An experimental study of Rayleigh–Bénard convection
in
the strongly turbulent
regime is presented. We report results obtained at low Prandtl number (in
mercury,
Pr = 0.025), covering a range of Rayleigh numbers
5 × 106 < Ra < 5 × 109, and
compare them with results at Pr∼1.
The convective chamber consists of a cylindrical cell of aspect ratio 1.Heat flux measurements indicate a regime with Nusselt number increasing
as
Ra0.26, close to the 2/7 power observed at
Pr∼1, but with a smaller prefactor, which
contradicts recent theoretical predictions. A transition to a new turbulent
regime is suggested for Ra ≃ 2 × 109,
with significant increase of the Nusselt number. The
formation of a large convective cell in the bulk is revealed by its thermal
signature on the bottom and top plates. One frequency of the temperature
oscillation is related
to the velocity of this convective cell. We then obtain the typical temperature
and
velocity in the bulk versus the Rayleigh number, and compare them with
similar
results known for Pr∼1.We review two recent theoretical models, namely the mixing zone model
of Castaing
et al. (1989), and a model of the turbulent boundary layer by
Shraiman & Siggia
(1990). We discuss how these models fail at low Prandtl number, and propose
modifications for this case. Specific scaling laws for fluids at low Prandtl
number are then obtained, providing an interpretation of our experimental
results in mercury, as well as extrapolations for other liquid metals.
On scaling laws in turbulent magnetohydrodynamic Rayleigh–Benard convection
