Numerical study of rotating convection with bi-directional temperature gradients

Abstract

In this work, we report results from three-dimensional numerical simulations of convection in a rotating cylindrical annulus with mean temperature gradients present along the radial and vertical directions. The simulations have been performed in OpenFOAM (Open-source Field Operation And Manipulation). The bi-directional temperature gradient is achieved by imposing uniform heat flux in a thin circular strip at the outer periphery of the bottom surface, and a uniform temperature at the entire inner cylindrical surface. The study has been carried out for a particular Rayleigh number, Ra = 4.76×108, and a range of Taylor numbers, Ta = 6.5×108–2.7×109. The Ra value is chosen so that some qualitative comparison could be done with available experimental data. A laminar flow solver has been used to perform the computations in a rotating frame of reference. Complex empirical orthogonal function analysis has been carried out for the velocity and temperature fields. The contour maps of the radial velocity field in the r−θ plane clearly show the existence of mode 4 and 4 AV (amplitude vacillation) baroclinic waves at low values of Ta, which break down into eddies as Ta increases. The mean temperature field in the r–z plane supports the existence of Convective Columnar Plumes (CCP) on the outer edge, which interacts with the baroclinic waves, aiding in the transport of heat in the system. The fluctuations in CCP disintegrate into smaller-scale structures at the highest Ta. Quantification of turbulent fluxes shows the effectiveness of the heat transport at Ta∼O(108), as compared to Ta∼O(109). Our results clearly demonstrate the role of waves, plumes, and eddies on heat transport in the presence of bi-directional temperature gradients.