The extension of the classic Rayleigh–Bénard problem of a horizontal layer heated from below to the three-dimensional convection in rectangular boxes is dealt with in this paper both numerically and experimentally. Also discussed is the influence of shear flows in tilted boxes and the transition to time-dependent oscillatory convection. Three-dimensional numerical simulations allow the calculation of stationary solutions and the direct simulation of oscillatory instabilities. We limited ourselves to laminar and transcritical flows. For studying the particular characteristics of three-dimensional convection in horizontal containers, we carefully selected two container geometries with aspect ratios of 10:4:1 and 4:2:1. The onset of steady cellular convection in tilted boxes is calculated by an iterative application of a combined finite-difference method and a Galerkin method. The appearance of longitudinal and transverse convection rolls is determined by means of inter-ferometrical measuring techniques and is compared with the results of the linear stability theory. The spatial flow structure and the transition to oscillatory convection is calculated for selected examples in the range of supercritical Rayleigh numbers. Experimental investigations concerning the stability behaviour of the steady solutions with regard to time-dependent disturbances show a distinct influence of the Prandtl number and confirm the importance of nonlinear effects.
Steady and unsteady free convection within rotating and nonrototing rectongular boxes which are heated from below and cooled from above have been investigated. The onset of steady convection was calculated using the Boussinesq approximation and a Galerkin method. The influences of different heating rates and rotation rates on the flow configurations were measured optically. The test fluids used for demonstrating the influence of the Prandtl number and the application range of linear stability theory were silicone oil and nitrogen.
The sequence of instabilities in Rayleigh-Benard convection is studied for the case of rectangular boxes with low aspect ratio (length:width:height) which are heated from below and cooled from above. The different steady, transient and time-dependent solutions are calculated by means of an explicit finite difference method for selected values of Rayleigh number, Prandtl number and aspect ratio. The numerical results are compared with experimental observations using optical measuring techniques like interferometry and streakline-photography.
Physical Model, Basic Equations, Experimental MethodsRayleigh-Benard convection is a suitable object to study the laminar-turbulent transition in low order systems. Because turbulence in its essential properties is threedimensional, those problems should be selected, which show a high three-dimensionality also in the primary steady flow field. By this reason we have investigated the sequence of instabilities in thermal convection flows using closed rectangular boxes of low aspect ratio -especially cubical boxes -which are heated from below and cooled from above. This problem is characterized by the following dimensionless parameters: the Rayleigh number, the Prandtl number and the two aspect ratios Hz and H II , as defined below:Two types of geometries are selected: flat boxes of low aspect ratio, where flow regimes of cellular convection can be observed and cubical boxes with pronounced threedimensional flow pattern. All sidewalls are perfectly conducting.The Boussinesq-approximation is applied which leads to the following set of basic equations for the conservation of mass, momentum and energy:
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