Vortex waves in fluid–structure interaction with high Froude number and a damped structure

Abstract

In this paper, we study the non-linear dynamic response generated as a result of a fluid–structure interaction between a flexible structure and a flowing fluid, when the structure is subjected to non-linear excitations. In first place, the use of semi-discrete approximations allowed us to show that the motion of a flexible structure coupled with a surrounding fluid flowing could be modelled and analysed via a coupled Complex Cubic Ginzburg–Landau equations (CCGLEs). Through the obtained CCGLEs, we were able to show that modulational instability (MI) is the main mechanism responsible for the generation of vortex shedding. Moreover, we showed that the stability of continuous wave depends on the coupling parameters between the fluid and the structure. Secondly, using a mathematical method, namely the G’/G expansion method, we found that vortex wave trains could be generated as cylindrical waves. These results are highly significant from a theoretical point of view and could be a plus to explain the process of generation of Kármán Vortex as a consequence of unstable coupling between two continuous wave in the fluid–structure system. Moreover, considering the industrial interest, such as floating wind turbines, this work aims to provide an additional understanding of the interactions between a flexible body and a surrounding flow.