Analysis of the approach to the convection instability point (original) (raw)

Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection

Physical Review E, 2004

We present experimental data and their theoretical interpretation for the decay rates of temperature fluctuations in a thin layer of a fluid heated from below and confined between parallel horizontal plates. The measurements were made with the mean temperature of the layer corresponding to the critical isochore of sulfur hexafluoride above but near the critical point where fluctuations are exceptionally strong. They cover a wide range of temperature gradients below the onset of Rayleigh-Bénard convection, and span wave numbers on both sides of the critical value for this onset. The decay rates were determined from experimental shadowgraph images of the fluctuations at several camera exposure times. We present a theoretical expression for an exposure-time-dependent structure factor which is needed for the data analysis. As the onset of convection is approached, the data reveal the critical slowing-down associated with the bifurcation. Theoretical predictions for the decay rates as a function of the wave number and temperature gradient are presented and compared with the experimental data. Quantitative agreement is obtained if allowance is made for some uncertainty in the small spacing between the plates, and when an empirical estimate is employed for the influence of symmetric deviations from the Oberbeck-Boussinesq approximation which are to be expected in a fluid with its density at the mean temperature located on the critical isochore.

The origin of instability in enclosed horizontally driven convection

We demonstrate that instability in enclosed horizontally driven convection is due to a convective buoyancy-driven transverse-roll instability resembling the classical Rayleigh–Bénard convection in the thermal forcing boundary layer rather than a shear instability in the corresponding kinematic boundary layer. Instability growth is weakly sensitive to the local velocity profile, with velocity shear acting to select a transverse roll mode in preference to longitudinal rolls. The convectively unstable region grows from the hot end of the forcing boundary with increasing Rayleigh number two orders of magnitude lower than the natural onset of unstable horizontal convection. This analysis highlights the importance of the thermal boundary layer to the instability dynamics of horizontal convection, elucidating the path towards an understanding of turbulence and heat transport scaling in horizontal convection at oceanic Rayleigh numbers

Oscillatory instabilities of two-layer Rayleigh–Marangoni–Benard convection

Acta Astronautica, 2006

The Rayleigh-Marangoni-Bénard convective instability (R-M-B instability) in the two-layer systems such as Silicone oil (10cSt)/Fluorinert (FC70) and Silicone oil (2cSt)/water liquids are studied. Both linear instability analysis and nonlinear instability analysis (2D numerical simulation) were performed to study the influence of thermocapillary force on the convective instability of the two-layer system. The results show the strong effects of thermocapillary force at the interface on the time-dependent oscillations at the onset of instability convection. The secondary instability phenomenon found in the real two-layer system of Silicone oil over water could explain the difference in the comparison of the Degen's experimental observation with the previous linear stability analysis results of Renardy et al.

Spatio-temporal instability of the natural-convection boundary layer in thermally stratified medium

Journal of Fluid Mechanics, 2004

This paper investigates the spatio-temporal instability of the natural-convection boundary-layer flow adjacent to a vertical heated flat plate immersed in a thermally stratified ambient medium. The temperature on the plate surface is distributed linearly. By introducing a temperature gradient radio a between the wall and the medium, we obtain a similarity solution which can describe in a smooth way the evolution between the states with isothermal and uniform-heat-flux boundary conditions. It is shown that the flow reversal in the basic flow vanishes when a is larger than a critical value. A new absolute-convective instability transition of this flow is identified in the context of the coupled Orr-Sommerfeld and energy equations. Increasing a decreases the domain of absolute instability, and when a is large enough the absolute instability disappears. In particular, when a = 0 (isothermal surface), the interval of absolute instability becomes narrower for fluids of larger Prandtl numbers, and the absolute instability does not occur for Prandtl numbers greater than 70; when a = 1 (uniformheat-flux surface) the instability remains convective in a wide Prandtl number range. Analysis of the Rayleigh equations for this problem reveals that the basic flows supporting this new instability transition have inviscid origin of convective instability. Based on the steep global mode theory, the effects of a and Prandtl number on the global frequency are discussed as well.

Effects of modulation on Rayleigh-Benard convection. Part I

International Journal of Mathematics and Mathematical Sciences, 2004

The linear stability of a horizontal layer of fluid heated from below and above is considered. In addition to a steady temperature difference between the walls of the fluid layer, a time-dependent periodic perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. Numerical results for the critical Rayleigh number are obtained at various Prandtl numbers and for various values of the frequency. Some comparisons have been made with the known results.

Fluctuations of temperature gradients in turbulent thermal convection

Physical Review E, 2005

Broad theoretical arguments are proposed to show, formally, that the magnitude G of the temperature gradients in turbulent thermal convection at high Rayleigh numbers obeys the same advection-diffusion equation that governs the temperature fluctuation T, except that the velocity field in the new equation is substantially smoothed. This smoothed field leads to a −1 scaling of the spectrum of G in the same range of scales for which the spectral exponent of T lies between −7 / 5 and −5 / 3. This result is confirmed by measurements in a confined container with cryogenic helium gas as the working fluid for Rayleigh number Ra= 1.5ϫ 10 11. Also confirmed is the logarithmic form of the autocorrelation function of G. The anomalous scaling of dissipationlike quantities of T and G are identical in the inertial range, showing that the analogy between the two fields is quite deep.

The onset of nonpenetrative convection in a suddenly cooled layer of fluid

International Journal of Heat and Mass Transfer, 2006

Conditions for the onset of nonpenetrative convection in a horizontal Boussinesq fluid layer subject to a step change in temperature are studied using propagation theory. A wide range of Prandtl numbers and two different kinematic boundary conditions are considered. It is shown that for high Rayleigh numbers, critical conditions for the onset of convective motion reproduce exactly those for the unsteady Rayleigh-Bénard instability. Present results extend those of previous research and show a tendency of the rigid-rigid and free-rigid critical curves to converge for low Prandtl numbers. Comparison between present and previously reported results on critical conditions for the onset of instabilities and onset time using different methods yields good agreement on a middle to high Prandtl number range. A ratio of 10 between experimentally measured and theoretically predicted onset times is suggested for stress-free bounded systems.

Multi-mode spatio-temporal instability in non-Boussinesq convection

ANZIAM Journal, 2004

It is shown that nonlinear (non-Boussinesq) fluid property variations caused by large temperature differences between the walls of a vertical channel are responsible for the appearance of physically distinct types of instability in mixed convection flows: the previously known shear and new buoyancy-induced instabilities. Shear instability dominates the forced convection regimes, while the buoyancy instability prevails in nearly natural convection states. The most challenging situation requiring elaborate theoretical analysis and numerical verification arises in a mixed convection regime where both instabilities compete, forming a wide variety of possible flow patterns. Each of the instabilities is found to undergo the transition from a convective state (when disturbances grow and propagate away from their source)

Temperature fluctuations in the Ultimate Regime of Convection

Arxiv preprint arXiv: …, 2009

PACS 47.27.te-Turbulent convective heat transfer PACS 44.25.+f-Heat transfer: Natural convection PACS 47.80.-v-Instrumentation and measurement methods in fluid dynamics Abstract.-A new regime of turbulent convection has been reported nearly one decade ago, based on global heat transfer measurements at very high Rayleigh numbers. We examine the signature of this "Ultimate Regime" from within the flow itself. A systematic study of probe-size corrections shows that the earlier temperature measurements within the flow were altered by an excessive size of thermometer, but not according to a theoretical model proposed in the literature. Using a probe one order of magnitude smaller than the one used previously, we find evidence that the transition to the Ultimate Regime is indeed accompanied with a clear change in the statistics of temperature fluctuations in the flow.