Formation and interaction of multiple dipoles in a periodic driving flow

Abstract

We present herein the results of a numerical simulation of a periodic flow which take place in a channel and an open domain. To investigate this flow we solve the fluid dynamics equations in the vorticity-stream function formulation by using a pseudospectral method based on Chebyshev polynomials. According to these numerical simulations, a pair of counter-rotating vortices (known as a dipole) forms during each period. The lifetime of these vortices can exceed the driving period, which allows multiple dipoles to coexist. The attention is focused on the interaction of vortices. A possible outcome is that dipoles created in consecutive periods coalesce. Another outcome is the formation of vorticity spots in front of the emerging dipole which reduce the dipole speed. On the other hand, it is observed that a fraction of the vorticity created into the channel cannot incorporate to the vortices, leading to the formation of a vorticity band between the channel mouth and the dipole. Based on this fact an analytical model is proposed to describe the properties of dipoles emerging from the channel; the results of this model are consistent with numerical data. The parameters governing the development of this flow are the Strouhal number, whose value determines the intensity of the dipole interaction, and the Reynolds number, whose growth leads to the emergence of instabilities and to the breaking of the flow symmetries.