Spatio-temporal analysis of Rayleigh-B{acute e}nard convection
- Institut fuer Theoretische Physik, Technische Universitaet Graz, Petersgasse 16, A-8010 Graz, Oesterreich (Austria)
The analysis of Rayleigh-B{acute e}nard convection in a thin layer of an incompressible fluid caused by heating from below, is based on the Navier-Stokes equations. In planar geometry the Navier-Stokes equations in Bousinesq-approximation reduce to two nonlinear coupled partial differential equations for the velocity flux function {xi} and the temperature deviation {theta}. These equations are analyzed in form of spatial Fourier modes with time-dependent amplitudes. Only modes corresponding to free-free boundary conditions were selected. In this way, a set of ten coupled nonlinear ordinary differential equations for the mode amplitudes was obtained. These equations were solved numerically for different Rayleigh numbers. The temporal information in the ten dimensional phase space of the mode amplitudes is analyzed with respect to the dimension of the attractor. In addition, a time series of flow patterns in real space is constructed. For this spatio-temporal patterns the empirical orthonormal functions are determined and used to find the temporal evolution from the projection onto the basic vectors. Finally the result of different types of analysis were compared. This should lead to a better understanding how to analyze real systems in terms of observational data, e.g., thermal convection on the surface of the sun. {copyright} {ital 1996 American Institute of Physics.}
- OSTI ID:
- 401101
- Report Number(s):
- CONF-950730--
- Journal Information:
- AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 375; ISSN 0094-243X; ISSN APCPCS
- Country of Publication:
- United States
- Language:
- English
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