Abstract
A simple argument based on self-similarity is used to derive a relationship between pointwise energy-dissipation-rate moments, 〈εq〉, and inertial-range volume-averaged moments, 〈εqr〉, in homogeneous, isotropic and stationary turbulence. These results support the multifractal description of energy dissipation. The moment relationship implies that pointwise and inertial-range volume-averaged energy-dissipation rates cannot both be lognormally distributed. Some pointwise moments may not even exist if the volume-average counterpart is lognormal. The Schwartz inequalities for moments satisfying the self-similar relationship are examined and support the realizability of such processes.
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