### Abstract

The wake of an elliptical cylinder at low incident angles is investigated for different aspect 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 ; 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 and , become unstable; these modes have spatio-temporal symmetries similar to their circular cylinder wake counterparts, modes A and mode B, respectively. While mode persists for all incident angles investigated here, mode is found only to be unstable for incident angles up to . Surprisingly, for , 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.

Original language | English |
---|---|

Pages (from-to) | 245-283 |

Number of pages | 39 |

Journal | Journal of Fluid Mechanics |

Volume | 825 |

DOIs | |

Publication status | Published - 25 Aug 2017 |

### Keywords

- parametric instability
- vortex shedding
- wakes

### Cite this

*Journal of Fluid Mechanics*,

*825*, 245-283. https://doi.org/10.1017/jfm.2017.366

}

*Journal of Fluid Mechanics*, vol. 825, pp. 245-283. https://doi.org/10.1017/jfm.2017.366

**Three-dimensionality of elliptical cylinder wakes at low angles of incidence.** / Rao, Anirudh; Leontini, Justin S.; Thompson, Mark C.; Hourigan, Kerry.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Three-dimensionality of elliptical cylinder wakes at low angles of incidence

AU - Rao, Anirudh

AU - Leontini, Justin S.

AU - Thompson, Mark C.

AU - Hourigan, Kerry

PY - 2017/8/25

Y1 - 2017/8/25

N2 - The wake of an elliptical cylinder at low incident angles is investigated for different aspect 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 ; 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 and , become unstable; these modes have spatio-temporal symmetries similar to their circular cylinder wake counterparts, modes A and mode B, respectively. While mode persists for all incident angles investigated here, mode is found only to be unstable for incident angles up to . Surprisingly, for , 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.

AB - The wake of an elliptical cylinder at low incident angles is investigated for different aspect 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 ; 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 and , become unstable; these modes have spatio-temporal symmetries similar to their circular cylinder wake counterparts, modes A and mode B, respectively. While mode persists for all incident angles investigated here, mode is found only to be unstable for incident angles up to . Surprisingly, for , 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.

KW - parametric instability

KW - vortex shedding

KW - wakes

UR - http://www.scopus.com/inward/record.url?scp=85025168991&partnerID=8YFLogxK

U2 - 10.1017/jfm.2017.366

DO - 10.1017/jfm.2017.366

M3 - Article

VL - 825

SP - 245

EP - 283

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -