Ridge Localization Driven by Natural Imperfections

While buckling is a time independent phenomena 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 could 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.