Chaos and the role of vortices in turbulence are investigated in the context of a two-dimensional Josephson-junction-array model. A dc current is injected perpendicular to one edge of the array. The current varies linearly from ${\mathit{I}}_{\max }$ at one corner of the edge to ${\mathit{I}}_{\min }$ at the other corner. The two control parameters are ${\mathit{I}}_{\max }$ and the transverse gradient of the current ΔI=${\mathit{I}}_{\max }$-${\mathit{I}}_{\min }$ that is equivalent to an injected vorticity. The kinetics, determined by current conservation, is in terms of phase angles, but vortices and their dynamic behavior can be monitored. The main results are the following: (a) a ΔI-vs-${\mathit{I}}_{\max }$ phase diagram for the steady-state, periodic, quasiperiodic, and various spatially varying chaotic or ‘‘turbulent’’ regimes; (b) an identification of the voltage-spectrum frequencies with appearance rates of the vortex ‘‘collective variables’’; (c) a physical picture of turbulence as a spatial rearrangement and mixing of positive and negative vortices at the drive edge, with irregular vortex appearances producing voltage chaos. The idea of collective variables for turbulence may have applications elsewhere.

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