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Lifetime of the intense vorticity structures in isotropic turbulence

Published online by Cambridge University Press:  17 March 2025

Afonso A. Ghira Open the ORCID record for Afonso A. Ghira [Opens in a new window] ,
Gerrit E. Elsinga Open the ORCID record for Gerrit E. Elsinga [Opens in a new window]  and
Carlos B. da Silva Open the ORCID record for Carlos B. da Silva [Opens in a new window]
Afonso A. Ghira
Affiliation:
LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal
Gerrit E. Elsinga
Affiliation:
Laboratory for Aero and Hydrodynamics, Department of Mechanical Engineering, Delft University of Technology, Delft, The Netherlands
Carlos B. da Silva*
Affiliation:
LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal
*
Corresponding author: Carlos B. da Silva, [email protected]
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Abstract

A new temporal vortex tracking algorithm allows the first long-term temporal observation of the lives of the intense vorticity structures (IVS). The algorithm is applied to direct numerical simulations of statistically stationary isotropic turbulence, with Taylor-based Reynolds numbers in the range $54 \leqslant Re_{\lambda } \leqslant 239$. In the highest Reynolds number case, the continuous time tracking of millions of ‘worms’ is achieved for more than seven integral time scales and close to 200 Kolmogorov time scales. Within an integral scale volume, more than 66 structures exist, and approximately 20 new structures are created per Kolmogorov time. More than $80\, \%$ of the structures live a solitary ‘life’ without any visible interaction with the other structures, while approximately $15\, \%$ break into new structures. Less than $2\, \%$ of the structures merge with others to form new vortices. A ‘population model’ is developed to estimate the numbers of existing vortices for very long simulated times, and it is observed that the birth rate density of these structures slowly increases with the Reynolds number. The survival functions of the IVS lives exhibit an exponential distribution, with some structures living for more than $35$ Kolmogorov time scales (more than four integral time scales). The mean lifetime of the IVS scales with the mean turnover time scale of the worms, defined by their radii and tangential velocity, attaining $\approx 6.5$ turnover time scales at high Reynolds numbers.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1007 , 25 March 2025 , A62
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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