Influence of Prandtl number on instability mechanisms and transition in a differentially heated square cavity

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Abstract
The transition from laminar to turbulent of the natural-convection flow inside a square, differentially heated cavity with adiabatic horizontal walls is calculated, using the finite-volume method. The purpose of this study is firstly to determine the dependence of the laminar-turbulent transition on the Prandtl number and secondly to investigate the physical mechanisms responsible for the bifurcations observed. It is found that in the square cavity, for Prandtl numbers between 0.25 and 2.0, the transition occurs through periodic and quasi-periodic flow regimes. One of the bifurcations is related to an instability occurring in a jet-like fluid layer exiting from those corners of the cavity where the vertical boundary layers are turned horizontal. This instability is mainly shear-driven and the visualization of the perturbations shows the occurrence of vorticity concentrations which are very similar to Kelvin–Helmholtz vortices in a plane jet, suggesting that the instability is a Kelvin–Helmholtz-type instability. The other bifurcation for Prandtl numbers between 0.25 and 2.0 occurs in the boundary layers along the vertical walls. It differs however from the related instability in the natural-convection boundary layer along an isolated vertical plate: the instability in the cavity is shear-driven whereas the instability along the vertical plate is mainly buoyancy-driven. For Prandtl numbers between 2.5 and 7.0, it is found that there occurs an immediate transition from the steady to the chaotic flow regime without intermediate regimes. This transition is also caused by instabilities originating and concentrated in the vertical boundary layers.

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