103 research outputs found
Azimuthal diffusion of the large-scale-circulation plane, and absence of significant non-Boussinesq effects, in turbulent convection near the ultimate-state transition
We present measurements of the orientation and temperature
amplitude of the large-scale circulation in a cylindrical sample of
turbulent Rayleigh-Benard convection (RBC) with aspect ratio ( and are the diameter and height respectively) and for the
Prandtl number . Results for revealed a preferred
orientation with upflow in the West, consistent with a broken azimuthal
invariance due to Earth's Coriolis force [see \cite{BA06b}]. They yielded the
azimuthal diffusivity and a corresponding Reynolds number
for Rayleigh numbers over the range . In the classical state () the results
were consistent with the measurements by \cite{BA06a} for and
which gave , and with the
Prandtl-number dependence as found previously
also for the velocity-fluctuation Reynolds number \cite[]{HGBA15b}. At
larger the data for revealed a transition to a new
state, known as the "ultimate" state, which was first seen in the Nusselt
number and in at and
. In the ultimate state we found .
Recently \cite{SU15} claimed that non-Oberbeck-Boussinesq effects on the
Nusselt and Reynolds numbers of turbulent RBC may have been interpreted
erroneously as a transition to a new state. We demonstrate that their reasoning
is incorrect and that the transition observed in the G\"ottingen experiments
and discussed in the present paper is indeed to a new state of RBC referred to
as "ultimate".Comment: 12 pages, 4 figures, to be pub. in JFM
Absense of slow transients, and the effect of imperfect vertical alignment, in turbulent Rayleigh-Benard convection
We report experimental results for the influence of a tilt angle beta
relative to gravity on turbulent Rayleigh-Benard convection of cylindrical
samples. The measurements were made at Rayleigh numbers R up to 10^11 with two
samples of height L equal to the diameter D (aspect ratio Gamma = D/L = 1). The
fluid was water with a Prandtl number sigma = 4.38. In contrast to the
experiences reported by Chilla et. al. (2004) for a similar sample but with
Gamma = 0.5 (D = 0.5 and L = 1.0 m), we found no long relaxation times. For R =
9.4 times 10^10 we measured the Nusselt number N as a function of tilt angle
beta and obtained a small beta dependence about a factor of 50 smaller than the
result found by Chilla et. al. (2004) for their Gamma = 0.5 sample. We measured
side-wall temperatures at eight equally spaced azimuthal locations on the
horizontal mid-plane of the sample and used their cross-correlation functions
to find the turn-over time of the large-scale circulation (LSC). The resulting
Reynolds numbers R_e^cc were found to increase with beta. An important
conclusion is that the increase of R_e^cc with beta of the LSC does not
significantly influence the heat transport. Over the range 10^9 < R < 10^11 the
enhancement of R_e^cc at constant beta due to the tilt could be described by a
power law of R with an exponent of -1/6, consistent with a simple model that
balances the additional buoyancy due to the tilt angle by the shear stress
across the boundary layers. Even a small tilt angle dramatically suppressed the
azimuthal meandering and the sudden reorientations characteristic of the LSC in
a sample with beta = 0. The azimuthal mean of the temperature at the horizontal
mid-plane within our resolution was independent of beta.Comment: 32 pages, 17 figures. Under consideration for publication in J. Fluid
Mec
Logarithmic temperature profiles of turbulent Rayleigh-B\'enard convection in the classical and ultimate state for a Prandtl number of 0.8
We report on experimental determinations of the temperature field in the
interior (bulk) of turbulent Rayleigh-Benard convection for a cylindrical
sample with aspect ratio (diameter over height) of 0.50, both in the classical
and in the ultimate state. The Prandtl number was close to 0.8. We find a
"logarithmic layer" in which the temperature varies as A*ln(z/L) + B with the
distance z from the bottom plate of the sample. The amplitude A varies with
radial position r. In the classical state these results are in good agreement
with direct numerical simulations (DNS); in the ultimate state there are as yet
no DNS. A close analogy between the temperature field in the classical state
and the "Law of the Wall" for the time-averaged down-stream velocity in shear
flow is discussed.Comment: 27 pages, 15 figure
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