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The interaction of two spatially resonant patterns in thermal convection. I. Exact 1:2 resonance. (English) Zbl 0649.76018
A two-layer model in Cartesian geometry is defined which allows the study of exact 2:1 resonance where two distinct convective modes with preferred horizontal wavenumbers in the ratio 1:2 bifurcate simultaneously. The proposed model consists of two superimposed fluid layers which are separated by a thin conducting plate and are heated from below. If the ratio of the depths of the two layers is close to 1:2 two distinct linear modes of convection can occur with a preferred horizontal wavenumber ratio of 1:2. Using weakly nonlinear theory the nonlinear interaction of these two convective modes is studied, displaying a rich variety of behavior. The mathematics should be applicable in many other problems. A full discussion of the evolution equations is presented demonstrating the occurrence of travelling waves for a wide range of parameters. In addition modulated waves and an attracting homoclinic orbit are discussed and the importance of imperfections in the system is stressed.
Reviewer: W.Koch

76E15 Absolute and convective instability and stability in hydrodynamic stability
76V05 Reaction effects in flows
76M99 Basic methods in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
Full Text: DOI
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