Wed March 13th 2019
11:00 – 12:00
Seminar Unstable front propagation
Anne Juel


Front-propagating systems provide some of the most fundamental physical examples of interfacial instability and pattern formation. However, their nonlinear dynamics are rarely addressed. We focus on the canonical viscous fingering instability, which arises when a more viscous fluid is displaced by a less viscous one in a quasi-two-dimensional channel. For example, this system exhibits a sub-critical transition at finite values of the driving parameter from a steadily propagating finger, which is linearly stable for all values of the driving parameter, to an unsteady, disordered front. This scenario is reminiscent of the transition to turbulence in shear flows where weakly unstable solutions, referred to as 'edge states', determine the basin boundary separating initial conditions decaying to laminar flow from those growing to turbulence. In this talk, we explore the role of unstable modes of propagation (and edge states) in the dynamics of two viscous fingering systems exhibiting sub-criticality: a rigid channel with a small depth perturbation and a channel where the top boundary has been replaced with an elastic sheet.
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The 10th Complex Motion in Fluids 2021
Max Planck Gesellschaft
Centre for Scientific Computing