ANOMALOUS SCALING AND GENERIC STRUCTURE-FUNCTION IN TURBULENCE

We discuss on an example a general mechanism of apparition of anomalou s scaling in scale invariant systems via zero modes of a scale invaria nt operator. We discuss the relevance of such mechanism in turbulence, and point out a peculiarity of turbulent hows, due to the existence o f both forcing and dissipation. Following these considerations, we sho w that if this mechanism of anomalous scaling is operating in turbulen ce, the structure functions can be constructed by simple symmetry cons iderations. We find that the generical scale behavior of structure fun ctions in the inertial range is not self-similar S-n(l) proportional t o l(zeta,n) but includes an ''exponential self-similar'' behavior S-n( l) proportional to exp[zeta(n) alpha(-1)l(alpha)] where alpha is a par ameter proportional to the inverse of the logarithm of the Reynolds nu mber. The solution also follows exact General Scaling and approximate Extended Self-Similarity.