UC San Diego

The stability and dynamics of two-dimensional (2D) ideal fluid vortices are studied under the influence of externally imposed irrotational strain flows. Laboratory experiments are conducted using pure electron plasmas. This is made possible by the isomorphism between the Drift-Poisson equations describing the dynamics of a single-component plasma perpendicular to the magnetic field and the 2D Euler equations describing inviscid, incompressible (ideal) fluids. Here, electron density is the analog of vorticity in a neutral fluid. The experimental apparatus used in this work was designed specifically to study vortex dynamics under the influence of external flows. It features a long, cylindrical electrode spanning the length of the plasma which is divided into eight azimuthal segments that can be electrically biased. Advantages of using electron plasmas to study 2D ideal fluid dynamics are that the system is dissipationless over many vortex rotation periods, the vorticity can be diagnosed directly, and the initial vorticity profile and boundary conditions can be precisely controlled. Quasi-flat, axisymmetric vorticity profiles are prepared and subjected to external strain. The results are in quantitative agreement with a dynamical theory assuming the vorticity is piecewise-constant inside an elliptical boundary. Dynamical oscillations of the ellipses are observed, as well as stationary modes, and stretching modes that lead to vortex destruction. When non-flat (e.g., Gaussian) radial vorticity profiles are used, the vortices suffer loss of outer circulation, the stability threshold for vortex destruction is lowered, and the dynamical orbits undergo inviscid damping, thus driving the system toward a stationary elliptical state. Preliminary experiments are also described in which the strength of the strain flow was varied in time. The relationship of these results to other theoretical, experimental, and numerical work is discussed, as are prospects for future research studying the dynamics of electron vortices in strain and shear flows.