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Article
Publication date: 1 March 2000

Edoardo Bucchignani and Daniela Mansutti

We develop a numerical analysis of the buoyancy driven natural convection of a fluid in a three dimensional shallow cavity (4 ⋅ 1 ⋅ 1) with a horizontal gradient of temperature…

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Abstract

We develop a numerical analysis of the buoyancy driven natural convection of a fluid in a three dimensional shallow cavity (4 ⋅ 1 ⋅ 1) with a horizontal gradient of temperature along the larger dimension. The fluid is a liquid metal (Prandtl number equal to 0. 015) while the Grashof number (Gr) varies in the range 100,000‐300,000. The Navier‐Stokes equations in vorticity‐velocity formulation have been integrated by means of a linearized fully implicit scheme. The evaluation of fractal dimension of the attractors in the phase space has allowed the detection of the chaotic regime. The Ruelle‐Takens bifurcation sequence has been observed as mechanism for the transition to chaos: the quasi periodic regime with three incommensurate frequencies is the instability mechanism responsible for the transition to chaos. Physical experiments confirm the existence of this scenario.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 10 no. 2
Type: Research Article
ISSN: 0961-5539

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