5:15 PM - 6:30 PM
[MGI35-P04] Effects of hyper viscosity on surface banded structure produced by thermal convection in a rotating spherical shell
Keywords:Jovian planets, banded structure, rotating convection
Banded structures and alternating zonal jets observed in the surface atmospheres of Jupiter and Saturn have attracted many researchers in planetary atmospheric sciences, however, satisfactory physical explanations and understandings are not yet obtained. In this study, we perform massive parallel numerical experiments treating both small scale convection and planetary scale flows simultaneously, solve fine structures of turbulent motions which have not yet been resolved by the previous numerical models so far, and try to illustrate dynamical origin of global scale structures of surface flows of Jovian planets.
One of the model categories explaining the surface patterns of the gas giant plants is so called ``deep'' models, which describe thermal convection in rapidly rotating spherical shells whose thickness is comparable to the radius of the planet. The models proposed in the early stage can produce equatorial prograde flows easily, while it seems to be difficult to generate alternating jets in mid- and high-latitudes. Heimpel and Aurnou (2007) try to solve this difficulty by considering a thinner spherical shell model than that used in the previous studies performed so far, and show that the equatorial prograde zonal jets and alternating zonal jets in mid- and high-latitudes can be produced simultaneously when the Rayleigh number is sufficiently large and convection becomes active even inside the tangent cylinder. Several successive studies with the anelastic system have been performed to explain the banded structure of the gas giants. However, in these studies, longitudinal symmetry is assumed and the computational domains are not the whole but the sectorial regions of the spherical shells. Moreover, they introduced hyper viscosity in order to save the numerical resources and compensate for the model resolution. Such artificial dissipation process may influence on the structure of the global flow field, however, the effects of hyper viscosity have not been examined so far.
In the present study, we perform numerical simulations of thermal convection n the whole thin spherical shell domain for various strength of hyper viscosity. We follow the set up of Heimpel and Aurnou (2007) but we do not assume any longitudinal symmetry. The non-dimensional parameters appearing in the governing equations, the Prandtl number, the Ekman number, the modified Rayleigh number, and the radius ratio, are fixed to 0.1, 3x10-6, 0.05, and 0.85, respectively. The initial condition of the velocity field is state of rest and that of the temperature field is conductive state with random temperature perturbations.
In the initial stage of the time integrations, a strong equatorial prograde surface zonal jet and several alternating zonal jets in the mid and high latitudes, which resembles the surface zonal velocity structure of Jovian planets for all cases with different strength of hyper viscosity. However, after long time integrations, alternating jets in mid- and high- latitudes merge together and only one prograde jet appears in each hemisphere, independent of the hyper viscosity parameter.
The results suggest possibility that the surface zonal flows of the gas giants are not directly produced by fluid motions in the deep interior of the planets.
One of the model categories explaining the surface patterns of the gas giant plants is so called ``deep'' models, which describe thermal convection in rapidly rotating spherical shells whose thickness is comparable to the radius of the planet. The models proposed in the early stage can produce equatorial prograde flows easily, while it seems to be difficult to generate alternating jets in mid- and high-latitudes. Heimpel and Aurnou (2007) try to solve this difficulty by considering a thinner spherical shell model than that used in the previous studies performed so far, and show that the equatorial prograde zonal jets and alternating zonal jets in mid- and high-latitudes can be produced simultaneously when the Rayleigh number is sufficiently large and convection becomes active even inside the tangent cylinder. Several successive studies with the anelastic system have been performed to explain the banded structure of the gas giants. However, in these studies, longitudinal symmetry is assumed and the computational domains are not the whole but the sectorial regions of the spherical shells. Moreover, they introduced hyper viscosity in order to save the numerical resources and compensate for the model resolution. Such artificial dissipation process may influence on the structure of the global flow field, however, the effects of hyper viscosity have not been examined so far.
In the present study, we perform numerical simulations of thermal convection n the whole thin spherical shell domain for various strength of hyper viscosity. We follow the set up of Heimpel and Aurnou (2007) but we do not assume any longitudinal symmetry. The non-dimensional parameters appearing in the governing equations, the Prandtl number, the Ekman number, the modified Rayleigh number, and the radius ratio, are fixed to 0.1, 3x10-6, 0.05, and 0.85, respectively. The initial condition of the velocity field is state of rest and that of the temperature field is conductive state with random temperature perturbations.
In the initial stage of the time integrations, a strong equatorial prograde surface zonal jet and several alternating zonal jets in the mid and high latitudes, which resembles the surface zonal velocity structure of Jovian planets for all cases with different strength of hyper viscosity. However, after long time integrations, alternating jets in mid- and high- latitudes merge together and only one prograde jet appears in each hemisphere, independent of the hyper viscosity parameter.
The results suggest possibility that the surface zonal flows of the gas giants are not directly produced by fluid motions in the deep interior of the planets.