Low-dimensional description of oscillatory thermal convection: The small Prandtl number limit

H. Gunes*, A. Liakopoulos, R. A. Sahan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


Low-dimensional models are derived for transitional, buoyancy-driven flow in a vertical channel with prescribed spatially periodic heating. Stationary characteristic structures (empirical eigenfunctions) are identified by applying proper orthogonal decomposition to numerical solutions of the governing partial differential equations. A Galerkin procedure is then employed to obtain suitable low-order dynamical models. Stability analysis of the fixed points of the low-order systems predicts conditions at the primary flow instability that are in very good agreement with direct numerical solutions of the full model. This agreement is found to hold as long as the low-order system possesses a possible Hopf bifurcation (minimum two-equation) mechanism. The effect of the number of retained eigenmodes on amplitude predictions is examined.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalTheoretical and Computational Fluid Dynamics
Issue number1
Publication statusPublished - 1997
Externally publishedYes


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