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