Bifurcations and chaos in large Prandtl-number Rayleigh-B\'{e}nard Convection

TL;DR

This paper develops a low-dimensional model for large Prandtl-number Rayleigh-Bénard convection, revealing complex bifurcation scenarios including chaos, with results aligning well with previous simulations and experiments.

Contribution

The study introduces a low-dimensional model capturing the rich bifurcation and chaos phenomena in large Prandtl-number RBC, extending understanding of flow dynamics.

Findings

Identification of multiple co-existing attractors.

Observation of chaos through quasiperiodicity and phase locking.

Match with past experimental and simulation results.

Abstract

A low-dimensional model of large Prandtl-number ($P$) Rayleigh B\'{e}nard convection is constructed using some of the important modes of pseudospectral direct numerical simulations. A detailed bifurcation analysis of the low-dimensional model for $P=6.8$ and aspect ratio of $2\sqrt{2}$ reveals a rich instability and chaos picture: steady rolls, time-periodicity, quasiperiodicity, phase locking, chaos, and crisis. Bifurcation analysis also reveals multiple co-existing attractors, and a window with time-periodicity after chaos. The results of the low-dimensional model matches quite closely with some of the past simulations and experimental results where they observe chaos in RBC through quasiperiodicity and phase locking.