Analytical model of rotating two-cell convection at Saturn

We use an analytical model of magnetosphere-ionosphere coupling to show that an asymmetric ring current (RC) pressure with an m = 1 longitudinal dependence can initiate a rotating two-cell interchange potential. The model extends prior similar work by considering both cold plasma interchange and warm plasma pressure. This model predicts that within 7 h the magnitude of the interchange potential equals the RC seed potential. Within 13 to 26 h, the model reproduces the degree of cold density nonaxisymmetry at the outer density gradient of the Enceladus plume, as observed by the Cassini Plasma Spectrometer. The interchange growth time bears a strong dependence on the particular value of height-integrated ionospheric conductivity and a weaker dependence on the magnitude of the initial RC perturbation. The model also extends prior work by including an outer boundary. We discuss the qualitative effect of a realistically shaped magnetopause that is anchored to the nonrotating frame. For high-m interchange, the magnetopause presence has no significant effect. In contrast, low-m interchange modes experience a rotating, asymmetric boundary condition that alternately enhances and inhibits interchange growth each rotation period. Several published studies have proposed interchange-driven, rotating two-cell convection; our results suggest that an asymmetric RC pressure distribution, coupled to Saturn's ionosphere, is one possible means of generating it. Our model predicts that the two-cell interchange potential should be long-lived and relatively insensitive to subsequent ring current injections, because after two Saturnian rotations the interchange potential is an order of magnitude larger than the seed potential that initiated it.