Low-dimensional description of oscillatory thermal convection: The small Prandtl number limit
type: Item
instance of: scholarly article
title: Low-dimensional description of oscillatory thermal convection: The small Prandtl number limit
zbMATH Open document ID: 0904.76080
author: J. Ning
published in: Theoretical and Computational Fluid Dynamics
publication date: 1997-10-28T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76R10
Mathematics Subject Classification ID: 76E15
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 1080973
zbMATH Keywords: empirical eigenfunctions
zbMATH Keywords: Boussinesq fluid
zbMATH Keywords: vertical channel
zbMATH Keywords: orthogonal decompositions
zbMATH Keywords: Galerkin procedure
zbMATH Keywords: fixed points
zbMATH Keywords: Hopf bifurcations
reviewed by: Ioan Pop
MaRDI profile type: Publication
full work available at URL: s001620050028
OpenAlex ID: W2086905645
DOI: 10.1007/S001620050028
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description: scientific article; zbMATH DE number 1080973