Abstract:
The differentially heated square cavity, consisting of a fluid filled square enclosure with a temperature difference imposed between the two side walls, is a classical problem in natural convection that is widely used to study fundamental features of buoyancy driven flow. For low Rayleigh numbers the flow is laminar and steady. However, as the Rayleigh number is increased above a critical value, the flow is unstable, and at still higher Rayleigh numbers it is fully turbulent. The value of the critical Rayleigh number is strongly dependant upon the Prandtl number of the fluid, as is the frequency of the initial instability. In this study we use a combination of direct stability analysis and the linearised stability equations to find the critical Rayleigh number for Prandtl numbers in the range 0.011 < Pr < 1.4. Over this range we find four distinct modes of oscillation at the onset of instability.