Bifurcation and chaos in zero Prandtl number convection

TL;DR

This paper investigates the complex bifurcation structures and flow patterns in zero Prandtl number Rayleigh-Bénard convection, revealing routes to chaos and various flow states through numerical and modeling approaches.

Contribution

It provides a detailed analysis of bifurcations and flow patterns near the onset of convection at zero Prandtl number, combining simulations and low-dimensional modeling.

Findings

Identification of bifurcation sequences leading to chaos

Observation of global chaos, intermittency, and crises near onset

Agreement between numerical simulations and low-dimensional models

Abstract

We present the detailed bifurcation structure and associated flow patterns near the onset of zero Prandtl number Rayleigh B\'enard convection. We employ both direct numerical simulation and a low-dimensional model ensuring qualitative agreement between the two. Various flow patterns originate from a stationary square observed at a higher Rayleigh number through a series of bifurcations starting from a pitchfork followed by a Hopf and finally a homoclinic bifurcation as the Rayleigh number is reduced to the critical value. Global chaos, intermittency, and crises are observed near the onset.