From deterministic to distributed chaos/turbulence in Rayleigh-B\'{e}nard convection: generalized Birkhoff-Saffman invariant

TL;DR

This paper investigates the transition from deterministic to distributed chaos and turbulence in Rayleigh-Bénard convection as the Rayleigh number increases, using direct numerical simulations and a generalized Birkhoff-Saffman invariant.

Contribution

It introduces a generalized Birkhoff-Saffman invariant to analyze the transition to turbulence in Rayleigh-Bénard convection and discusses its applications to various flow scenarios.

Findings

Transition from deterministic to distributed chaos observed with increasing Rayleigh number

Generalized Birkhoff-Saffman invariant effectively characterizes turbulence onset

Applications extend to rotating convection, stratified flows, and atmospheric observations

Abstract

The transition from deterministic to distributed chaos/turbulence at the increase of Rayleigh number (from $10^4$ to $10^8$) in Rayleigh-B\'{e}nard convection, controlled by generalized Birkhoff-Saffman invariant, has been studied using the results of direct numerical simulations. The applications of this approach to rotating Rayleigh-B\'{e}nard convection, to stably stratified flows, and to observations in the atmosphere and in the solar photosphere have been briefly discussed.