Turbulent Thermal Convection - Selected Topics of Computational and Experimental Fluid Mechanics - page 42

fundamental role in determining the heat transport. Further, the flow structure and
the mean wind are affected by the geometry of the system. Yet, the mean wind is
interesting in its own right. This large-scale mean flow was first observed experimen-
tally by Krishnamurti and Howard ( 1981 ) and, in experiments with helium, by Sano
et al. ( 1989 )upto10 12 and by Niemela et al. ( 2001 )upto10 13 . The importance of
the aspect ratio for the mean wind was evident already in the experiments of Niemela
and Sreenivasan Niemela and Sreenivasan ( 2003 , 2006 , 2010 ) for aspect ratios 1/2,
1 and 4, all other aspects remaining the same. Other experiments have examined dif-
ferent aspects of the mean wind. Several studies characterized the dynamics of these
large scale motions (Ciliberto et al. 1996 ; Qiu and Tong 2001 ;Xietal. 2004 ;Brown
and Ahlers 2007 ; Funfschilling et al. 2008 ) in cells of aspect ratio 1 and mod-

erate Ra . One important observation is that, once in a while, the mean wind reverses
direction. Such dramatic phenomenon has fascinating analogies. Statistics of the
wind reversal in convection experiments show the same statistical signature as solar
flare activity, which is driven by Sun's outer layer convective motion (Sreenivasan
et al. 2002 ), and the abrupt changes in mean flow direction in large-scale atmospheric
winds (van Doorn et al. 2000 ). Another important analogy is the reversal of Earth's
magnetic field which, despite the data from past reversals obtained from geological
footprints, lacks full understanding with predictive power (even for a short time).
As for Nusselt number scaling, meager amount of data is available for the case
of high aspect ratio and high Ra .For

ʓ

10 and moderate Rayleigh numbers,
simulations show the presence of cellular coherent structures (Cattaneo et al. 2001 ;
Hartlep et al. 2003 ; Parodi et al. 2004 ; Shishkina and Wagner 2005 ; von Hardenberg
et al. 2008 ). In particular, recent direct numerical simulations up to Ra

ʓ

10 8
(Bailon-Cuba et al. 2010 ) detected polygonal structures that resemble those observed
right above the onset of convection. Experimentally it would be a challenging task
to visualize these structures at high Ra . See Fig. 5 .
The work of Niemela and Sreenivasan ( 2006 )for

=

4 suggests the presence of a
single coherent mean wind over the whole container, consistent with the observations
of Krishnamurti and Howard ( 1981 ) at much lower Rayleigh numbers. However, at
very high Ra the former authors reported the absence of the wind, a result confirmed

ʓ =

Fig. 5 Images from Bailon-Cuba et al. ( 2010 ) showing the polygonal structures of the time-averaged
streamlines of the direct numerical simulations in a Rayleigh-Bénard cell with ʓ = 8for Ra =

6,000, 10 7 , and 10 8 , respectively