SELF-SIMILARITY AND MULTIFRACTALS IN TURBULENCE

A simple argument based on self-similarity is used to derive a relatio nship between pointwise energy-dissipation-rate moments, (epsilon(q)), and inertial-range volume-averaged moments, (epsilon(r)(q)), in homog eneous, isotropic and stationary turbulence. These results support the multifractal description of energy dissipation. The moment relationsh ip implies that pointwise and inertial-range volume-averaged energy-di ssipation rates cannot both be lognormally distributed. Some pointwise moments may not even exist if the volume-average counterpart is logno rmal. The Schwartz inequalities for moments satisfying the self-simila r relationship are examined and support the realizability of such proc esses.