the structure functions of velocity differences that satisfy inertial range scaling laws S-n(R)similar to R(zeta n), and the correl ation of energy dissipation K-epsilon epsilon(R)similar to R(-mu). The goal is to understand from first principles what is the mechanism tha t is responsible for changing the exponents zeta(n) and mu from their classical Kolmogorov values. In paper II of this series [V. S. L'vov a nd I. Procaccia, Phys. Rev. E 52, 3858 (1995)] it was shown that the e xistence of an ultraviolet scale (the dissipation scale eta) is associ ated with a spectrum of anomalous exponents that characterize the ultr aviolet divergences of correlations of gradient fields. The leading sc aling exponent in this family was denoted Delta. The exact resummation of ladder diagrams resulted in a ''bridging relation,'' which determi ned Delta in terms of zeta(2): Delta = 2-zeta(2). In this paper we con tinue our analysis and show that nonperturbative effects may introduce multiscaling (i.e., zeta(n) not linear in n) with the renormalization scale being the infrared outer scale of turbulence L. It is shown tha t deviations from the classical Kolmogorov 1941 theory scaling of S-n( R) (zeta(n) not equal n/3) must appear if the correlation of dissipati on is mixing (i.e., mu>0). We suggest possible scenarios for multiscal ing, and discuss the implication of these scenarios on the values of t he scaling exponents zeta(n) and their ''bridge'' with mu.