Steady convection in a horizontal fluid layer

Experimental study of the competition between convective rolls in an enclosure

“…3) for our experimental conditions (horizontal boundaries moderately heat conductors and with finite thickness, the critical value of Ra : Rac is equal to t318 and critical wavenumber Kc = 2.6 instead of Rac = 1705 and Kc = 3.11 for the case of a layer infinitely extended in the horizontal direction and between perfect thermal conductors horizontal boundaries). It can also be seen that the wavenumber of supercritical convective motions decreases with increasing Rayleigh number in our case as in other experiments [1,[32][33][34][35][36] where horizontal boundaries are perfect thermal conductors As discussed by Gershuni and Zhukhovtskii [37], longitudinal rolls represent the preferred form of convection at high Pr (let us recall that for our experiment Pr = 880) for almost all inclinations as long as there exists a finite component of the temperature gradient opposite to the direction of gravity. Figure 4 shows two longitudinal rolls and two transverse rolls near A and A'.…”

“…The same behaviour was observed by other authors [1,[32][33][34][35][36][37] for perfect heat conductors boundaries. We confirmed the presence, predicted analytically and observed experimentally by Masuoka and Shimizu [39], of transverse rolls near short side walls for small inclinations.…”

Critical effects in Rayleigh-Benard convection

“…Rc its critical value ; in the case of a horizontal layer with rigid boundaries Re = 1 707. At R = Re the asymmetry of the non convecting fluid with respect to infinitesimal translations and rotations is spontaneously broken and an ordered convective state is established in the form of a remarkable spatial periodicity of the velocity [2] and of the perturbation of the temperature [3,4] ; this corresponds in the case of a rectangular cell to the well known system of parallel convecting rolls. Such behaviour presents an analogy with a second order phase transition, where the order parameter should be the velocity.…”

Flow transitions and pattern selection of the rayleigh-bénard problem in rectangular enclosures

“…Below a certain critical Rayleigh number, there is no motion since the buoyant forces cannot overcome the viscous forces. Davis (1967) and Catton (1970) Similar calculations by Biihler et al (1979) using a more complete set of trial functions showed that the critical Rayleigh number is a function of the geometrical aspect ratios. The critical Rayleigh number for the onset of motion decreases with an increase in the aspect ratio and is the lowest for the infinite layer case which is 1707.8.…”