From deterministic to distributed chaos/turbulence in Rayleigh-Bénard convection: generalized Birkhoff-Saffman invariant

The transition from deterministic to distributed chaos/turbulence at the increase of Rayleigh number (from ${10}^4$ to ${10}^8$) in Rayleigh-Bénard 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-Bénard convection, to stably stratified flows, and to observations in the atmosphere and in the solar photosphere have been briefly discussed.