Abstract

--- - While buckling is a time independent phenomenon for filaments or films bonded to soft elastic substrates, time evolution plays an important role when the substrate is a viscous fluid. Here we show that buckling instabilities in fluid-structure interactions can be reduced to the analysis of a growth function that amplifies the initial noise characterizing experimental or numerical error. The convolution between a specific growth function and noise leads to natural imperfections that emerge in the form of wave packets with a large scale modulation that can transform into localized structures depending on nonlinear effects. Specifically, we provide an experimental example where these wave packets are amplified into ridges for sufficiently low compression rates or are diluted into wrinkles for high compression rates. - A thin film can sometimes buckle in a localized fashion where high-curvature buckled regions coexist with substantially-flat regions. We propose a new mechanism wherein localization is not a post-buckling phenomenon, but emerges from packet-like fluctuations near the buckling threshold.