An official website of the United States government
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.
more »
« less
Vortex splitting in two-dimensional fluids and non-neutral electron plasmas with smooth vorticity profiles
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.
more »
« less
- Award ID(s):
- 2106332
- PAR ID:
- 10591891
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Physics of Plasmas
- Volume:
- 31
- Issue:
- 5
- ISSN:
- 1070-664X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
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.more » « less
-
A computational study of vorticity reconnection, associated with the breaking and reconnection of vortex lines, during vortex cutting by a blade is reported. A series of Navier–Stokes simulations of vortex cutting with different values of the vortex strength are described, and the different phases in the vortex cutting process are compared to those of the more traditional vortex tube reconnection process. Each of the three phases of vortex tube reconnection described by Melander & Hussain ( Phys. Fluids A, vol. 1(4), 1989, pp. 633–635) are found to have counterparts in the vortex cutting problem, although we also point out numerous differences in the detailed mechanics by which these phases are achieved. Of particular importance in the vortex cutting process is the presence of vorticity generation from the blade surface within the reconnection region and the presence of strong vortex stretching due to the ambient flow about the blade leading edge. A simple exact Navier–Stokes solution is presented that describes the process by which incident vorticity is stretched and carried towards the surface by the ambient flow, and then interacts with and is eventually annihilated by diffusive interaction with vorticity generated at the surface. The model combines a Hiemenz straining flow, a Burgers vortex sheet and a Stokes first problem boundary layer, resulting in a nonlinear ordinary differential equation and a partial differential equation in two scaled time and distance variables that must be solved numerically. The simple model predictions exhibit qualitative agreement with the full numerical simulation results for vorticity annihilation near the leading-edge stagnation point during vortex cutting.more » « less
-
null (Ed.)Abstract Tropical cyclogenesis (TCG) is a multiscale process that involves interactions between large-scale circulation and small-scale convection. A near-global aquaplanet cloud-resolving model (NGAqua) with 4-km horizontal grid spacing that produces tropical cyclones (TCs) is used to investigate TCG and its predictability. This study analyzes an ensemble of three 20-day NGAqua simulations, with initial white-noise perturbations of low-level humidity. TCs develop spontaneously from the northern edge of the intertropical convergence zone (ITCZ), where large-scale flows and tropical convection provide necessary conditions for barotropic instability. Zonal bands of positive low-level absolute vorticity organize into cyclonic vortices, some of which develop into TCs. A new algorithm is developed to track the cyclonic vortices. A vortex-following framework analysis of the low-level vorticity budget shows that vertical stretching of absolute vorticity due to convective heating contributes positively to the vorticity spinup of the TCs. A case study and composite analyses suggest that sufficient humidity is key for convective development. TCG in these three NGAqua simulations undergoes the same series of interactions. The locations of cyclonic vortices are broadly predetermined by planetary-scale circulation and humidity patterns associated with ITCZ breakdown, which are predictable up to 10 days. Whether and when the cyclonic vortices become TCs depend on the somewhat more random feedback between convection and vorticity.more » « less
-
The bistable fluttering response of heavy inverted flags with different aspect ratios ( $AR$ ) is investigated to determine how the vortical structures affect the intermittent vibration response of the flag. A heavy inverted flag in a uniform flow may exhibit several response modes; amongst them are three major modes that occur over an extended velocity range: stationary, large-scale periodic oscillation and one-sided deflected modes. Significant hysteretic bistability is observed at the transition between these modes for all $AR$ , which is notably different from the conventional flag vibration with a fixed leading edge and free trailing edge where no hysteresis is observed at the lower $AR$ limit ( $AR<1$ ). The difference is associated with the distinct roles of vortices around the flag. Experiments with flags made of spring steel are conducted in a wind tunnel, where the flow speed is steadily increased and later decreased to obtain different oscillatory modes of the heavy inverted flags. The experimental results are used to validate the numerical model of the same problem. It is found that different critical velocities exist for increasing and decreasing flow velocities, and there is a sustained hysteresis for all $AR$ controlled by the initiation threshold and growth of the leading-edge and side-edge vortices. The effect of the vortices in the bistable oscillation regime is quantified by formulating a modal force partitioning approach. It is shown that $AR$ can significantly alter the static and dynamic vortex interaction with the flexible plate, thereby changing the flag's hysteresis behaviour and bistable response.more » « less
