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Vortex crystals are quasiregular arrays of like-signed vortices in solid-body rotation embedded within a uniform background of weaker vorticity. Vortex crystals are observed at the poles of Jupiter and in laboratory experiments with magnetized electron plasmas in axisymmetric geometries. We show that vortex crystals form from the free evolution of randomly excited two-dimensional turbulence on an idealized polar cap. Once formed, the crystals are long lived and survive until the end of the simulations (300 crystal-rotation periods). We identify a fundamental length scale, L γ = ( U / γ ) 1 / 3 , characterizing the size of the crystal in terms of the mean-square velocity U of the fluid and the polar parameter γ = f p / a p 2 , with f p the Coriolis parameter at the pole and a p the polar radius of the planet.
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Evolution of secondary vorticity following vortex ring impact on a concave hemicylindrical cavity
The generation of secondary vortices from a wall-bounded vorticity sheet is a frequent occurrence in vortex ring–structure interactions. Such interactions arise in both engineering and biomedical applications, including tracheoesophageal speech. This study investigated the evolution of secondary vorticity following impact of an axisymmetric vortex ring on a concave hemicylindrical cavity. A primary vortex ring (PVR) with a formation number of F=2.00 and Reynolds number of ReΓ=1500 was generated within a water tank. Five different ratios of hemicylindrical cavity radius (Rcyl) to PVR radius (Rv) were examined; namely, γ=4, 3, 212, 2, and 112. Flow visualization and particle image velocimetry analysis of the scenarios revealed the asymmetric impact of the PVR on the cavity surface. This asymmetric impact leads to distinctive flow dynamics in the evolution of secondary vorticity across both the transverse and longitudinal planes. In the transverse plane, the PVR impact generated a secondary vortex ring (SVR) and a tertiary vortex ring (TVR). Following generation, the SVR and TVR rotated completely around the PVR. In the longitudinal plane, the SVR produced a horseshoe-like loop instead of rotating around the PVR completely. For γ=4, 3, and 212, the SVR loop moved upward due to self-induction. For γ=2 and 112, the legs of the SVR horseshoe-like loop experienced reconnection and produced two new vortex rings. The upward trajectory of the SVR horseshoe-like loop varied with γ, tending to move further from the primary ring's axis as γ decreased.
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- Award ID(s):
- 2211294
- PAR ID:
- 10580430
- Publisher / Repository:
- AIP Publishing
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 36
- Issue:
- 11
- ISSN:
- 1070-6631
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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