Transition to turbulence in Rayleigh-Benard convection

Two major aspects of thermal convection that are of importance for an understanding of the general phenomenon of fluid turbulence in Rayleigh-Benard convection are considered: (1) the existence of discrete structure in turbulent convection, as indicated by the kinks in the heat transport dependence and by the evidence for discrete wave numbers in the horizontal spectrum of convection; and (2) the onset of apparent randomness of fluid motions. The latter aspect is traditionally conceptualized by the Landau-Hopf picture of subsequent bifurcations leading to increasingly complex solutions. Hopf (1948) considered problems described by ordinary differential equations, but it has been established that the number of bifurcating solutions in problems of fluid mechanics increases quickly, so that highly complex turbulent motion states can be rapidly reached.