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

Gunes H., LIAKOPOULOS A., SAHAN R.

THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS, cilt.9, sa.1, ss.1-16, 1997 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 1
  • Basım Tarihi: 1997
  • Doi Numarası: 10.1007/s001620050028
  • Dergi Adı: THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1-16
  • İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

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.