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  • Letter
  • Open Access

Joint multifractal description of small-scale turbulence: Unifying longitudinal and transverse velocity intermittency

Dhawal Buaria*

  • *Contact author: dhawal.buaria@ttu.edu
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Phys. Rev. Fluids 11, L092601 – Published 18 September, 2026

DOI: https://doi.org/10.1103/24bv-jqps

Abstract

Small-scale intermittency is a defining feature of fully developed fluid turbulence, marked by rare and extreme fluctuations of velocity increments and gradients that defy mean-field descriptions. Existing multifractal descriptions of intermittency focus primarily on longitudinal increments and gradients, despite mounting evidence that transverse components exhibit distinct and stronger intermittency. Here, we develop a unified multifractal framework that jointly prescribes longitudinal and transverse velocity increments, and extends to gradients. We derive explicit relations linking inertial-range scaling exponents of structure functions to moments of velocity gradients in dissipation range, which are consistent with known exact third moment relations (4/5th and 4/15th laws) and dissipation anomaly. Our results reveal that longitudinal gradient scaling is solely prescribed by longitudinal structure functions, as traditionally expected; however, transverse gradient scaling is prescribed by mixed longitudinal-transverse structure functions. Validation with high-resolution direct numerical simulations of isotropic turbulence, at Taylor-scale Reynolds number up to 1300 demonstrates excellent agreement, paving the way for a more complete and predictive description of intermittency faithful to the underlying turbulence dynamics.

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Phys. Rev. Fluids 11, L092601– Published 18 September, 2026
  • Received 14 January 2026
  • Accepted 1 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. Open access publication funded by Max Planck Society.

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