10:45 AM - 12:15 PM
[MGI30-P07] Long-time integration of anelastic thermal convection in a rapidly rotating spherical shell
Keywords:Jovian planets, anelastic system, mean zonal flows, banded structure
The banded structures composed of alternating zonal jets observed in the surface atmospheres of Jupiter and Saturn have attracted many researchers in planetary atmospheric sciences. However, their satisfactory physical understandings have not been obtained yet. In this study, we perform massive parallel numerical experiments treating both small scale convection and planetary scale flows simultaneously, reveal 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'' model, where the concerned fluid motion is assumed as thermal convection in a rapidly rotating spherical shell whose thickness is comparable to the radius of the planet. The early models of this category could produce equatorial prograde flows rather easily, while they were unable to generate alternating jets in mid- and high-latitudes. Heimpel and Aurnou(2007) tried to solve this difficulty by considering a thinner spherical shell model than those used in the previous studies, and argued 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. Since then, substituting the Boussinesq system of Heimpel and Aurnou (2007) with the more realistic anelastic system, several successive studies have been performed to explain the banded structure of the gas giants.
However, in Heimpel and Aurnou (2007) and the succeeding studies, longitudinal symmetries were assumed to reduce the computational domains to be not the whole but some sectorial regions of the spherical shells. Moreover, they introduced hyper viscosity in order to save the numerical resources and to compensate for the model resolutions. Although such an artificial dissipation process may influence the structures of the global flow field, the effects of hyper viscosity have not been examined so far. We have therefore performed, with the Boussinesq system, long-time numerical simulations of thermal convection in a thin rotating spherical shell in the full global domain. As a result, we found that multiple zonal jets in mid- and high-latitudes in each hemisphere merged into a single prograde jet with time, and the banded structure in mid- and high-latitudes disappeared.
We expect the same long-time evolution as that of the Boussinesq system may occur in the anelastic system. Therefore, in this study, we perform long-time numerical simulations of thermal convection in a thin rotating spherical shell in the full global domain with the anelastic system by following the set up of Heimpel et al. (2015), which is the most realistic and highest-resolution simulation of Jovian-type atmospheric circulation using the anelastic system. We focus on whether the banded structure disappears after a long time due to the merger of multiple jets in mid- and high-latitudes. For comparison, we also perform the numerical calculation with the 4-fold longitudinal symmetry, which is adopted in Heimpel et al. (2015). Our results show that a trend toward the merger of alternating jets in the mid- and high-latitudes can be observed, and the kinetic energy is still increasing and has not yet reached a statistical equilibrium. Since the integration time is still 1000 rotations, which is about a half of that of our numerical experiments with the Boussinesq system where disappearance of banded structure was observed, we will continue to carry out time integration and observe the transitions and properties of the banded structure.
One of the model categories explaining the surface patterns of the gas giant plants is so called "deep'' model, where the concerned fluid motion is assumed as thermal convection in a rapidly rotating spherical shell whose thickness is comparable to the radius of the planet. The early models of this category could produce equatorial prograde flows rather easily, while they were unable to generate alternating jets in mid- and high-latitudes. Heimpel and Aurnou(2007) tried to solve this difficulty by considering a thinner spherical shell model than those used in the previous studies, and argued 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. Since then, substituting the Boussinesq system of Heimpel and Aurnou (2007) with the more realistic anelastic system, several successive studies have been performed to explain the banded structure of the gas giants.
However, in Heimpel and Aurnou (2007) and the succeeding studies, longitudinal symmetries were assumed to reduce the computational domains to be not the whole but some sectorial regions of the spherical shells. Moreover, they introduced hyper viscosity in order to save the numerical resources and to compensate for the model resolutions. Although such an artificial dissipation process may influence the structures of the global flow field, the effects of hyper viscosity have not been examined so far. We have therefore performed, with the Boussinesq system, long-time numerical simulations of thermal convection in a thin rotating spherical shell in the full global domain. As a result, we found that multiple zonal jets in mid- and high-latitudes in each hemisphere merged into a single prograde jet with time, and the banded structure in mid- and high-latitudes disappeared.
We expect the same long-time evolution as that of the Boussinesq system may occur in the anelastic system. Therefore, in this study, we perform long-time numerical simulations of thermal convection in a thin rotating spherical shell in the full global domain with the anelastic system by following the set up of Heimpel et al. (2015), which is the most realistic and highest-resolution simulation of Jovian-type atmospheric circulation using the anelastic system. We focus on whether the banded structure disappears after a long time due to the merger of multiple jets in mid- and high-latitudes. For comparison, we also perform the numerical calculation with the 4-fold longitudinal symmetry, which is adopted in Heimpel et al. (2015). Our results show that a trend toward the merger of alternating jets in the mid- and high-latitudes can be observed, and the kinetic energy is still increasing and has not yet reached a statistical equilibrium. Since the integration time is still 1000 rotations, which is about a half of that of our numerical experiments with the Boussinesq system where disappearance of banded structure was observed, we will continue to carry out time integration and observe the transitions and properties of the banded structure.