Synchronized flutter of two slender flags

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 of 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 non-uniform flow on the second flag. In the limit of slender flags in close proximity, we show that the effect of the wakes has little influence on the long-time coupled dynamics and can be neglected in the modelling. 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.