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arXiv · 1511.03326

Complex bifurcations in Bénard-Marangoni convection

Sergey Vakulenko·Ivan Sudakov
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Abstract

We study the dynamics of a system defined by the Navier-Stokes equations for a non-compressible fluid with Marangoni boundary conditions in the two dimensional case. We show that more complicated bifurcations can appear in this system for a certain nonlinear temperature profile as compared to bifurcations in the classical Rayleigh-Bénard and Bénard-Marangoni systems with simple linear vertical temperature profiles. In terms of the Bénard-Marangoni convection, the obtained mathematical results lead to our understanding of complex spatial patterns at a free liquid surface, which can be induced by a complicated profile of temperature or a chemical concentration at that surface. In addition, we discuss some possible applications of the results to turbulence theory and climate science.

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Sergey Vakulenko, Ivan Sudakov. 2016-08-17. Complex bifurcations in Bénard-Marangoni convection. https://doi.org/10.1088/1751-8113%2F49%2F42%2F424001

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