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Self-similar profiles of velocity moments in turbulent round jets: A symmetry approach

Nils Benedikt1, Nrupa Chandra Girish Chandra1, and Martin Oberlack1,2,*

  • 1Chair of Fluid Dynamics, TU Darmstadt, Darmstadt, Germany
  • 2Graduate School of Computational Engineering, TU Darmstadt, Germany

  • *Contact author: oberlack@fdy.tu-darmstadt.de
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Phys. Rev. Fluids 11, 104601 – Published 5 October, 2026

DOI: https://doi.org/10.1103/f6s1-3glr

Abstract

The differential equations describing the self-similar profiles of velocity moments in turbulent round jets are investigated by the Lie-symmetry method. From this, solutions are constructed, which depend on free functions. Truncated Taylor expansion of the free functions yields expressions for the profiles. If the Taylor expansion is truncated after the leading term, the classical Gaussian profile for the mean velocity is recovered, constituting the first rigorous derivation of this well-known empirical result. Comparison to DNS data shows good agreement of the derived expressions with the actual profiles.

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References (10)

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Phys. Rev. Fluids 11, 104601– Published 5 October, 2026
  • Received 10 April 2026
  • Accepted 3 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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