The emergence of jets and vortices in freely evolving, shallow-water turbulence on a sphere

Results from a series of simulations of unforced turbulence evolving within a shallow layer of fluid on a rotating sphere are presented. Simulations show that the turbulent evolution in the spherical domain is strongly dependent on numerical and physical conditions. The independent effects of ~1! ~hyper!dissipation and initial spectrum, ~2! rotation rate, and ~3! Rossby deformation radius are carefully isolated and studied in detail. In the nondivergent and nonrotating case, an initially turbulent flow evolves into a vorticity quadrupole at long times, a direct consequence of angular momentum conservation. In the presence of sufficiently strong rotation, the nondivergent long-time behavior yields a field dominated by polar vortices—as previously reported by Yoden and Yamada. In contrast, the case with a finite deformation radius ~i.e., the full spherical shallow-water system! spontaneously evolves toward a banded configuration, the number of bands increasing with the rotation rate. A direct application of this shallow-water model to the Jovian atmosphere is discussed. Using standard values for the planetary radius and rotation, we show how the initially turbulent flow self-organizes into a potential vorticity field containing zonal structures, where regions of steep potential vorticity gradients ~jets! separate relatively homogenized bands. Moreover, Jovian parameter values in our simulations lead to a strong vorticity asymmetry, favoring anticyclonic vortices—in further agreement with observations. © 1996 American Institute of Physics. @S1070-6631~96!02004-9#