Symmetry-breaking-induced rare fluctuations in a time-delay dynamic system

Inspired by the experimental and numerical findings, we study the dynamic instabilities of two coupled nonlinear delay differential equations that are used to describe the coherent oscillations between the top and bottom boundary layers in turbulent Rayleigh-Benard convection. By introducing two sensitivity parameters for the instabilities of the top and bottom boundary layers, we find three different types of solutions, namely in-phase single-period oscillations, multi-period oscillations and chaos. The chaos solution contains rare but large amplitude fluctuations. The statistical properties of these fluctuations are consistent with those observed in the experiment for the massive eruption of thermal plumes, which causes random reversals of the large-scale circulation in turbulent Rayleigh-Benard convection. Our study thus provides new insights into the origin of rare massive eruptions and sudden changes of large-scale flow pattern that are often observed in convection systems of geophysical and astrophysical scales.

Automated summary

Inspired by experimental and numerical findings, this study investigates the dynamic instabilities of two coupled nonlinear delay differential equations describing coherent oscillations in turbulent Rayleigh-Benard convection. The research identifies three types of solutions - in-phase single-period oscillations, multi-period oscillations, and chaos, with the chaos solution exhibiting rare but large amplitude fluctuations consistent with experimental observations. The findings shed new light on the origin of rare massive eruptions and sudden changes in large-scale flow patterns in convection systems on geophysical and astrophysical scales.