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Measuring the effect of spatial dimension on hydrodynamic turbulence using direct numerical simulation

Richard D. J. G. Ho1,2,*, Daniel Clark3, Andres Armua3, Xichao Yang3, Daniel J. Brener3, and Arjun Berera3,†

  • 1Njord Centre, Department of Physics, University of Oslo, 0371 Oslo, Norway
  • 2Department of Clinical and Molecular Medicine, Faculty of Medicine and Health Sciences, NTNU, 7491 Trondheim, Norway
  • 3School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom

  • *Contact author: richh@uio.no
  • †Contact author: ab@ed.ac.uk
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Phys. Rev. Fluids 11, 104604 – Published 14 October, 2026

DOI: https://doi.org/10.1103/5px6-bh56

Abstract

We perform direct numerical simulation of the incompressible Navier-Stokes equation with forcing at different spatial dimensions and measure turbulent and chaotic properties. Lyapunov exponents, λ, decrease with dimension, and λ<0 for all simulations in six dimensions up to Reλ=21.2. These six-dimensional simulations display non-Gaussian statistics and other behavior similar to well developed turbulence despite their lack of chaos. Further, we find that small scale perturbations do not extend to the largest scales and that this terminal scale between correlation and decorrelation shrinks with dimension. We theorize that this change is related to the increased rate of vortex stretching. We find the interplay between turbulent and chaotic properties changes with increasing dimension.

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Phys. Rev. Fluids 11, 104604– Published 14 October, 2026
  • Received 20 November 2025
  • Accepted 3 September 2026
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