Polar vortex crystals: Emergence and structure

Vortex crystals, geometric arrays of like-signed vortices, are observed in natural systems with vastly different space and time scales: at the poles of Jupiter (∼10,000-km radius and lifetime of at least 5 y) and in laboratory experiments with pure-electron plasma (∼3.5-cm radius, lifetime of about 1.7 s). We follow the adage “less is more” and show that minimal physics is required for polar vortex crystals formation and persistence. Crystals, resembling those of Jupiter, form from the free evolution of an unstratified and rapidly rotating fluid in an axisymmetric geometry. An essential ingredient in this minimal model is the decrease of the vertical component of the Coriolis force with distance from the pole. Once formed, the crystal seems to survive indefinitely.

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, Lγ=(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=fp/ap2, with f_p the Coriolis parameter at the pole and a_p the polar radius of the planet.

Transition from geostrophic turbulence to inertia-gravity waves in the atmospheric energy spectrum

Midlatitude fluctuations of the atmospheric winds on scales of thousands of kilometers, the most energetic of such fluctuations, are strongly constrained by the Earth's rotation and the atmosphere's stratification. As a result of these constraints, the flow is quasi-2D and energy is trapped at large scales—nonlinear turbulent interactions transfer energy to larger scales, but not to smaller scales. Aircraft observations of wind and temperature near the tropopause indicate that fluctuations at horizontal scales smaller than about 500 km are more energetic than expected from these quasi-2D dynamics. We present an analysis of the observations that indicates that these smaller-scale motions are due to approximately linear inertia-gravity waves, contrary to recent claims that these scales are strongly turbulent. Specifically, the aircraft velocity and temperature measurements are separated into two components: one due to the quasi-2D dynamics and one due to linear inertia-gravity waves. Quasi-2D dynamics dominate at scales larger than 500 km; inertia-gravity waves dominate at scales smaller than 500 km.