The evolution of unforced and weakly damped two-dimensional turbulence over random rough topography presents two extreme states. If the initial kinetic energy E is sufficiently high, evolution is determined by the spontaneous formation and mutual interaction of coherent vortices. High-energy vortices roam throughout the domain and mix the background potential vorticity (PV) to homogeneity.

If E is low, then vortices still form but they soon become locked to topographic features: Anticyclones sit above topographic depressions and cyclones above elevated regions. We develop a unified framework of topographic turbulence spanning these two extreme states of low and high energy. A main organizing concept is that PV homogenization demands a particular kinetic energy level E# which is the separator between high-energy evolution and low-energy evolution.

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