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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. The fall of an ellipse in a stratified fluid

   https://doi.org/10.1088/1873-7005/ad9861  

   C_Hurlen, Erik; Llewellyn_Smith, Stefan G (December 2024, Fluid Dynamics Research)

   The free fall of an ellipse in an infinite linearly-stratified fluid is investigated using a linear two-dimensional, Boussinesq, diffusionless, inviscid model. The oscillations of the ellipse decay because of radiation damping, but unlike the case of a circular cylinder, the ellipse can also rotate and move horizontally. The resulting equations are solved analytically for some simple cases for which there is little or no rotation. Motions with rotation are studied numerically using a spectral method to solve for the wave field in the fluid. 

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3. Wave-induced shallow-water monopolar vortex: large-scale experiments

   https://doi.org/10.1017/jfm.2020.980  

   Kalligeris, N.; Kim, Y.; Lynett, P.J. (March 2021, Journal of Fluid Mechanics)

   null (Ed.)

   Numerous field observations of tsunami-induced eddies in ports and harbours have been reported for recent tsunami events. We examine the evolution of a turbulent shallow-water monopolar vortex generated by a long wave through a series of large-scale experiments in a rectangular wave basin. A leading-elevation asymmetric wave is guided through a narrow channel to form a flow separation region on the lee side of a straight vertical breakwater, which coupled with the transient flow leads to the formation of a monopolar turbulent coherent structure (TCS). The vortex flow after detachment from the trailing jet is fully turbulent ( $$Re_h \sim O(10^{4}\text {--}10^{5}$$ )) for the remainder of the experimental duration. The free surface velocity field was extracted through particle tracking velocimetry over several experimental trials. The first-order model proposed by Seol & Jirka ( J. Fluid Mech. , vol. 665, 2010, pp. 274–299) to predict the decay and spatial growth of shallow-water vortices fits the experimental data well. Bottom friction is predicted to induce a $$t^{-1}$$ azimuthal velocity decay and turbulent viscous diffusion results in a $$\sqrt {t}$$ bulk vortex radial growth, where $$t$$ represents time. The azimuthal velocity, vorticity and free surface elevation profiles are well described through an idealised geophysical vortex. Kinematic free surface boundary conditions predict weak upwelling in the TCS-centre, followed by a zone of downwelling in a recirculation pattern along the water column. The vertical confinement of the flow is quantified through the ratio of kinetic energy contained in the secondary and primary surface velocity fields and a transition point towards a quasi-two-dimensional flow is identified. 

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4. 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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5. Two-way wave–vortex interactions in a Lagrangian-mean shallow water model

   https://doi.org/10.1017/jfm.2022.889  

   Maitland-Davies, Cai; Bühler, Oliver (January 2023, Journal of Fluid Mechanics)

   We derive and investigate numerically a reduced model for wave–vortex interactions involving non-dispersive waves, which we study in a two-dimensional shallow water system with an eye towards applications in atmosphere–ocean fluid dynamics. The model consists of a coupled set of nonlinear partial differential equations for the Lagrangian-mean velocity and the wave-related pseudomomentum vector field defined in generalized Lagrangian-mean theory. It allows for two-way interactions between the waves and the balanced flow that is controlled by the distribution of Lagrangian-mean potential vorticity, and for strong solutions it features a desirable exact energy conservation law for the sum of wave energy and mean flow energy. Our model goes beyond standard ray tracing as we can derive weak solutions that contain discontinuities in the pseudomomentum field, using the theory of weakly hyperbolic systems. This allows caustics to form without predicting infinite wave amplitudes, as would be the case in the standard ray-tracing theory. Suitable wave forcing and dissipation terms are added to the model and a numerical scheme for the model is implemented as a coupled set of pseudo-spectral and finite-volume integrators. Idealized examples of interactions between wavepackets and simple vortex structures are presented to illustrate the model dynamics. The unforced and non-dissipative simulations suggest a heuristic rule of ‘greedy’ waves, i.e. in the long run the wave field always extracts energy from the mean flow. 

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