Direct numerical simulation of transition in a differentially heated vertical channel

The transition mechanisms of natural convection flows ensuing in a fluid layer between two differentially heated vertical plates at Prandtl number Pr = 0.71 are investigated by means of Direct Numerical Simulations. In accordance with several previous studies, results show a first bifurcation from the so-called laminar conduction regime to steady convection at Rayleigh number Ra = 5708. On the other hand, the subsequent transition to turbulence appears to be accompanied by a great sensitivity to some fundamental numerical choices such as domain size, accuracy, resolution and amplitude of the imposed perturbations. Results reveal the occurrence of a bifurcation branch which leads the system to chaos via a second bifurcation to a steady-state, a Hopf bifurcation and, seemingly, a period-doubling cascade. Although the described scenario compares well with previous findings, some doubts persist upon the possible pitfalls in the use of numerical simulation for the study of transition in this kind of systems. Indeed, several numerical aspects are found to become of crucial importance for the prediction of the dynamical behaviour and heat transfer rate of the system.