Strukturbildung und Turbulenz

Abstract

This work makes a contribution to the understanding of turbulent convection flows by numerically studying Rayleigh-Bénard convection in a fluid layer heated from below between two rigid horizontal boundaries. Periodic boundary conditions are used in horizontal directions. The simulations employ a pseudo-spectral method which is presented in detail. Simulations have been performed for a range of parameters with Prandtl numbers between 0.7 and 120, and Rayleigh numbers up to 10^7 (at a moderately high aspect ratio of 10) and 10^8 (for small aspect ratios). Visualizations of the flow for various cases are presented. Once the Rayleigh number exceed certain values, flow structures can be objectively classified as large or small scale structures due to a gap in spatial spectra. The typical size of the large scale structures is analysed. It broadly increases with increasing Rayleigh number. The role of mean flows whose average over horizontal planes differs from zero is also emphasized. From the simulations it is evident, that to a considerable extent the evolution towards turbulent convection at high Rayleigh numbers is governed by processes exhibited by instabilities of steady or time periodic forms of convection found at lower Rayleigh numbers. In addition, with increasing Rayleigh number the properties of convection are increasingly determined by the thermal boundary layers.