Taylan Sengul
Afilliation: Indiana University Mathematics Department
Title: Dynamic Transitions of Surface Tension Driven Convection
Abstract: We study the well-posedness and dynamic transitions of the surface tension driven convection in a three-dimensional (3D) rectangular box with non-deformable upper surface and with free-slip boundary conditions. It is shown that as the Marangoni number crosses the critical threshold, the system always undergoes a dynamic transition. In particular, two different scenarios are studied.
In the first scenario, a single mode losing its stability at the critical parameter gives rise to either a Type-I (continuous) or a Type-II (jump) transition. The type of transitions is dictated by the sign of a computable non-dimensional parameter, and the numerical computation of this parameter suggests that a Type-I transition is favorable.
The second scenario deals with the case where the geometry of the domain allows two critical modes which possibly characterize a hexagonal pattern. In this case we show that the transition can only be either a Type-II or a Type-III (mixed) transition depending on another computable non-dimensional parameter.
Finally we prove the well-posedness and existence of global attractors for the problem.
Slides: SengulTaylan.pdf
