Session Hi - Convection & Buoyancy.
ORAL session, Tuesday, November 25
309, Moscone Center

[Hi.01] Thermocapillary Flows with Low Frequency g-Jitter

A thermocapillary parallel flow is established in a fluid filled slot with an applied temperature gradient. Low frequency jitter is imposed in arbitrary directions. Vertical jitter proves to be relatively uninteresting, merely augmenting or opposing the basic thermocapillary flow. Streamwise jitter still produces parallel flows, but these now exhibit boundary layers or layered cellular structures for large Rayleigh number as the applied stratification alternates between stable and unstable. Runaways are possible for unstable stratification and these correspond to resonant excitation of stationary long wave Rayleigh-Bénard modes. Spanwise jitter produces fully three dimensional motion. A spanwise-streamwise circulation results for weak spanwise jitter, which advects the interfacial temperature establishing a subsidiary spanwise flow. This flow is strong at small Biot number when advected temperature is trapped in the slot, and has a counterintuitive dependence on the spanwise-streamwise aspect ratio.

[Hi.02] Time dependence in the two-layer Rayleigh-Bénard system

We present experimental results from our study of buoyancy-driven convection in a two-layer system of immiscible fluids heated from below and cooled from above. We have used shadowgraph imaging to study two different systems with two distinct geometries: annular and rectangular. We will describe the onset to time-dependence at a temperature difference slightly above the onset to convection with Rhone Poulenc's Rhodorsil 47v10 silicone oil and 3M's Fluorinert FC70 as the working fluids. The wavelengths and periods of the time-dependent states will be compared for the two systems. Additionally, the motion of the roll pattern will be characterized as the temperature difference is varied. Finally, the experimental results will be compared to theoretical predictions(Y.Renardy, ZAMP 47), 567, (1996). for this set of fluids.

[Hi.03] On the Onset of Thermal Convection with a Time-Periodic Thermal Gradient with Zero Mean

We study the stability of a fluid layer heated from below in a periodic manner with time when the mean temperatures of the horizontal boundaries are equal. For large values of nondimensional frequency parameter \beta, the problem reduces to determining the stability of a thermal Stokes layer. Previous research^1-3 has shown that a subharmonic disturbance is then the most critical. For \beta \sim O, however, subharmonic and synchronous disturbances alternate as being most critical. We determine the value of \beta at which the transition occurs in the nature of the solutions.

^1G.Z. Gershuni and E.M. Zhukhovitskii, Convective Stability of Incompressible Fluids (1976), Sect. 36.//

^2J.J. Niemela and R.J. Donnelly, Phys. Rev. Lett. 57, 583 (1986).//

^3P.C. Hohenberg and J.B. Swift, Phys. Rev. A 35, 3855 (1987).//

[Hi.04] The Flickering Candle:Transition to a Global Mode in a Thermal Plume

Observations of flickering candle flames are universal. Recently it has been associated with an instability of the flame and/or plume above it and the subsequent formation and growth of axisymmetric vortices from the flame base. A question arises as to the dynamics of this instability; is it of the convective type or does it represent the excitation of a global mode? Experiments with a wide range of burner types have shown firstly that the diffusion flame often just acts as a buoyancy source and only the instability of the plume is relevent. At low fuel flow rates the far-plume is unstable to helical disturbances. As the flow-rate is increased the instability approaches the source and becomes axisymmetric at a well-defined frequency. This frequency is robust to external perturbations. At intermediate flows the appearance of the axisymmetric mode is intermittent with near exponential growth and decay. We conclude tentatively that the instability has the characteristics of a global mode.

[Hi.05] Influence of a constant and uniform magnetic field on the convection in cylindrical cavity heated from below

Three dimensional steady flows are simulated in a cylindrical cavity of aspect ratio A=H/D, with H the height and D the diameter. The cavity is heated from below and its sidewalls are considered to be adiabatic. Continuation is used to construct bifurcation diagrams. Axisymmetric (m=0), and asymmetric (m=1 and m=2) modes are observed. Without magnetic field for A=0.5 the the axisymmetric solution loses stability at a secondary bifurcation point to a three-dimensional solution. The vertical magnetic field keeps the same symmetries for the flows in the cavity. Similar convection modes are obtained but they are not equally stabilized, so that the mode m=2 becomes a critical mode in the intermediate range of aspect ratio (around A=0.55) for sufficiently large intensity of the magnetic field. The use of a transverse magnetic field is more subtle as it breaks some symmetries of the flows. The three original modes (m=0, 1, 2) are now five : two m=1 modes, two m=02 modes and one m=2 mode. These modes are differently stabilized, weakly if the axis of the rolls is parallel to B, strongly if the axis is perpendicular. Beyond the primary thresholds, for A=0.5, the disappearance of the secondary bifurcation point is observed, because the first branche of solutions is already a m=02 mode.

