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1. The decay of Hill's vortex in a rotating flow

   https://doi.org/10.1017/jfm.2021.386  

   Crowe, Matthew N.; Kemp, Cameron J.D.; Johnson, Edward R. (July 2021, Journal of Fluid Mechanics)

   null (Ed.)

   Hill's vortex is a classical solution of the incompressible Euler equations which consists of an axisymmetric spherical region of constant vorticity matched to an irrotational external flow. This solution has been shown to be a member of a one-parameter family of steady vortex rings and as such is commonly used as a simple analytic model for a vortex ring. Here, we model the decay of a Hill's vortex in a weakly rotating flow due to the radiation of inertial waves. We derive analytic results for the modification of the vortex structure by rotational effects and the generated wave field using an asymptotic approach where the rotation rate, or inverse Rossby number, is taken to be small. Using this model, we predict the decay of the vortex speed and radius by combining the flux of vortex energy to the wave field with the conservation of peak vorticity. We test our results against numerical simulations of the full axisymmetric Navier–Stokes equations. 

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2. Vortex splitting in two-dimensional fluids and non-neutral electron plasmas with smooth vorticity profiles

   https://doi.org/10.1063/5.0201712  

   Hurst, N_C; Tran, A.; Wongwaitayakornkul, P.; Danielson, J_R; Dubin, D_H_E; Surko, C_M (May 2024, Physics of Plasmas)

   Initially, elliptical, quasi-two-dimensional (2D) fluid vortices can split into multiple pieces if the aspect ratio is sufficiently large due to the growth and saturation of perturbations known as Love modes on the vortex edge. Presented here are experiments and numerical simulations, showing that the aspect ratio threshold for vortex splitting is significantly higher for vortices with realistic, smooth edges than that predicted by a simple “vortex patch” model, where the vorticity is treated as piecewise constant inside a deformable boundary. The experiments are conducted by exploiting the E × B drift dynamics of collisionless, pure electron plasmas in a Penning–Malmberg trap, which closely model 2D vortex dynamics due to an isomorphism between the Drift–Poisson equations describing the plasmas and the Euler equations describing ideal fluids. The simulations use a particle-in-cell method to model the evolution of a set of point vortices. The aspect ratio splitting threshold ranges up to about twice as large as the vortex patch prediction and depends on the edge vorticity gradient. This is thought to be due to spatial Landau damping, which decreases the vortex aspect ratio over time and, thus, stabilizes the Love modes. Near the threshold, asymmetric splitting events are observed in which one of the split products contains much less circulation than the other. These results are relevant to a wide range of quasi-2D fluid systems, including geophysical fluids, astrophysical disks, and drift-wave eddies in tokamak plasmas. 

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3. An Impulse Ghost Fluid Method for Simulating Two-Phase Flows

   https://doi.org/10.1145/3687963  

   Sun, Yuchen; Chen, Linglai; Zeng, Weiyuan; Du, Tao; Xiong, Shiying; Zhu, Bo (November 2024, ACM Transactions on Graphics)

   This paper introduces a two-phase interfacial fluid model based on the impulse variable to capture complex vorticity-interface interactions. Our key idea is to leverage bidirectional flow map theory to enhance the transport accuracy of both vorticity and interfaces simultaneously and address their coupling within a unified Eulerian framework. At the heart of our framework is an impulse ghost fluid method to solve the two-phase incompressible fluid characterized by its interfacial dynamics. To deal with the history-dependent jump of gauge variables across a dynamic interface, we develop a novel path integral formula empowered by spatiotemporal buffers to convert the history-dependent jump condition into a geometry-dependent jump condition when projecting impulse to velocity. We demonstrate the efficacy of our approach in simulating and visualizing several interface-vorticity interaction problems with cross-phase vortical evolution, including interfacial whirlpool, vortex ring reflection, and leapfrogging bubble rings. 

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4. Evolution of secondary vorticity following vortex ring impact on a concave hemicylindrical cavity

   https://doi.org/10.1063/5.0234898  

   Ahmed, T; Erath, B D (November 2024, Physics of Fluids)

   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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5. Inviscid damping of an elliptical vortex subject to an external strain flow

   https://doi.org/10.1063/5.0086227  

   Wongwaitayakornkul, P.; Danielson, J. R.; Hurst, N. C.; Dubin, D. H.; Surko, C. M. (May 2022, Physics of Plasmas)

   Inviscid spatial Landau damping is studied experimentally for the case of oscillatory motion of a two-dimensional vortex about its elliptical equilibrium in the presence of an applied strain flow. The experiments are performed using electron plasmas in a Penning–Malmberg trap. They exploit the isomorphism between the two-dimensional Euler equations for an ideal fluid and the drift-Poisson equations for the plasma, where plasma density is the analog of vorticity. Perturbed elliptical vortex states are created using [Formula: see text] strain flows, which are generated by applying voltages to electrodes surrounding the plasma. Measurements of spatial Landau damping (also called critical-layer damping) are in agreement with previous studies in the absence of an applied strain, where the damping is due to a resonance between the local fluid motion and the vortex oscillations. Interestingly, the damping rate does not change significantly over a wide range of applied strain rates. This can be accurately predicted from the initial vorticity profile, even though the resonant frequency is reduced substantially due to the applied strain. For higher amplitude perturbations, nonlinear trapping oscillations also exhibit behavior similar to the strain-free case. In principle, higher-order effects of the applied strain, such as separatrix crossing of peripheral vorticity and interactions with harmonics of the fundamental resonance, are expected to change the damping rate. However, this occurs only for conditions that are not realized in the experiments described here. Vortex-in-cell simulations are used to investigate the possible roles of these effects. 

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