Abstract
In this work we study a finite dynamical system for the description of the bifurcation pattern of the convection flow of a fluid between two parallel horizontal planes which, under the hypothesis of the Oberbeck–Boussinesq approximation, sustains a horizontal gradient of temperature ( horizontal convection flow). Although in the two-dimensional case developed here, literature reports a long list of analytical and numerical solutions to this problem, the peculiar aim of this work makes it worthwhile. Actually, we develop the route that Saltzman (J. Atmos. Sci. 19 (1962) 329) and Lorenz (J. Atmos. Sci. 20 (1963) 130) proposed for the vertical convection flow that started successfully the approach to finite dynamical systems. We obtain steady-to-steady and steady-to-periodic bifurcations in qualitative agreement with already published results. At first we adopt the non-dimensional scheme used by Saltzman and Lorenz; as we obtained huge values of the bifurcation parameters, we introduce a different set of reference quantities for overcoming this drawback.
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