Geometry and scaling laws of excursion and iso-sets of enstrophy and dissipation in isotropic turbulence

ABSTRACT

Motivated by interest in the geometry of high intensity events of turbulent flows, we examine the spatial correlation functions of sets where turbulent events are particularly intense. These sets are defined using indicator functions on excursion and iso-value sets. Their geometric scaling properties are analysed by examining possible power-law decay of their radial correlation function. We apply the analysis to enstrophy, dissipation and velocity gradient invariants Q and R and their joint spatial distributions, using data from a direct numerical simulation of isotropic turbulence at Re_λ ≈ 430. While no fractal scaling is found in the inertial range using box-counting in the finite Reynolds number flow considered here, power-law scaling in the inertial range is found in the radial correlation functions. Thus, a geometric characterisation in terms of these sets’ correlation dimension is possible. Strong dependence on the enstrophy and dissipation threshold is found, consistent with multifractal behaviour. Nevertheless, the lack of scaling of the box-counting analysis precludes direct quantitative comparisons with earlier work based on multifractal formalism. Surprising trends, such as a lower correlation dimension for strong dissipation events compared to strong enstrophy events, are observed and interpreted in terms of spatial coherence of vortices in the flow.

KEYWORDS:

• Isotropic turbulence
• chaos and fractals
• direct numerical simulation

Acknowledgements

The authors are grateful to the Turbulence Research Group members for discussions and help with this project, Dr Gerard Lemson and Dr Stephen Hamilton for their help with the SciServer system. José Hugo Elsas is grateful to the Rio de Janeiro state science funding agency FAPERJ program for international Ph.D. exchange, grant number E-26/200.076/2016 and to Dr L. Moriconi for authorising the international exchange. Alexander Szalay and Charles Meneveau are supported by NSF's CDS&E: CBET-1507469 and BigData:OCE-1633124 projects. The SciServer project is supported by NSF's DIBBS program (OAC-1261715). SciServer is a collaborative research environment for large-scale data-driven science. It is being developed at, and administered by, the Institute for Data Intensive Engineering and Science at Johns Hopkins University. SciServer is funded by the National Science Foundation Award ACI-1261715. For more information about SciServer, please visit http://www.sciserver.org.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Division of Chemical, Bioengineering, Environmental, and Transport Systems [grant number CBET-1507469]; Division of Ocean Sciences [grant number OCE-1633124]; Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro [grant number E-26/200.076/2016]; National Science Foundation [grant number OAC-1261715]; Office of Cyberinfrastructure [grant number ACI-1261715, [grant number OAC- 1261715].