Low-dimensional description of oscillatory thermal convection: The small Prandtl number limit
This paper is concerned with the oscillatory free convection in a Boussinesq fluid at low Prandtl numbers \(\text{Pr} =0\) and 0.1) in a long vertical channel with periodically spaced heaters along the left wall. This configuration arises frequently in electronic equipment cooled by free convective flows. The authors identify stationary characteristic structures (empirical eigenfunctions) by applying proper orthogonal decompositions to numerical solutions of the governing equations. A Galerkin procedure is then employed to obtain suitable low-order dynamical modes. The authors show that the use of the fixed points of low-order systems predicts conditions on the primary flow instability which are in good agreement with direct numerical solutions for the full model. This agreement is found to hold as long as the low-order system possesses a mechanism for Hopf bifurcations. Finally, the authors examine the effect of the number of retained eigenmodes on amplitude predictions.
scientific article; zbMATH DE number 1080973
scientific article