Numerical study of rotating convection dynamics in a non-uniformly heated annulus

A new configuration for rotating convection is considered that mimics the localized heating of the earth’s equator for better modeling of the baroclinic waves and secondary structures in the atmosphere. Such a configuration is shown to overcome the limitation of the classical differentially heated rotating annulus by providing heating in both horizontal (meridional) and vertical directions using a localized heating strip near the outer bottom periphery and uniform cooling on the inner wall of the annulus. A finite volume method-based open-source CFD toolkit OpenFOAM is used to unravel the flow dynamics. The numerical solver is validated using the results from Williams (1971) and Ayan et. al. (2021). Numerical simulations are performed for a fixed Rayleigh number, Ra = 4.76×10⁸, and varying Taylor numbers, Ta = 6.5×10⁸, 1.5×10⁹, and 2.7×10⁹. The results show the co-existence of the baroclinic wave, meandering in the annulus, and convective columnar plume (CCP), present over the heating strip, in the annulus. For modal analysis, a Complex Empirical Orthogonal Function (CEOF) analysis of velocity and temperature data is performed which shows that the baroclinic wave is in a steady wave regime with wave mode, m = 4 at the lowest Ta. Further, with an increase in the Ta number, the baroclinic wave moves to the transition regime at Ta = 1.5×10⁹, and at Ta = 2.7×10⁹ wave moves to the irregular regime and completely breaks down into smaller eddies. Furthermore, we find that the CCP structure grows in number at Ta = 1.5×10⁹ and eventually disintegrates at Ta = 2.7×10⁹. In addition, the 1^st dominant mode of the baroclinic wave and CCP, with near 70% of the total variance, is present for Ta = 6.5×10⁸ and 1.5×10⁹. However, for the highest Ta, the dominant mode is absent due to the breakdown of the flow structures. In totality, the flow dynamics and heat transport in a non-homogenously heated annulus are governed by the non-linear interaction between the baroclinic waves and CCP.