Experimental assessment of fractal scale similarity in turbulent flows. Part 4. Effects of Reynolds and Schmidt numbers

Experimental results are presented for the influence of Reynolds number on multifractal scale similarity in turbulent flows. These are obtained from s ingle-point measurements of a dynamically passive Sc approximate to 1 conse rved scalar quantity zeta(t) in a turbulent shear flow at outer-scale Reyno lds numbers of 14000 less than or equal to Re-delta less than or equal to 1 10000. Statistical criteria based on the maximum allowable scale-to-scale v ariation L-1(6) in multiplier distributions P(M-epsilon) from multifractal gauge sets allow accurate discrimination between multifractal and non-multi fractal scaling. Results show that the surrogate scalar energy dissipation rate chi(s)(t) = (d zeta/dt)(2) is found to display a scale-invariant simil arity consistent with a random multiplicative cascade characterized by a bi linear multiplier distribution P(M-6) over a range of scales extending down ward from the outer scale T-delta. For a range of scales extending upward f rom the inner (diffusive) scale T-D,T- the dissipation rate displays a diff erent scale-invariant similarity characterized by a uniform multiplier dist ribution. The former scale-invariance becomes evident in the present Sc app roximate to 1 data only when Re-delta is sufficiently large. Comparisons wi th results from Sc much greater than 1 data indicate that this scale-invari ant similarity applies when the outer-to-inner scale ratio T-delta/T-D appr oximate to 0.09 (RedeltaSc1/2)-Sc-3/4 is greater than about 400. In contras t to the scalar dissipation rate field, the scalar field is found to lack a ny multifractal scale similarity.