Reduced Order Model for a Convective Rotating Annulus with Localized Forcing

Abstract

A low-order Galerkin model is developed for a rotating fluid annulus driven by localized heating at the outer bottom periphery, with uniform cooling at the inner cylindrical wall. The model retains the full cylindrical geometry and employs Bessel-function radial eigenfunctions satisfying physically correct Dirichlet-Neumann boundary conditions. A dual-series least-squares procedure determines the conductive base state under the mixed thermal boundary condition. Galerkin projection onto the leading radial and vertical basis functions yields a 10-variable dynamical system governing the mean meridional overturning, thermal wind, baroclinic wave amplitudes, and their nonlinear interactions. Linear stability analysis yields explicit critical Rayleigh numbers for both mean and wave instabilities, showing that rotation raises Ra_c in proportion to T^2. The model reproduces the Nu ~ Ra^(1/4) scaling, rotational suppression at low Ra, and the boundary-layer-dominated flow structure observed in companion axisymmetric simulations.

The article has been submitted to Proceedings of the Innovations in Engineering for Sustainable Transformations (InnoVEST) 2026 and is Under Review