Experimental assessment of fractal scale similarity in turbulent flows. Part 3. Multifractal scaling

Abstract

Earlier experimental assessments of fractal scale similarity in geometric properties of turbulent flows are extended to assess the applicability of multifractal scale-similarity in the conserved scalar field ζ(x, t) and in the true scalar energy dissipation rate field ∇ζ·∇ζ(x, t). Fully resolved four-dimensional spatio-temporal measurements from a turbulent flow at Re_λ≈41 and Re_δ≈3000 are analysed. The utility of various classical constructs for identifying multifractal scale similarity in data records of finite length is examined. An objective statistical criterion based on the maximum allowable scale-to-scale variation L₁(ε) in multiplier distributions 〈P(M_ε)〉 obtained from multifractal gauge fields is developed to allow accurate discrimination between multifractal and non-multifractal scaling in finite-length experimental data records. Results from analyses of temporal intersections show that for scales greater than 0.03 λ_ν/u, corresponding to 1.4 λ_D/u, the scalar dissipation field clearly demonstrates a scale-invariant similarity consistent with a multiplicative cascade process that can be modelled with a bilinear multiplier distribution. However, the conserved scalar field from precisely the same data does not follow any scale similarity consistent with a multiplicative cascade at scales below 0.5 λ_ν/u. At larger scales, there are indications of a possible scale-invariant similarity in the scalar field, but with a fundamentally different multiplier distribution.