Effects of sidewall thermal condition on the formation of poloidal circulation in rotating three-dimensional convection

Axisymmetric and three-dimensional (3 D) simulations of natural convective flows in a Boussinesq fluid contained inside a shallow rotating cylindrical domain are conducted. There is a constant and uniform heat flux into the domain from the bottom boundary. The simulation results are analyzed to shed light on the role of sidewall thermal boundary conditions on formation of poloidal circulation. Insulated sidewall (3 D-ISW) and conducting sidewall (3 D-CSW) conditions are used for both 3 D and axisymmetric calculations. The axisymmetric results show that the flow spins up rapidly, forming poloidal circulation when the heat flux (related to Rayleigh number, Ra) and rotation rate (related to Ekman number, E) are chosen carefully, which is consistent with past studies. For given values of these two parameters, the poloidal circulation is observed in 3 D-CSW but not for 3 D-ISW. A retrograde wave rotating faster near the center compared to the periphery inhibits the formation of poloidal circulation in 3 D-ISW cases, and the flow is made of depth invariant vertical convective rolls. Furthermore, the poloidal circulation forms under 3 D-CSW condition only when the global Rossby number is Ro≃C/ε, where C is a constant, and this is observed empirically over the range of parameters considered for this study with an aspect ratio of ε for the computational domain. Hence, features like cyclone eye and eyewall are not always observed in 3 D-CSW cases over the range of Ra and E yielding these features in axisymmetric calculations. Thus, the formation of poloidal circulation in 3 D domain may have stringent dynamical constraints compared to the axisymmetric model.