Fluid vortices are common in nature, often forming when fluid flows past a boundary, and playing a key role in the onset and relaxation of turbulence. In particular, two-dimensional (2D) vortices occur in thin layers of fluid, such as the oceans and atmospheres of Earth and other planets. Research into the physics of strongly magnetized plasmas has shown that these systems behave similarly to 2D fluids in the dimensions perpendicular to the magnetic field. We create cylindrical electron plasmas in our laboratory, which are confined using a vacuum chamber and superconducting magnet, and follow the same dynamics as 2D fluid vortices. Our apparatus allows us to impose strain flows which are capable of destroying the electron plasma "vortices". By studying how these plasmas are destroyed in a controlled setting, we can learn about the properties of 2D vortices such as large-scale atmospheric or oceanic eddies.