We present experimental measurements of a sidewall traveling wave in rotating Rayleigh-Bénard convection of water (Prandtl number about 6.3) in a cylindrical cell with a diameter of 10.0 cm and a height of 1.0 cm. We used simultaneous optical-shadowgraph, heat-transport, and local temperature measurements to determine the stability and characteristics of the traveling wave state under dimensionless rotation rates ranging from 60 to 420. The state is well decribed by the 1D complex Ginzburg-Landau equation for which we determined the linear and nonlinear coefficients as functions of rotation rate. Using shadowgraph method, we also observed space-time dislocations which lead to roll creation or annihilation, typical for Eckhaus-Benjamin-Feir instability. The time and length scales over which the dislocations affected the system increased as the wavenumber approached its critical value, and the dislocations were found to always propagate counter to the precession direction of the traveling wave.
[AG.02] Thermal Turbulence in Rayleigh-Bénard Convection with and without Rotation
Robert E. Ecke, Yuanming Liu (Los Alamos National Laboratory)
We present experimental studies of turbulent Rayleigh-Bénard convection with and without rotation about a vertical axis. The working fluid, water with Prandtl number (\sigma) about 7, was confined in a cell which had a square cross section of 7.3 cm \times 7.3 cm and a height of 9.4 cm. The measurements included heat transport and local temperature, flow visualization using thermochromic liquid crystals, vertical velocity using LDV and temperature cross correlation. The range of Rayleigh numbers (R) was 2 \times 10^6 < R < 5 \times 10^8 and dimensionless rotation rates (Ømega) from 0 to 3.6 \times 10^4. Without rotation, the scaling of heat transport with \sigma and the scaling of vertical velocity and thermal fluctuations with R was determined. For rotating flows with fixed convective Rossby numbers (R_o\equiv\sqrtR/4\sigma Ømega^2) between 0.3 and 1.5, the Nusselt number (Nu) was found to scale as the 2/7 power of the Rayleigh number for R> 4 \times 10^7. We also present the probability density functions (PDF) and Fourier power spectra of temperature fluctuations at various locations in the cell, and the boundary-layer temperature profiles with or without rotation.
[AG.03] Experimental and Theoretical Study of Spherical Convection with Central Gravity.
R.E. Rosensweig, A. Zebib (Rutgers University)
The design of an experimental study of mantle convection of terrestial planets is described. Our model employs a colloidal magnetic fluid (ferrofluid) as the working substance in a spherical shell heated from the interior. A central body force field is produced by reorienting the dipolar magnetic field of a high magnetic moment permanent magnet sufficiently rapidly over all orientations. The magnet source will be floated using the ferrofluid self-levitational phenomenon to achieve universal bearing support free of mechanical contacts or sticking friction. Thus in the Earth's environment there are two driving mechanisms in the laboratory experiment: buoyant and magnetic forces. However, the effective magnetic gravity can be manipulated to be more than an order of magnitude larger than gravitational acceleration and experiments with an essentially spherically symmetric "gravity" field on Earth can be performed. The "gravitational field" produced by our concept(s) falls off like r^-4. We use linear stability calculations to determine critical Rayleigh numbers as function of the shell size and the heat loss from the outer surface. We are thus able to demonstrate the feasibility of producing an intense, central, laboratory force field simulation of a planetary gravitational field in an Earth bound laboratory.
[AG.04] The onset of convection in horizontal cylinders
John McHugh (University of New Hampshire)
An infinite solid with a horizontal cylindrical cavity which is filled with a fluid is considered. Both the solid and the fluid are assumed to have a finite thermal conductivity. The flow is driven by a linear vertical temperature gradient at infinity. The conductivity of the fluid and solid are generally not the same. Neutral stability of the purely conducting state is considered.
The problem was previously considered by Zhukovitski(E. M. Zhukhovitskij, Prikl. Mat. Mekh., v. 18, 1954.), who used a polynomial expansion with only a few terms in the expansion. The problem is now considered with an arbitrary number of base functions, and using the natural base functions for the problem, which are Bessel functions. The new results agree approximately with the old results when two-dimensional disturbances are considered. However, the new results with three-dimensional disturbances show that the neutral stability curve for odd modes has a dramatically different trend with small axial wavenumber. The neutral stability curve for even modes is also much different than the previous work, and results in a smaller critical Rayleigh number for the problem. Eigenfunctions for the most unstable modes will also be discussed.
