### 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 L_{1}(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_{v}/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_{v}/u. At larger scales, there are indications of a possible scale-invariant similarity in the scalar field, but with a fundamentally different multiplier distribution.

Original language | English (US) |
---|---|

Pages (from-to) | 127-155 |

Number of pages | 29 |

Journal | Journal of Fluid Mechanics |

Volume | 338 |

State | Published - May 10 1997 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*338*, 127-155.

**Experimental assessment of fractal scale similarity in turbulent flows. Part 3. Multifractal scaling.** / Frederiksen, Richard D.; Dahm, Werner; Dowling, David R.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 338, pp. 127-155.

}

TY - JOUR

T1 - Experimental assessment of fractal scale similarity in turbulent flows. Part 3. Multifractal scaling

AU - Frederiksen, Richard D.

AU - Dahm, Werner

AU - Dowling, David R.

PY - 1997/5/10

Y1 - 1997/5/10

N2 - 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 Reλ ≈ 41 and Reδ ≈ 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(Mε)> 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 λv/u, corresponding to 1.4 λD/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 λv/u. At larger scales, there are indications of a possible scale-invariant similarity in the scalar field, but with a fundamentally different multiplier distribution.

AB - 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 Reλ ≈ 41 and Reδ ≈ 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(Mε)> 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 λv/u, corresponding to 1.4 λD/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 λv/u. At larger scales, there are indications of a possible scale-invariant similarity in the scalar field, but with a fundamentally different multiplier distribution.

UR - http://www.scopus.com/inward/record.url?scp=0031131539&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031131539&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031131539

VL - 338

SP - 127

EP - 155

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -