Scaling of hard thermal turbulence in Rayleigh-Bénard convection

Abstract

An experimental study of Rayleigh-Be'nard convection in helium gas at roughly 5 K is performed in a cell with aspect ratio 1. Data are analysed in a ' hard turbulence ' region (4 x 10' < Ra < 6 x 10l2) in which the F'randtl number remains between 0.65 and 1.5, The main observation is a simple scaling behaviour over this entire range of Ra. However the results are not the same as in previous theories. For example, a classical result gives the dimensionless heat flux, Nu, proportional to R d while experiment gives an index much closer to 5. A new scaling theory is described. This new approach suggests scaling indices very close to the observed ones. The new approach is based upon the assumption that the boundary layer remains in existence even though its Rayleigh number is considerably greater than unity and is, in fact, diverging. A stability analysis of the boundary layer is performed which indicates that the boundary layer may be stabilized by the interaction of buoyancy driven effects and a fluctuating wind.

Laboratory-numerical models of rapidly rotating convection in planetary cores

“…Such scalings have been predicted theoretically and confirmed experimentally over wide ranges of parameter space (e.g. Rossby 1969;Castaing et al 1989;Glazier et al 1999;Funfschilling et al 2005). There are two well-known Nu ∼ Ra α scaling regimes of RBC heat transfer that are accessible with our experiments.…”

“…It is often argued that the α = 1/3 law is appropriate for geophysical systems in which the boundary layers act in relative isolation, such as when they are much thinner than the total thickness of the fluid layer (e.g. Castaing et al 1989).…”

Turbulent Rayleigh–Bénard convection in low Prandtl–number fluids

“…These relatively soft fluct~ations of the velocity field are reflected in the nearly Gaussian character of the probability density functions observed in our experiments for the temperature histories recorded in the whole range of Rayleigh numbers achieved. Castaing et al (1989) introduced the notation 11 SOft turbulence .. for this type of fluctuating flow governed by a relatively small number of instability modes, which in the case of a closed flow are likely to be characterized by a finite number of discrete wave lengths giving rise to chaotic interactions.…”

“…This indicates that a uniform small scale fluctuation .. rides" on a long term, !arge scale motion. The Gauss like distribution of the fittered signal suggests, that a quite regularly structured, weakly turbulent convection exists for Rayleigh numbers of the order 106 which Castaing et al (1989) term"soft turbulence". lt is obvious from the filtering process, that the skewness S=-0.52 of the unfiltered signal originates from the oscillatory, low frequency content of the temperature signal.…”

“…{1996) lt has been debated by several research groups whether the heat transfer correlation in form of the 1/3 power law describes the experimental observations properly within the experimental error bounds or whether a power of 2/7::::::0.286 applies as derived by Castaing et al (1989). lt is not obvious a priori why careful measurements in water, conducted by Krishamurti (1994} and by Goldstein et.…”