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  • Open Access

Effect of hyperdiffusion on rotating Rayleigh-Bénard convection

B. Davy*

C. J. Davies and J. E. Mound

S. M. Tobias

  • EPSRC Centre for Doctoral Training in Fluid Dynamics, University of Leeds, Leeds LS2 9JT, United Kingdom

  • *Contact author: scbd@leeds.ac.uk
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Phys. Rev. Fluids 11, 013502 – Published 8 January, 2026

DOI: https://doi.org/10.1103/jvgr-d2mw

Abstract

We analyze the effect of a scale-dependent horizontal hyperdiffusivity in rotating Rayleigh-Bénard convection. The hyperdiffusion (HD) is parametrized by a cutoff wave number k0 and a growth rate q to limit its effects to the smaller scales, enabling simulations to be conducted at more rapid rotation rates and buoyancy forcing (as measured by the Ekman number Ek and Rayleigh number Ra, respectively) than in conventional direct numerical simulations (DNSs). We have performed 107 simulations spanning the ranges E=10−4--10−7 and Ra=106--7×1010 and directly compared HD and DNS heat transfer (measured by the Nusselt number Nu), flow speeds (quantified by the Péclet number Pe), force balances, and boundary layer thicknesses. We identify two different effects of HD that are particularly clear when k0 is below the dominant scale of the flow k⊥: At low supercriticality Rã, Nu, and Pe are increased compared to DNS due to a weakening of the rotational constraint; at high Rã, Nu and Pe are decreased compared to DNS owing to suppression of energy at scales greater than k⊥. The thermal boundary layer thickness changes in proportion to Nu, while the mechanical boundary layer thickness is marginally affected because it is determined by a vertical balance, whereas HD is applied horizontally. Heat transfer diagnostics are more strongly affected by HD than flow diagnostics, while changing k0 has a greater impact on solution behavior than changing q over the range of values studied. For all HD simulations with k0≥3k⊥, all diagnostics remain within the standard deviation of the DNS.

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Phys. Rev. Fluids 11, 013502– Published 8 January, 2026
  • Received 22 August 2024
  • Accepted 12 September 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.

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