Polar vortex crystals: Emergence and structure

Vortex crystals are quasiregular arrays of like-signed vortices in solid-body rotation embedded within a uniform background of weaker vorticity. Vortex crystals are observed at the poles of Jupiter and in laboratory experiments with magnetized electron plasmas in axisymmetric geometries. We show that vortex crystals form from the free evolution of randomly excited two-dimensional turbulence on an idealized polar cap. Once formed, the crystals are long lived and survive until the end of the simulations (300 crystal-rotation periods). We identify a fundamental length scale, L_γ = (U/γ)^(1/3), characterizing the size of the crystal in terms of the mean-square velocity U of the fluid and the polar parameter γ = f_p/a²_p, with f_p the Coriolis parameter at the pole and a_p the polar radius of the planet.