Pattern dynamics near homoclinic bifurcation in Rayleigh-B\'{e}nard convection

TL;DR

This paper investigates the pattern dynamics near an inverse homoclinic bifurcation in Rayleigh-Bénard convection, revealing a transition from nonlocal to local pattern behavior and supporting findings with numerical simulations and a simplified model.

Contribution

It is the first to analyze pattern dynamics near an inverse homoclinic bifurcation in an extended dissipative system, combining numerical simulations with a minimal model.

Findings

Divergence of the time period of patterns near the bifurcation

Transition from nonlocal to local pattern dynamics

A simple four-mode model effectively captures the observed behavior

Abstract

We report for the first time the pattern dynamics in the vicinity of an inverse homoclinic bifurcation in an extended dissipative system. We observe, in direct numerical simulations of three dimensional Rayleigh-B\'{e}nard convection, a spontaneous breaking of a competition of two mutually perpendicular sets of oscillating cross rolls to one of two possible sets of oscillating cross rolls as the Rayleigh number is raised above a critical value. The time period of the cross-roll patterns diverges, and shows scaling behavior near the bifurcation point. This is an example of a transition from nonlocal to local pattern dynamics near an inverse homoclinic bifurcation. We also present a simple four-mode model that captures the pattern dynamics quite well.