A Lagrangian Analysis of Vortex Formation in the Wake behind a Transversely Oscillating Cylinder

Abstract

A vortex pair + single vortex (P+S) wake behind a transversely oscillating cylinder is investigated from the Lagrangian point of view. The Lagrangian coherent structures (LCSs) of the flow are computed to analyze formation of vortices in the wake. An asymmetric vortex street is obtained by using a dynamic mesh method. The corresponding vorticity field is found to agree well with real experiments. The LCSs are approximated by ridges of the finite-time Lyapunov exponents computed from transient velocity fields. The formation process is investigated using the vorticity field and the LCSs. It is found that details of the wake pattern are sensitive to initial oscillation conditions, and that the cylinder motion causes an early roll-up of boundary layers to form new vortex structures in the wake. Lagrangian description of the flow with the help of the LCSs provides further details about formation of vortices in the cylinder flow and helps to get a new insight into the flow structure in the wake region.