Buckling a tail-clamped filament in inertia-dominated flow

This study investigates the buckling behavior of a flexible filament clamped at one end and exposed to an inertia-dominated flow. Water-tunnel experimental data are used to construct contours of the filament's tip coordinates across the parameter space defined by filament length and flow velocity. The filament first exhibits two-dimensional (2D) buckling, followed by three-dimensional (3D) symmetry breaking, and ultimately fractures at higher velocities. A power-law scaling relationship between filament deformation and the Cauchy number (Ca) is identified in the high-Reynolds number regime. To complement the experiments and high Reynolds (Re) number simulations, extra numerical simulations are performed in the very low-Re regime, revealing that the elastoviscous number (η) dominates filament deformation in this regime. Our work offers insights into the nonlinear deformation behavior of filamentous structures in axial flows dominated by inertia.