[Hi.06] Effect of Gravity Modulation on the Stability of Convection in a Vertical Slot

We consider the stability of convection in a differentially heated vertical slot under a modulated gravity field, g = g_0 + g_1\cos ømega t. Applying normal mode analysis to the linear stability equations, a set of simultaneous ordinary differential equations with periodic coefficients are obtained for the perturbation amplitute. When the Floquet theory is applied to find the asymptotically stable state, it is necessary to integrate the amplitute equations over a complete period. At low modulation frequencies, numerical integration becomes more time consuming and less accurate. To alleviate this difficulty, we apply the Chebyshev expansion method developed by Sinha and Wu (1991, J. Sound and Vibration 151 91-117) for the analysis of periodic systems. Results show that instability onsets in the synchronous model when Pr is small and in the quasi-periodic mode when Pr is large. For a Pr = 1 fluid at a nondimensional modulation frequency of 20, the neutral stability curve is bimodal. As a consequence, the critical Grashoff number exhibits discontinuous slope with respect to the modulation amplitude ratio, g_1/g_0.

This research was supported by NASA, Micrograbity Science and Applications Division.

[Hi.07] Prandtl number dependence of Nusselt number in DNS

Simulation results on the Prandtl and Rayleigh number dependence of the Nussult number for Pr=0.07 to 7 are reported. Ra up to 10^7 is used for Pr>1, but for Pr=0.07 the largest Ra is 2\times10^6 due to the vigorous turbulent motion and high Reynolds number. Initial results support experimental work for a strong dependence on Prandtl number for Pr<1 and nearly no dependence for Pr>1. Statistical errors are still too large to determine the exact trend for Pr>1.

[Hi.08] Transition to Turbulence in Non-Linear Convective Wave-Patterns

We obtain experimental wave-patterns by destabilizing a fluid layer subjected to a horizontal temperature gradient with a free surface. These waves have been compared to the hydrothermal waves predicted by a linear stability analysis of a parallel flow(M.K.~Smith and S.H.~Davis, J. Fluid Mech. 132), 119 (1983).. The experimental setups consist in a rectangular box whose larger extension is perpendicular to the horizontal temperature gradient and an annular box. A new wave-pattern transition to turbulence is evidenced in the annular case. First the supercritical traveling wave pattern undergoes a phase instability: a supercritical Eckhaus instability. This secondary bifurcation is the first experimental observation of a second order phase instability for non-linear traveling waves as predicted by Fauve(S.~Fauve, in Instabilities and Nonequilibrium Structures), eds. E.~Tira\-pe\-gui and D.~Villaroel, Reidel, pp 63--88, (1987).. This leads to a small wavenumber phase-modulated mode which, at higher forcing level, is subject to a tertiary instability. This mode is an amplitude mode characterized by traveling holes patterns(N.~Bekki and K.~Nozaki, Physics Letters 110A) 133 (1985)., i.e., topological defects that qualitatively transform the wave pattern.

[Hi.09] Roughness Effects on Convection in a Rectangular Cubic Box

Effects of rough boundary on nonlinear convection in a finite rectangular cubic box of fluid saturated porous material and with arbitrary aspect ratios are investigated for the values of the Rayleigh number near the classical critical value.The finiteness of the box and its geometry allow only finite number of solutions.The preferred nonlinear solutions are determined by a stability analysis.Roughness elements with appropriate size,number and locations have significant effects on the resulting solutions.In particular,2 or 3-D solutions,admitted by the box aspect ratios and by the nonlinear system,can be made stable,unstable,subcritical or supercritical and the associated heat flux can be made maximum or minimum by the roughness elements.

[Hi.10] Measured Temperature Boundary Layers in a Convection Cell with Rough Surfaces

Temperature boundary layer measurements were carried out in a convection cell with rough upper and lower surfaces. The vertical heat flux in the rough cells is found to be increased by 75% compared with that in the smooth cells, when the Rayleigh number Ra becomes much larger than a transition value Ra_c. The boundary layer measurements indicate that at high Rayleigh numbers the temperature profile follows the contour of the rough surface. It is found that temperature fluctuations are enhanced in the interstice region between the roughness elements. The experiment reveals that the main effect of the surface roughness is to increase the emission of large thermal plumes.

Part H of program listing