A preliminary report is made of some numerical calculations of two‐dimensional and geostrophic turbulent flows. The primary result is that, under a broad range of circumstances, the flow structure has its vorticity concentrated in a small fraction of the spatial domain. When such vorticity concentrations occur, they tend to assume an axisymmetric shape and persist under passive advection by the large‐scale flow except for relatively rare encounters with other centers of concentration. This structure can arise from random initial conditions without vorticity concentration. The concentrations subsequently evolve out of what has been traditionally characterized as isotropic, homogeneous, large‐Reynolds‐number turbulence with its systematic elongation of isolines of vorticity associated with the transfer of vorticity to smaller scales, eventually to dissipation scales, and the transfer of energy to larger scales. The demonstration of persistent vorticity concentrations on intermediate scales‐smaller than the scale of the peak of the energy spectrum and larger than the dissipation scales‐does not invalidate most of the traditional characterizations of two‐dimensional turbulence, but I believe it shows them to be substantially incomplete. I also believe it is likely to alter our conceptions of the phenomena involved, as well as our understanding of the predictability of such flows.