Buoyancy-Driven Flow Transitions in Deep Cavities Heated From Below

Abstract

A numerical investigation has been conducted of flow transitions in deep three-dimensional cavities heated from below. The first critical Rayleigh number, RaI, below which the flow is at rest, and the second critical Rayleigh number, RaII, for transition from steady state to oscillatory flow, have been found for cavities of aspect ratios Ar in the range 1–5. Transition to chaos has also been examined for these cases. The results show that RaI=3583,2.545×104 and 5.5×105 and RaII=4.07×105,1.65×106 and 1.30×107 for aspect ratios of 1, 2, and 5 respectively. The route to chaos is PPeriodic→QP2(Quasi-periodic with two incommensurate frequencies)→QP3(Quasi-periodic with three incommensurate frequencies)→NChaotic for Ar=1 with the Rayleigh number varying from 4.07×105 to 4.89×105. The route is PPeriodic→P2(Periodic doubling)→I(Intermittent)→P(Periodic)→N(Chaotic) for Ar=2 over a Ra range of 1.65×106 to 1.83×106. The interval between periodic and chaotic flow is very short for Ar=5.