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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. Simple two-layer dispersive models in the Hamiltonian reduction formalism

   https://doi.org/10.1088/1361-6544/ace3a0  

   Camassa, R. ; Falqui, G. ; Ortenzi, G. ; Pedroni, M. ; Vu Ho, T. T. ( July 2023 , Nonlinearity)

   A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids in two-dimensional domains. Beginning with the general Hamiltonian formalism of Benjamin (1986J. Fluid Mech.165445–74) for an ideal, stably stratified Euler fluid, the corresponding structure is systematically reduced to the setup of two homogeneous fluids under gravity, separated by an interface and confined between two infinite horizontal plates. A long-wave, small-amplitude asymptotics is then used to obtain a simplified model that encapsulates most of the known properties of the dynamics of such systems, such as bidirectional wave propagation and maximal amplitude travelling waves in the form of fronts. Further reductions, and in particular devising an asymptotic extension of Dirac’s theory of Hamiltonian constraints, lead to the completely integrable evolution equations previously considered in the literature for limiting forms of the dynamics of stratified fluids. To assess the performance of the asymptotic models, special solutions are studied and compared with those of the parent equations

    

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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. An idealized numerical study of tropical cyclogenesis and evolution at the Equator

   https://doi.org/10.1002/qj.3701  

   Kilroy, Gerard ; Smith, Roger K. ; Montgomery, Michael T. ( January 2020 , Quarterly Journal of the Royal Meteorological Society)

   Tropical cyclone formation and evolution at, or near, the Equator is explored using idealized three‐dimensional model simulations, starting from a prescribed, initial, weak counterclockwise rotating vortex in an otherwise quiescent,nonrotatingenvironment. Three simulations are carried out in which the maximum tangential wind speed (5 m s) is specified at an initial radius of 50, 100, or 150 km. After a period of gestation lasting between 30 and 60 hr, the vortices intensify rapidly, the evolution being similar to that for vortices away from the Equator. In particular, the larger the initial vortex size, the longer the gestation period, the larger the maximum intensity attained, and the longer the vortex lifetime. Beyond a few days, the vortices decay as the cyclonic vorticity source provided by the initial vortex is depleted and negative vorticity surrounding the vortex core is drawn inwards by the convectively driven overturning circulation. In these negative vorticity regions, the flow is inertially/centrifugally unstable. The vortex evolution during the mature and decay phases differs from that in simulations away from the Equator, where inertially unstable regions are much more limited in area. Vortex decay in the simulations appears to be related intimately to the development of inertial instability, which is accompanied by an outward‐propagating band of deep convection. The degree to which this band of deep convection is realistic is unknown.

    

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