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 single-point measurements of a dynamically passive Sc ≈ 1 conserved scalar quantity ζ(t) in a turbulent shear flow at outer-scale Reynolds numbers of 14000 ≤ Re_δ 110000. Statistical criteria based on the maximum allowable scale-to-scale variation L₁(ε) in multiplier distributions P(M_ε) from multifractal gauge sets allow accurate discrimination between multifractal and non-multifractal scaling. Results show that the surrogate scalar energy dissipation rate χ_s(t) ≡ (dζ/dt)² is found to display a scale-invariant similarity consistent with a random multiplicative cascade characterized by a bilinear multiplier distribution P(M_ε) over a range of scales extending downward from the outer scale T_δ. For a range of scales extending upward from the inner (diffusive) scale T_D, the dissipation rate displays a different scale-invariant similarity characterized by a uniform multiplier distribution. The former scale-invariance becomes evident in the present Sc ≈ 1 data only when Re_δ is sufficiently large. Comparisons with results from Sc ≫ 1 data indicate that this scale-invariant similarity applies when the outer-to-inner scale ratio T_δ/T_D ≈ 0.09 Re_δ^3/4 is greater than about 400. In contrast to the scalar dissipation rate field, the scalar field is found to lack any multifractal scale similarity.