Two-dimensional turbulence above topography: Vortices and potential vorticity homogenization

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, then the topography is a weak perturbation, and evolution is determined by the spontaneous formation and mutual interaction of coherent axisymmetric vortices. High-energy vortices roam throughout the domain and mix the background potential vorticity (PV) to homogeneity, i.e., in the region between vortices, which is most of the domain, the relative vorticity largely cancels the topographic PV. 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. the low-energy case, with topographically locked vortices, the background PV retains some spatial variation. 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. Ep is the separator between high-energy evolution and low-energy evolution.

Automated summary

The evolution of unforced and weakly damped two-dimensional turbulence over random rough topography can exhibit two extreme states. When the initial kinetic energy is high, the evolution is determined by the spontaneous formation and interaction of coherent axisymmetric vortices, which mix the background potential vorticity to homogeneity. When the initial kinetic energy is low, the vortices still form but become locked to topographic features, resulting in spatial variation of the background potential vorticity.