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| Numerical studies of the first inverse pitchfork bifurcations for natural convections enclosed in a 2D horizontal rectangular cavity |
| Received:September 05, 2010 Revised:June 06, 2011 |
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| DOI：10.7511/jslx20122017 |
| KeyWord:enclosed horizontal rectangular cavity natural convection the first inverse pitchfork bifurcation cell merging saddles Prandtl numbers effect |
| Author | Institution |
| 王小华 |
浙江大学 航空航天学院 流体工程研究所, 杭州 |
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| Abstract: |
| A second order Euler-Taylor-Galerkin finite element method of fractional steps was used in the numerical study of the evolution processes of bifurcations for natural convections of water at three different Pr enclosed in a rectangular cavity with aspect ratio L/B=3.5 (plotted in Fig.1).A new phenomenon of vortex merging in laminar flow has been found for all the three Pr.The vortex merging phenomenon discovered in the present paper is a new mode pitchfork bifurcation,the inverse pitchfork bifurcation.Moreover,aided by the variation of flow topologies and velocity profiles of velocity v vs.x at y=0.5 for each cavity,corresponding critical Rayleigh numbers were numerical predicted by using the bisection method.It can be deduced f rom the presented results that the critical Ra increased with the increase in Pr. |