Bifurcation of laterally unconstrained flexible filaments in an inclined flow

The dynamics of laterally unconstrained flexible filaments in an inclined uniform flow is investigated numerically, inspired by the self-propelled behaviour of droplets and filaments in a crosswind. It is found that in addition to conventional downwind drifting, the filament can also undergo counterintuitive upwind motion, arising from a supercritical pitchfork bifurcation. Depending on the Reynolds number, bending stiffness and inflow inclination angle, the filament exhibits multiple wake and motion states, including static, quasi-static, vibrational and translational modes. In the reference frame translating laterally with the incoming flow, the upwind and downwind drifting states induced by different initial perturbations form a pair of dynamically equivalent, symmetry-related branches. Force decomposition shows that both the streamwise drag and lateral thrust predominantly originate from the normal force, and the corresponding scaling relations are identified. Stability analysis further reveals that the hydrodynamic forces near the equilibrium states behave as restoring forces. The resulting stable equilibria can be characterised by a generalised hydrodynamic potential, whose potential wells correspond to the stable states of the system. These findings provide insight into the dynamics of flexible structures in uniform flow.