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  • Letter
  • Open Access

Intermittency and nonuniversality of pair dispersion in isothermal compressible turbulence

Sadhitro De1,2,*, Dhrubaditya Mitra3,†, and Rahul Pandit2,‡

  • *Contact author: sadhitro.de@physics.ox.ac.uk
  • †Contact author: dhrubaditya.mitra@su.se
  • ‡Contact author: rahul@iisc.ac.in
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Phys. Rev. Research 8, L012037 – Published 11 February, 2026

DOI: https://doi.org/10.1103/kr1z-rf6b

Abstract

We study statistical properties of the pair dispersion of Lagrangian particles in transonic to supersonic compressible turbulence of an isothermal ideal gas in two dimensions, driven by large-scale solenoidal and irrotational stirring forces, via direct numerical simulations. We find that the scaling exponents of the order-p negative moments of the doubling and halving times of pair separations are nonlinear functions of p. Furthermore, the doubling- and halving-time statistics are different. The halving-time exponents are universal—they satisfy their multifractal model-based prediction, irrespective of the nature of the stirring. The doubling-time exponents are not. In the solenoidally stirred flows, the doubling-time exponents can be expressed solely in terms of the multifractal scaling exponents obtained from the structure functions of the solenoidal component of the velocity. Moreover, they depend strongly on the Mach number, Ma. In contrast, in the irrotationally stirred flows, the doubling-time exponents do not satisfy any known multifractal model-based relation, and are independent of Ma. Our work is a generalization of Richardson's law of pair dispersion to compressible turbulence.

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Phys. Rev. Research 8, L012037– Published 11 February, 2026
  • Received 23 July 2025
  • Accepted 19 December 2025
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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. Funded by Bibsam.

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