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Three-dimensionality of elliptical cylinder wakes at low angles of incidence

  • Anirudh Rao (a1), Justin S. Leontini (a2), Mark C. Thompson (a1) and Kerry Hourigan (a1)
Abstract

The wake of an elliptical cylinder at low incident angles is investigated for different aspect ratio ( $\unicode[STIX]{x1D6E4}=\text{major:minor axis ratio}$ ) cylinders using stability analysis and direct simulations. In particular, two- and three-dimensional transitions are mapped for cylinders of aspect ratios between 1 and 4 using Floquet stability analysis. The transition scenario for near-unity aspect ratio cylinders resembles that for a circular cylinder wake as Reynolds number is increased to $Re\lesssim 400$ ; first, with the transition from steady two-dimensional flow to unsteady two-dimensional flow, followed by the onset of three-dimensional flow via a long-wavelength instability (mode A), then, a short-wavelength instability (mode B) and, finally, an intermediary wavelength instability which is quasi-periodic in nature (mode QP). The effect of the incident angle on this transition scenario for the low-aspect-ratio cylinders is minimal. As the aspect ratio is increased towards 2, two synchronous modes, modes $\widehat{\text{A}}$  and $\widehat{\text{B}}$ , become unstable; these modes have spatio-temporal symmetries similar to their circular cylinder wake counterparts, modes A and mode B, respectively. While mode $\widehat{\text{A}}$  persists for all incident angles investigated here, mode $\widehat{\text{B}}$  is found only to be unstable for incident angles up to $10^{\circ }$ . Surprisingly, for $1.8\lesssim \unicode[STIX]{x1D6E4}\lesssim 2.9$ , the mode A instability observed at zero incident angle emerges as a quasi-periodic mode as the incident angle is increased even slightly. At higher incident angles, this quasi-periodic mode once again transforms to a real mode on increasing the Reynolds number. The parameter space maps for the various aspect ratios are presented in the Reynolds number–incident angle plane, and the three-dimensional modes are discussed in terms of similarities to and differences from existing modes. A key aim of the work is to map the different modes and various transition sequences as a simple body geometry is systematically changed and as the flow symmetry is systematically broken; thus, insight is provided on the overall path towards fully turbulent flow.

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Corresponding author
Email address for correspondence: mark.thompson@monash.edu
References
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