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 w ithin a shallow layer of fluid on a rotating sphere are presented. Sim ulations show that the turbulent evolution in the spherical domain is strongly dependent on numerical and physical conditions. The independe nt effects of (1) (hyper)dissipation and initial spectrum, (2) rotatio n rate, and (3) Rossby deformation radius are carefully isolated and s tudied in detail. In the nondivergent and nonrotating case, an initial ly 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 y ields a field dominated by polar vortices-as previously reported by Yo den 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 th e rotation rate. A direct application of this shallow-water model to t he Jovian atmosphere is discussed. Using standard values for the plane tary radius and rotation, we show how the initially turbulent flow sel f-organizes into a potential vorticity held containing zonal structure s, where regions of steep potential vorticity gradients (jets) separat e relatively homogenized bands. Moreover, Jovian parameter values in o ur simulations lead to a strong vorticity asymmetry, favoring anticycl onic vortices-in further agreement with observations. (C) 1996 America n Institute of Physics.