Low-order models for the flow in a differentially heated cavity

The proper orthogonal decomposition (P.O.D.) is applied to the flow in a differentially heated cavity. The fluid considered is air, and the aspect ratio of the cavity is 4. At a fixed Rayleigh number, P.O.D. empirical functions are extracted, and low-dimensional models are built and compared to the numerical simulation. Generally speaking, low-D models provide a coarse picture of the flow, which is also quick, cheap, and easy to understand. They can help pinpoint leading instability mechanisms. They are potentially key players in a number of applications such as optimization and control. Our goal in this study is to determine how well the flow can be represented by very low-dimensional models. Two moderately complex situations are examined. In the first case, at some distance from the bifurcation point, the dynamics can still be reduced down to two modes, although it is necessary to account for the effect of higher-order modes in the model. In the second case, farther away from the bifurcation, the flow is chaotic. A ten-dimensional model successfully captures the essential dynamics of the flow. The procedure was seen to be robust. It clearly illustrates the power of the P.O.D. as a reduction tool. (C) 2001 American Institute of Physics.