Synchronized flutter of two slender flags

TL;DR

This paper extends Lighthill's theories to model the hydrodynamic coupling and synchronization of two slender flags in a flow, revealing how their interaction influences stability and flapping regimes.

Contribution

It introduces a simplified LAEBT-based framework for coupled flag dynamics, accounting for hydrodynamic interactions and analyzing synchronization phenomena.

Findings

Hydrodynamic coupling destabilizes flags for most parameters.

Flags tend to synchronize in-phase or out-of-phase over time.

Wake effects are negligible in the long-term coupled dynamics.

Abstract

The interactions and synchronization of two parallel and slender flags in a uniform axial flow are studied in the present paper by generalizing Lighthill's Elongated Body Theory (EBT) and Lighthill's Large Amplitude Elongated Body Theory (LAEBT) to account for the hydrodynamic coupling between flags. The proposed method consists in two successive steps, namely the reconstruction of the flow created by a flapping flag within the LAEBT framework and the computation of the fluid force generated by this nonuniform flow on the second flag. In the limit of slender flags in close proximity, we show that the effect of the wakes have little influence on the long time coupled-dynamics and can be neglected in the modeling. This provides a simplified framework extending LAEBT to the coupled dynamics of two flags. Using this simplified model, both linear and large amplitude results are reported to explore the selection of the flapping regime as well as the dynamical properties of two side-by-side slender flags. Hydrodynamic coupling of the two flags is observed to destabilize the flags for most parameters, and to induce a long-term synchronization of the flags, either in-phase or out-of-phase.