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Generalization of the Lorenz model to the two-dimensional convection of second-grade fluids |
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| Authors: | Carlo Ferrario |
| Affiliation: | a Dipartimento di Fisica e Sezione INFN, Università di Ferrara, via Paradiso, 12, I-44100 Ferrara, Italy b Dipartimento di Matematica, Università di Ferrara, via N. Machiavelli, 35, I-44100 Ferrara, Italy c Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany |
| Abstract: | We apply the truncation of the Navier-Stokes-Fourier equations which leads to the Lorenz model, to the investigation of second-grade fluids. The new set of equations proves to work as an approximated approach to 2D-convective dynamics, under the same restrictions as for Newtonian fluids. The different behaviour depends only on α1 and consists in a “modified” Prandtl number. |
| Keywords: | Oberbeck-Boussinesq approximation Second-grade fluids Onset of convection Lorenz model |
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