Complex bifurcations in B\'enard-Marangoni convection

TL;DR

This paper investigates complex bifurcations in Bénard-Marangoni convection systems with nonlinear temperature profiles, revealing intricate spatial patterns and potential implications for turbulence and climate science.

Contribution

It demonstrates the emergence of more complex bifurcations in Bénard-Marangoni convection with nonlinear temperature profiles compared to classical models.

Findings

Identification of complex bifurcations in nonlinear temperature profiles

Insights into spatial pattern formation at free liquid surfaces

Potential applications to turbulence and climate science

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.