Role of buoyancy work in forming superstructures in rapidly rotating Rayleigh-B{'e}nard convection

Turbulent superstructures in the form of large-scale vortices are an intrinsic feature in the rotating convection framework often used to study physics in geophysical and astrophysical systems. It is presumed that work done by buoyancy plays a minor role compared to non-linear energy transfer in forming large-scale vortices and only influences the dynamics of small-scale motions. Here we performed a direct numerical simulation in rapidly rotating Rayleigh-B{'e}nard convection paradigm at $Ra = 5 imes 10^{8}$, $E = 5 imes 10^{-6}$, $Pr=1$ and for an aspect ratio of unity to simulate a domain-filling large-scale coexisting cyclone and anticyclone superstructure. The role of buoyancy work in forming the superstructure is understood by decomposing the flow into 3D (eddies) and depth-averaged 2D (vortex) motions to understand their energy evolution from a quiescent initial state. The time evolution of energy budget equations is studied separately for 3D and 2D flow during the growth phase of the superstructure. It is observed that convective eddies organise at domain size corresponding to horizontal wavenumber $k_h=1$ during the start of the growth phase of the superstructure and acts as a dominant energy source through the buoyancy term to non-linear 3D to 2D energy transfer term, which in turn helps in the energy growth of 2D motions at $k_h=1$ resulting in the large-scale superstructure. Thus, we show that the buoyancy work has a direct influence on the formation of the large-scale superstructure.