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

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.