Microscopic and Macroscopic Rayleigh-Benard Flows : Continuum and Particle Simulations, Turbulence, Fluctuations, Time Reversibility, and Lyapunov Instability

TL;DR

This paper explores the complex behaviors of Rayleigh-Bénard convection using various simulation methods, analyzing irreversibility, fluctuations, and instabilities across different flow regimes.

Contribution

It compares atomistic, smooth-particle, and finite-difference simulations to study flow instabilities and fluctuations in Rayleigh-Bénard convection, highlighting the effects of controlling the Rayleigh number.

Findings

Identification of flow morphologies across different Rayleigh numbers

Analysis of Lyapunov and hydrodynamic instabilities in simulations

Insights into irreversibility and fluctuations in convection flows

Abstract

We discuss the irreversibility, nonlocality, and fluctuations, as well as the Lyapunov and hydrodynamic instabilities characterizing atomistic, smooth-particle, and finite-difference solutions of the two-dimensional Rayleigh-B\'enard problem. To speed up the numerical analysis we control the time-dependence of the Rayleigh number so as to include many distinct flow morphologies in a single simulation. The relatively simple nature of these computational algorithms and the richness of the results they can yield make such studies and their interpretation particularly well suited to graduate-level research.