Anomalous scaling of velocity and temperature structure functions

Scaling-range power-law exponents of velocity and temperature structure functions are examined through the dimensional analysis framework of the refined similarity hypotheses using measurements in a variety of turbulent flows and Reynolds numbers. The resulting magnitude of the scaling exponent associated with the locally averaged energy dissipation rate epsilon(r) is always larger than 2/3, whereas the exponent for the locally averaged temperature dissipation rate chi(r) is always smaller than 2/3. While the epsilon(r) exponent may be reconciled with the exponent of the velocity structure function, the distributions of the chi(r) and temperature structure function exponents are inherently different.