Sequence of bifurcations of natural convection of air in a laterally heated cube with perfectly insulated horizontal and spanwise boundaries

TL;DR

This paper investigates the complex sequence of bifurcations in natural convection within a heated cube, revealing how competing eigenmodes lead to various flow states and stability transitions influenced by buoyancy and stratification effects.

Contribution

It introduces a detailed numerical analysis of bifurcation sequences in buoyancy-driven convection, highlighting the role of eigenmode interactions and subcritical bifurcations in flow stability.

Findings

Primary instability involves two competing eigenmodes.

Bifurcations are subcritical, leading to oscillatory and stochastic states.

Flow stability is influenced by centrifugal and stratification effects.

Abstract

A sequence of three steady - oscillatory transitions of buoyancy convection of air in a laterally heated cube with perfectly thermally insulated horizontal and spanwise boundaries is studied. The problem is treated by Newton and Arnoldi methods based on Krylov subspace iteration. The finite volume grid is gradually refined from 100^3 to 256^3 finite volumes. It is shown that the primary instability is characterized by two competing eigenmodes, whose temporal development results in two different oscillatory states that differ by their symmetries. Bifurcations due to both modes are subcritical. These modes develop into different oscillatory and then stochastic flow states, which, at larger Grashof number, stabilize and arrive to single stable steady flow. With further increase of the Grashof number this flow loses it stability again. It is argued that in all the three transitions, the instabilities onsets, as well as reinstatement of stability, take place owing to an interaction between a destabilizing centrifugal mechanism and stabilizing effect of thermal stratification.