Influence of Aspect ratio in the Convection in Rotating Annulus In the Presence of Localized Heating

Abstract

Two-dimensional (2D) axisymmetric simulations are conducted to investigate convection in a rotating cylindrical annulus with localized heating at the outer bottom edge and uniform cooling at the inner cylindrical wall. The resulting radial and vertical temperature gradients generate buoyancy-driven motion and produce a stratification pattern relevant to atmospheric circulation. The effects of aspect ratio (\(Γ\)), Rayleigh number (\(Ra = 2.4 \times 10^{7}\)--\(1.2 \times 10^{9}\)), and Taylor number (\(Ta = 1.6 \times 10^{7}\)--\(1.2 \times 10^{9}\)), including the non-rotating limit (\(Ta=0\)), are examined. Convection is largely confined to thin boundary layers, while the fluid interior remains diffusion dominated. Without rotation, the temperature field exhibits nearly horizontal isotherms. Rotation establishes quasi-hydrostatic and geostrophic balances that redistribute heat and promote deeper penetration of isotherms into the interior. Heat transfer, quantified by the Nusselt number (\(Nu\)), depends strongly on \(Ra\), \(Ta\), and \(Γ\). For moderate and high \(Ra\), \(Nu\) follows the scaling \(Nu \sim Ra^{1/4}\) and is only weakly influenced by rotation. At low \(Ra\) and high \(Ta\), rotational suppression of buoyancy reduces \(Nu\) significantly. Increasing \(Γ\) enhances heat transfer, although the growth rate diminishes for \(Γ> 1\). The relative thermal and Ekman boundary-layer thicknesses govern the sensitivity of heat transfer to rotation.