title: Bifurcation diversity of dynamic thermocapillary liquid layers.
abstract: We study, from the theoretical point of view, instabilities appearing in a liquid layer, where a dynamic flow is imposed through a nonzero temperature gradient at the bottom. Experimentally many interesting dynamical behaviors have been discovered in this system. In this Brief Report we prove that the basic solution can display great richness of bifurcations which are controlled by heat related parameters. Different kinds of spatially extended and localized structures appear, which are both stationary or oscillatory. These last ones can present amazing patterns such as squares or spirals. Also competing solutions at codimension-two bifurcation points have been found: stationary radial rolls with different wave numbers, radial rolls with hydrothermal waves, and hydrothermal waves with different wave numbers. Remarkably our results recover many features of numerous reported experiments, predict new instabilities, and by giving a deeper insight into how physical parameters contribute to bifurcations, open a gateway to control those instabilities.
authors.affiliation: Departamento de Matemáticas, Facultad de Ciencias Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain. sergio.hoyas@uclm.es
authors.forename: S
authors.initials: S
authors.lastname: Hoyas
authors.forename: H
authors.initials: H
authors.lastname: Herrero
authors.forename: A M
authors.initials: AM
authors.lastname: Mancho