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Onset of spontaneous beating and whirling in the follower force model of an active filament

Year: 2025
Type: article
Abstract: We study the onset of spontaneous dynamics in the follower force model of an active filament, wherein a slender elastic filament in a viscous liquid is clamped normal to a wall at one end and subjected to a tangential compressive force at the other. Clarke et al. (Phys. Rev. Fluids, vol. 9, 2024, 073101) recently conducted a thorough investigation of this model using methods of computational dynamical systems; inter alia, they showed that the filament first loses stability via a supercritical double-Hopf bifurcation, with periodic ‘planar-beating’ states (unstable) and ‘whirling’ states (stable) simultaneously emerging at the critical follower-force value. We complement their numerical study by carrying out a weakly nonlinear analysis close to this unconventional bifurcation, using the method of multiple scales. The main outcome is an ‘amplitude equation’ governing the slow modulation of small-magnitude oscillations of the filament in that regime. Analysis of this reduced-order model provides insights into the onset of spontaneous dynamics, including the creation of the nonlinear whirling states from particular superpositions of linear planar-beating modes as well as the selection of whirling over planar beating in three-dimensional scenarios.
DOI: 10.1017/jfm.2025.128
Language: English
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4408997771
FWCI: 2.696
Cites: 17
Cited by: 7
Related to: 10