Natural convection in air-filled differentially heated isoflux cavities: Scalings and transition to unsteadiness, a long story made short

Abstract

We investigate numerically the transition to unsteadiness of natural convection in air filled differentially heated cavities heated and cooled with uniform flux at their vertical boundaries. This is done using both time integration of the nonlinear equations and of the linearized equations around a steady solution and computation of the leading eigenvalues of the Jacobian of steady solutions. Results are given for values of the vertical aspect ratio ranging from 0.2 to 8. In the square air filled cavity the transition occurs at a value of the flux Rayleigh number very close to 4.5×1012. We characterize different groups of eigenmodes of the Jacobian. We show that the modes responsible for the transition are characterized by a wavelike structure of constant wavelength whose amplitude increases exponentially with height in the upward boundary layer along the heated wall. We show that, at criticality, the wave characteristics are in fair agreement with values of the linear stability analysis of the buoyancy layer. We also discuss the evolution of the eigenvalues layout with the aspect ratio.