Complex bifurcations in B\'enard-Marangoni convection
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-B\'enard and B\'enard-Marangoni systems with simple linear vertical temperature profiles. In terms of the B\'enard-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.
Cite
@article{arxiv.1511.03326,
title = {Complex bifurcations in B\'enard-Marangoni convection},
author = {Sergey Vakulenko and Ivan Sudakov},
journal= {arXiv preprint arXiv:1511.03326},
year = {2017}
}
Comments
Accepted for publication in J. Phys. A: Math. Theor. arXiv admin note: text overlap with arXiv:1511.02047