  Starting from stationary bifurcations in Couette-Dean flow, we compute
nontrivial stationary solutions in inertialess viscoelastic circular Couette
flow. These solutions are strongly localized vortex pairs, exist at arbitrarily
large wavelengths, and show hysteresis in the Weissenberg number, similar to
experimentally observed ``diwhirl'' patterns. Based on the computed velocity
and stress fields, we elucidate a heuristic, fully nonlinear mechanism for
these flows. We propose that these localized, fully nonlinear structures
comprise fundamental building blocks for complex spatiotemporal dynamics in the
flow of elastic liquids.
