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Local origin of mode-B secondary instability in the flow past a circular cylinder

Yogesh Jethani, Kamal Kumar, A. Sameen, and Manikandan Mathur*

  • Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India

  • *manims@ae.iitm.ac.in
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Phys. Rev. Fluids 3, 103902 – Published 31 October, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.103902

Abstract

We perform a three-dimensional, short-wavelength stability analysis on the numerically simulated two-dimensional, unsteady wake resulting from a uniform flow past a circular cylinder at Reynolds numbers in the range 50≤Re≤300; here, Re=U∞D/ν with U∞, D, and ν being the free-stream velocity, the diameter of the cylinder, and the kinematic viscosity of the fluid, respectively. For a given Re, inviscid local stability equations from the geometric optics approach are solved on all the closed fluid particle trajectories with the same period as the time period of the flow. For each of the six distinct closed trajectories, denoted orbits 1–6, the growth rate is plotted as a function of Re for purely transverse perturbations. The inviscid instability on orbits 1 and 2, which are symmetric counterparts of one another, is shown to undergo bifurcations at Re≈50 and Re≈250. The bifurcation at Re≈250 from an asynchronous to a synchronous instability is argued to be related to the emergence of mode-B secondary instability, which experimental, numerical, and theoretical studies have shown to occur at Re≈260. Incorporating finite-wave-number, finite-Reynolds-number effects in the local stability framework, and comparing the corrected local stability growth rates with the global stability growth rates further support our main conclusion: The bifurcation to three-dimensional short-wavelength synchronous instability on orbits 1 and 2 is a possible local mechanism for the emergence of mode-B secondary instability. The relevance (or lack thereof) of the local instabilities on the other orbits is also discussed.

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Phys. Rev. Fluids 3, 103902– Published 31 October, 2018
  • Received 27 December 2017
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