The multifractal nature of turbulent energy dissipation

  title={The multifractal nature of turbulent energy dissipation},
  author={Charles Meneveau and Katepalli R. Sreenivasan},
  journal={Journal of Fluid Mechanics},
  pages={429 - 484}
The intermittency of the rate of turbulent energy dissipation ε is investigated experimentally, with special emphasis on its scale-similar facets. This is done using a general formulation in terms of multifractals, and by interpreting measurements in that light. The concept of multiplicative processes in turbulence is (heuristically) shown to lead to multifractal distributions, whose formalism is described in some detail. To prepare proper ground for the interpretation of experimental results… 
On the multifractal properties of the energy dissipation derived from turbulence data
Various difficulties can be expected in trying to extract from experimental data the distribution of singularities, the f(α) function, of the energy dissipation. One reason is that the multifractal
Spatial correlations in turbulence: Predictions from the multifractal formalism and comparison with experiments
Questions about applicability of multiplicative cascade models for turbulent small‐scale intermittency (such as lognormal, random curdling, β, α, p models, etc.) are addressed by using the
The notion of self-similar energy cascades and multifractality has long since been connected with fully developed, homogeneous and isotropic turbulence. We introduce a number of amendments to the
The multifractal lagrangian nature of turbulence
  • M. Borgas
  • Physics
    Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences
  • 1993
The multifractal formalism for the eulerian statistics of small-scale dynamics in turbulent flows is reviewed. Theoretical extensions of these results (the statistics of small volume averages of the
Statistics of Temperature Increments in Fully Developed Turbulence
To interpret the turbulent energy transfer from the large scales to the dissipative ones, Richardson has introduced the fundamental concept of an energy cascade on which is based Kolmogorov’s
Intermittency and relative scaling of subgrid-scale energy dissipation in isotropic turbulence
The rate at which large-scale kinetic energy in turbulent flows is transferred to, or from, unresolved scales (smaller than a filter scale Δ) is given by Π(x,t)=−τijSij, where τij is the subgrid
Intermittency in Turbulence
On dissipation intermittency and its modelling in terms of turbulence-chemistry interactions
A key challenge in combustion research is to model complex turbulence-chemistry interactions during extinction and re-ignition of non-premixed flames. These are caused when the scalar dissipation, χ,


The effects of intermittency on statistical characteristics of turbulence and scale similarity of breakdown coefficients
The influence of intermittency on turbulent diffusion is expressed in terms of the statistics of the dissipation field. The high‐order moments of relative diffusion are obtained by using the concept
Some specific features of atmospheric turbulence
The specific features of atmospheric turbulence can hardly be observed in the laboratory and should be studied in the atmosphere, where the range of scales of disturbances is very broad. Slow
On the fine-scale intermittency of turbulence
This paper presents a simple theory for evaluating the several measures used to characterize the intermittency of fine-scale turbulence, and corroborates the theoretical results from comparison with
A simple dynamical model of intermittent fully developed turbulence
We present a phenomenological model of intermittency called the β-model and related to the Novikov-Stewart (1964) model. The key assumption is that in scales ∼ l02−n only a fraction βn of the total
Interpretation of Time Spectra Measured in High‐Intensity Shear Flows
Fisher and Davies have suggested several mechanisms which can prevent the direct interpretation of time spectra as space spectra by the frozen pattern hypothesis. It is shown that, when various
The nature of turbulent motion at large wave-numbers
  • G. Batchelor, A. Townsend
  • Physics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1949
This paper presents some measurements which describe the distribution of turbulent energy over Fourier components of large wave-number. According to Kolmogoroff’s theory these components of the
A statistical theory for the distribution of energy dissipation in intermittent turbulence
A new statistical theory involving the gamma distribution is presented for the local average rate of dissipation er. The gamma distribution for er leads to results for the high‐order moments of the
Breakdown of Eddies and Probability Distributions for Small‐Scale Turbulence
A rigorous mathematical description is given for the physical concept of the cascade process of sequential breakdown of turbulent eddies. It is assumed that the probability distribution for the ratio