1,854 research outputs found
Competition between Spiral-Defect Chaos and Rolls in Rayleigh-Benard Convection
We present experimental results for pattern formation in Rayleigh-Benard
convection of a fluid with a Prandtl number, Pr~ 4. We find that the
spiral-defect-chaos (SDC) attractor which exists for Pr~1 has become unstable.
Gradually increasing the temperature difference from below to well above its
critical value no longer leads to SDC. A sudden jump of temperature difference
from below to above onset causes convection to grow from thermal fluctuations
and does yield SDC. However, the SDC is a transient; it coarsens and forms a
single cell-filling spiral which then drifts toward the cell wall and
disappears.Comment: 9 pages(RevTeX), 5 jpg figures, To appear as Rapid Communication in
PR
Heat transport in turbulent Rayleigh-Benard convection: Effect of finite top- and bottom-plate conductivity
We describe three apparatus, known as the large, medium, and small apparatus,
used for high-precision measurements of the Nusselt number N as a function of
the Rayleigh number R for cylindrical samples of fluid and present results
illustrating the influence of the finite conductivity of the top and bottom
plates on the heat transport in the fluid. We used water samples at a mean
temperature of 40 degrees C (Prandtl number sigma = 4.4). The samples in the
large apparatus had a diameter D of 49.69 cm and heights L = 116.33, 74.42,
50.61, and 16.52 cm. For the medium apparatus we had D = 24.81 cm, and L =
90.20 and 24.76 cm. The small apparatus contained a sample with D = 9.21 cm,
and L = 9.52 cm. For each aspect ratio Gamma = D/L the data covered a range of
a little over a decade of R. The maximum R = 10^12 with Nusselt numbers N = 600
was reached for Gamma = 0.43. Measurements were made with both Aluminum and
Copper top and bottom plates of nominally identical size and shape. For the
large and medium apparatus the results with Aluminum plates fall below those
obtained with Copper plates, thus confirming qualitatively the prediction by
Verzicco that plates of finite conductivity diminish the heat transport in the
fluid. The Nusselt number N_infinity for plates with infinite conductivity was
estimated by fitting simultaneously Aluminum- and Copper-plate data sets to an
effective powerlaw for N_infinity multiplied by a correction factor f(X) = 1 -
exp[-(aX)^b] that depends on the ratio X of the thermal resistance of the fluid
to that of the plates as suggested by Verzicco. Within their uncertainties the
parameters a and b were independent of Gamma for the large apparatus and showed
a small Gamma-dependence for the medium apparatus. The correction was larger
for the large, smaller for the medium, and negligible for the small apparatus.Comment: 35 pages, 11 figures. Under consideration for publication in Phys. of
Fluid
Effect of the Centrifugal Force on Domain Chaos in Rayleigh-B\'enard convection
Experiments and simulations from a variety of sample sizes indicated that the
centrifugal force significantly affects rotating Rayleigh-B\'enard
convection-patterns. In a large-aspect-ratio sample, we observed a hybrid state
consisting of domain chaos close to the sample center, surrounded by an annulus
of nearly-stationary nearly-radial rolls populated by occasional defects
reminiscent of undulation chaos. Although the Coriolis force is responsible for
domain chaos, by comparing experiment and simulation we show that the
centrifugal force is responsible for the radial rolls. Furthermore, simulations
of the Boussinesq equations for smaller aspect ratios neglecting the
centrifugal force yielded a domain precession-frequency
with as predicted by the amplitude-equation model for domain
chaos, but contradicted by previous experiment. Additionally the simulations
gave a domain size that was larger than in the experiment. When the centrifugal
force was included in the simulation, and the domain size closely agreed
with experiment.Comment: 8 pages, 11 figure
Wave-number Selection by Target Patterns and Side Walls in Rayleigh-Benard Convection
We present experimental results for Rayleigh-Benard convection patterns in a
cylindrical container with static side-wall forcing induced by a heater. This
forcing stabilized a pattern of concentric rolls (a target pattern) with the
central roll (the umbilicus) at the center of the cell after a jump from the
conduction to the convection state. A quasi-static increase of the control
parameter (epsilon) beyond 0.8 caused the umbilicus of the pattern to move off
center. As observed by others, a further quasi-static increase of epsilon up to
15.6 caused a sequence of transitions. Each transition began with the
displacement of the umbilicus and then proceeded with the loss of one
convection roll at the umbilicus and the return of the umbilicus to a location
near the center of the cell. Alternatively, with decreasing epsilon new rolls
formed at the umbilicus but large umbilicus displacements did not occur. In
addition to quantitative measurements of the umbilicus displacement, we
determined and analyzed the entire wave-director field of each image. The wave
numbers varied in the axial direction, with minima at the umbilicus and at the
cell wall and a maximum at a radial position close to 2/3 Gamma. The wave
numbers at the maximum showed hysteretic jumps at the transitions, but on
average agreed well with the theoretical predictions for the wave numbers
selected in the far field of an infinitely extended target pattern.Comment: ReVTeX, 11 pages, 16 eps figures include
Confinement of the Sun's interior magnetic field: some exact boundary-layer solutions
High-latitude laminar confinement of the Sun's interior magnetic field is
shown to be possible, as originally proposed by Gough and McIntyre (1998) but
contrary to a recent claim by Brun and Zahn (A&A 2006). Mean downwelling as
weak as 2x10^-6cm/s -- gyroscopically pumped by turbulent stresses in the
overlying convection zone and/or tachocline -- can hold the field in
advective-diffusive balance within a confinement layer of thickness scale ~
1.5Mm ~ 0.002 x (solar radius) while transmitting a retrograde torque to the
Ferraro-constrained interior. The confinement layer sits at the base of the
high-latitude tachocline, near the top of the radiative envelope and just above
the `tachopause' marking the top of the helium settling layer. A family of
exact, laminar, frictionless, axisymmetric confinement-layer solutions is
obtained for uniform downwelling in the limit of strong rotation and
stratification. A scale analysis shows that the flow is dynamically stable and
the assumption of laminar flow realistic. The solution remains valid for
downwelling values of the order of 10^-5cm/s but not much larger. This suggests
that the confinement layer may be unable to accept a much larger mass
throughput. Such a restriction would imply an upper limit on possible internal
field strengths, perhaps of the order of hundreds of gauss, and would have
implications also for ventilation and lithium burning.
The solutions have interesting chirality properties not mentioned in the
paper owing to space restrictions, but described at
http://www.atmos-dynamics.damtp.cam.ac.uk/people/mem/papers/SQBO/solarfigure.htmlComment: 6 pages, 3 figures, to appear in conference proceedings: Unsolved
Problems in Stellar Physic
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