Complex bifurcations in Bénard–Marangoni convection. (26th September 2016) - Vakulenko, Sergey; Sudakov, Ivan
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.