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Effect of confinement on the transition from two- to three-dimensional fast-rotating turbulent flows

Chandra Shekhar Lohani1,*,†, Suraj Kumar Nayak1,*,‡, and Kannabiran Seshasayanan1,2

  • 1Department of Physics, Indian Institute of Technology Kharagpur, 721302, India
  • 2Department of Applied Mechanics and Biomedical Engineering, Indian Institute of Technology Madras, 600036, India

  • *These authors contributed equally to this work.
  • †cslohani25@gmail.com
  • ‡surajkumarnayak96@gmail.com
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Phys. Rev. Fluids 9, 034604 – Published 11 March, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.034604

Abstract

We study the effect of confinement on the three-dimensional linear instability of fast-rotating two-dimensional turbulent flows. Using large-scale friction to model the effect of rigid boundaries at the top and bottom, we study the onset of three-dimensional perturbations on a rapidly rotating flow. The friction term is taken to affect both the evolution of the two-dimensional turbulent flow and the perturbations that evolve on top of it. Using direct numerical simulations, the threshold for the onset of three-dimensional perturbations is traced out as a function of the control parameters. As reported in the earlier work of Seshasayanan et al. [J. Fluid Mech. 901, R5 (2020)], we find that the two different mechanisms, namely the centrifugal and parametric-type instabilities, are responsible for the destabilization across the wide range of parameters explored in this study. In the turbulent regime, we find that the large-scale friction term does not affect the threshold in the case of centrifugal instability, while in the case of parametric instability, the large-scale friction makes the flow stable for a wider range of parameters. For the parametric instability, the length scale of the unstable mode is found to scale as the inverse square root of the rotation rate and the growth rate of the unstable mode is found to be correlated with the minimum of the determinant of the strain rate tensor of the underlying two-dimensional turbulent flow, showing resemblance with elliptical type instabilities. Results from the turbulent flow are then compared with the oscillatory Kolmogorov flow, which also undergoes parametric instability resulting into inertial waves. The dependence of the threshold on the aspect ratio of the system is discussed for both the turbulent and the oscillating Kolmogorov flows.

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Phys. Rev. Fluids 9, 034604– Published 11 March, 2024
  • Received 23 August 2023
  • Accepted 2 February 2024
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