[AG.05] Control of Streamwise Vortices in a Free Convection Boundary Layer over a Heated, Inclined Flat Plate
M. Trautman, A. Glezer (Georgia Institute of Technology)
Flow instabilities leading to the formation of streamwise vortices and heat transfer enhancement in a free convection boundary layer over a heated inclined plate (59 cm on the side) are investigated. The plate is submerged in a water tank, and the base flow is driven by a uniform, constant-heat flux film heater and forcing is provided by a lower mosaic of 32 x 10 individually controlled heating elements. The flow in planes parallel to the test surface is visualized using a double-pass shadowgraph system and the temperature distribution on the surface is measured using liquid crystal sensors. Time- invariant and harmonic spanwise-periodic excitation programs result in controlled formation of counter-rotating streamwise vortex pairs and substantial modification of the surface temperature (and heat transfer). The receptivity of the flow to the excitation input increases with inclination angle and surface heat flux. Spanwise- periodic merging of groups of vortices appear to be a precursor to the development of a secondary instability which is followed by breakdown.
Supported by NSF Grant CTS-9318332
[AG.06] Measured Temperature Fluctuations in a Convection Cell with Rough Surfaces
Yibing Du, Penger Tong (Oklahoma State University)
We report results of an experimental study of turbulent convection in water. Temperature measurements were carried out at the center of a convection cell with rough upper and lower surfaces. The vertical heat flux in the rough cells is found to be increased by \sim 25% when compared with that in the smooth cells. Probability density functions (PDF) and power spectra of the temperature fluctuations were measured at different Rayleigh numbers. It is found that the functional form of the temperature PDF's and power spectra remain unchanged in the rough cells. The RMS values and the cut-off frequencies for the temperature fluctuations in the rough cells obey similar power laws as those in the smooth cells. The experiment suggests that the surface roughness affects mainly the amplitude of the power laws whereas the scaling exponents are not changed.\par
^1 Supported by National Science Foundation grant No. DMR 93-12398.
[AG.07] Degenerate 1:2 steady mode interaction in a vertical slot
Kaoru Fujimura (Japan Atomic Energy Research Institute), Masato Nagata (University of Birmingham)
A thermal convection in a vertical slot with infinite extent is
investigated in the presence of a horizontal magnetic field
which is perpendicular to the side-walls. The 1:2 mode interaction
between two quasi-neutral steady modes sets in for relatively
small Prandtl number. In the limit of small Prandtl number and
small magnetic Prandtl number, the cubic or the quadratic coefficient
of the amplitude equations vanishes at specific Hartmann numbers,
4.04 or 8.77, respectively. In order to unfold the degeneracy,
amplitude equations of the quintic order are derived by means
of the center manifold reduction. The bifurcation diagram is
obtained based on the actual numerical coefficients of the
amplitude equations. How the local bifurcation changes as
the parameter passes through the degenerate situation is discussed.
[AG.08] Buoyancy Driven Flow in an Axisymmetric Spherical Annular Sector
Chandrasekhar Thamire, Neil T. Wright, Christian H. Von Kerczek (University of Maryland Baltimore County, Baltimore,MD)
Results from analysis of axisymmetric, laminar buoyancy driven flows
in a spherical annular sector with its outer radius equal to
1.5 times the inner radius and a sector angle of .75\pi are
presented. The spherical surfaces of the enclosure are assumed to be
heated and cooled isothermally, the radial surface being insulated.
A time marching finite differencing scheme is used to solve the
governing equations. The effects of Grashof number Gr and Prandtl
number Pr on convective motion and heat transfer are examined.
Flow patterns, changing from unicellular to multicellular flows with
increasing Gr, and heat transfer results are graphically illustrated.
Interesting recirculation zones develop at the insulated boundary for
Gr = 10^5. The heat transfer calculations indicate that the
Nusselt number depends strongly on Gr, and weakly on Pr in the range
of parameters studied.
[AG.09] Electroconvection in Sheared Annular Films
Z. A. Daya, S. W. Morris, T. C. A. Molteno (Dept. of Physics, University of Toronto), J. R. de Bruyn (Dept. of Physics, Memorial University)
We report experiments on electroconvection in thin suspended films of a smectic A liquid crystal (8CB). These films behave as nearly ideal 2D isotropic fluids. The films were annular with radius ratio (inner/outer electrode radius) \sim 0.8. Shears may be applied by rotating the inner electrode. When no shear is applied, the film is unstable to a stationary roll state when the voltage between the inner and outer edges of the annulus exceeds a critical voltage, V_c^o. The periodic units of the flow pattern are pairs of symmetric counter-rotating vortices. From the current-voltage characteristic of the film, we find the onset to be supercritical. When the inner electrode is rotated at a constant angular velocity ømega, the base state is 2D Couette flow. At a critical voltage V_c(ømega)>V_c^o, the film is unstable to a travelling roll state whose periodic units are pairs of asymmetric counter-rotating vortices. In each pair, the roll whose circulation is in the same sense as the rotation of the inner electrode is narrower while the opposite sense roll is broader. The pattern travels azimuthally at a constant angular speed which depends on ømega. From the current-voltage characteristic, we find a subcritical bifurcation with an ømega-dependent hysteresis.