Spatio-temporal symmetry-breaking in the flow past an oscillating cylinder

Puneet Matharu, Andrew Hazel, Matthias Heil

Research output: Contribution to journalArticlepeer-review

Abstract

We study the flow past a cylinder whose axis undergoes prescribed oscillations, translating uniformly in a direction transverse to the oncoming flow. We consider modest Reynolds numbers ( Re≤100), for which the flow is two-dimensional; when the cylinder is fixed, vortices are shed periodically in a so-called 2S pattern. We choose the period of the prescribed oscillation to be identical to the period of the vortex shedding for a fixed cylinder. At a fixed Reynolds number of Re=100, an increase in the amplitude of the oscillations leads to a change in the topology of the shed vortices: the 2S pattern becomes a P+S pattern. We employ a space–time discretisation to directly compute time-periodic solutions of the Navier–Stokes equations and thus demonstrate that the transition between the two vortex shedding patterns arises through a spatio-temporal symmetry-breaking bifurcation of the time-periodic 2S solution. The P+S solution exists only for a finite range of amplitudes, however, and eventually reconnects with the 2S solution branch via a second symmetry-breaking bifurcation. There are ranges of amplitudes over which the system is bistable and both 2S and P+S could, in principle, be seen in experiments. As the Reynolds number is reduced, the 2S and P+S branches disconnect, but a bistable region remains until the isolated P+S solutions ultimately disappear, leaving only the 2S solution. The inferred stability of the various time-periodic solution branches is confirmed through time integration of the Navier–Stokes equations. Finally, we illustrate the evolution of the vorticity field along the solution branches.
Original languageEnglish
JournalJournal of Fluid Mechanics
Early online date17 May 2021
DOIs
Publication statusPublished - 10 Jul 2021

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