Due to the coherent nature of dynamics in a condensate, the cloud does not simply "spin down", rather the vortex lattice undergoes a series of dramatic distortions -- apparently "melting" into stripes. Here is an animation of our theoretical calculation of these coherent non-equilibrium dynamics. The images represent the density of the cloud of atoms. White areas correspond to high densities, dark areas to low densities. Initially the cloud contains a regular array of dark spots. These dark spots are quantized vortices. As time goes on, this array of spots periodically merge to form "stripes". The animation is configured to run for roughly 4 seconds, pause for 1 second, then rewind to the beginning and repeat.
One can understand the behavior of the vortex lattice by assuming that the vortices move with the local flow velocity. There are two major sources of flow. (1) The cloud is rotating, giving a solid-body flow pattern where the azimuthal velocity is proportional to the displacement from the center. (2) The distorted trap drives a quadrupolar flow pattern, where the x component of the velocity is proportional to the y displacement and the y component of the velocity is proportional to the x displacement. Such a quadrupolar flow is illustrated in the following figure. The black dots represent the positions of vortices which are moving with a quadrupolar flow.
Both flows (1) and (2) have the feature that the velocity is linearly related to the displacement. Thus a regular lattice of vortices remains in a regular lattice. The "stripes" are therefore just an optical illusion. If one actually looks at the location of the vortex cores, they stay at discrete points. This structure is investigated in the paper by analyzing the asymptotic behavior of theta functions.