Rayleigh number

About: Rayleigh number is a research topic. Over the lifetime, 15164 publications have been published within this topic receiving 367799 citations.

Finite amplitude cellular convection

Abstract: When a layer of fluid is heated uniformly from below and cooled from above, a cellular regime of steady convection is set up at values of the Rayleigh number exceeding a critical value. A method is presented here to determine the form and amplitude of this convection. The non-linear equations describing the fields of motion and temperature are expanded in a sequence of inhomogeneous linear equations dependent upon the solutions of the linear stability problem. We find that there are an infinite number of steady-state finite amplitude solutions (having different horizontal plan-forms) which formally satisfy these equations. A criterion for ‘relative stability’ is deduced which selects as the realized solution that one which has the maximum mean-square temperature gradient. Particular conclusions are that for a large Prandtl number the amplitude of the convection is determined primarily by the distortion of the distribution of mean temperature and only secondarily by the self-distortion of the disturbance, and that when the Prandtl number is less than unity self-distortion plays the dominant role in amplitude determination. The initial heat transport due to convection depends linearly on the Rayleigh number; the heat transport at higher Rayleigh numbers departs only slightly from this linear dependence. Square horizontal plan-forms are preferred to hexagonal plan-forms in ordinary fluids with symmetric boundary conditions. The proposed finite amplitude method is applicable to any model of shear flow or convection with a soluble stability problem.

Turbulent convection at very high Rayleigh numbers

Abstract: Turbulent convection occurs when the Rayleigh number (Ra)--which quantifies the relative magnitude of thermal driving to dissipative forces in the fluid motion--becomes sufficiently high. Although many theoretical and experimental studies of turbulent convection exist, the basic properties of heat transport remain unclear. One important question concerns the existence of an asymptotic regime that is supposed to occur at very high Ra. Theory predicts that in such a state the Nusselt number (Nu), representing the global heat transport, should scale as Nu proportional to Ra(beta) with beta = 1/2. Here we investigate thermal transport over eleven orders of magnitude of the Rayleigh number (10(6) < or = Ra < or = 10(7)), using cryogenic helium gas as the working fluid. Our data, over the entire range of Ra, can be described to the lowest order by a single power-law with scaling exponent beta close to 0.31. In particular, we find no evidence for a transition to the Ra(1/2) regime. We also study the variation of internal temperature fluctuations with Ra, and probe velocity statistics indirectly.

Bénard cells and Taylor vortices

Abstract: Part I. Benard Convection and Rayleigh-Benard Convection: 1. Benard's experiments 2. Linear theory of Rayleigh-Benard convection 3. Theory of surface tension driven Benard convection 4. Surface tension driven Benard convection experiments 5. Linear Rayleigh-Benard convection experiments 6. Supercritical Rayleigh-Benard convection experiments 7. Nonlinear theory of Rayleigh-Benard convection 8. Miscellaneous topics Part II. Taylor Vortex Flow: 9. Circular Couette flow 10. Rayleigh's stability criterion 11. G. I. Taylor's work 12. Other early experiments 13. Supercritical Taylor vortex experiments 14. Experiments with two independently rotating cylinders 15. Nonlinear theory of Taylor vortices 16. Miscellaneous topics.

Many routes to turbulent convection

Abstract: Using automated laser-Doppler methods we have identified four distinct sequences of instabilities leading to turbulent convection at low Prandtl number (2·5–5·0), in fluid layers of small horizontal extent. Contour maps of the structure of the time-averaged velocity field, in conjunction with high-resolution power spectral analysis, demonstrate that several mean flows are stable over a wide range in the Rayleigh number R, and that the sequence of time-dependent instabilities depends on the mean flow. A number of routes to non-periodic motion have been identified by varying the geometrical aspect ratio, Prandtl number, and mean flow. Quasi-periodic motion at two frequencies leads to phase locking or entrainment, as identified by a step in a graph of the ratio of the two frequencies. The onset of non-periodicity in this case is associated with the loss of entrainment as R is increased. Another route to turbulence involves successive subharmonic (or period doubling) bifurcations of a periodic flow. A third route contains a well-defined regime with three generally incommensurate frequencies and no broadband noise. The spectral analysis used to demonstrate the presence of three frequencies has a precision of about one part in 104 to 105. Finally, we observe a process of intermittent non-periodicity first identified by Libchaber & Maurer at lower Prandtl number. In this case the fluid alternates between quasi-periodic and non-periodic states over a finite range in R. Several of these processes are also manifested by rather simple mathematical models, but the complicated dependence on geometrical parameters, Prandtl number, and mean flow structure has not been explained.