Lagrangian analysis of the vortex shedding and mixing in the wake of a streamwise oscillating cylinder

Lagrangian analysis is capable of revealing the underlying structure and complex phenomena in unsteady flows. We present Particle-Image Velocimetry measurements of the wake of a cylinder undergoing streamwise vortex-induced vibrations and calculate the Finite-Time Lyapunov Exponents (FTLE) in backward- and forward-time. The FTLE fields are compared to the phase-averaged vorticity fields for the four different wake modes which occur throughout the streamwise response regime. The backward-time FTLE fields characterise the formation of vortices, with the roll up of spiral-shaped ridges coinciding with the roll up of the shear layers to form the vortices. Ridges in the forward-time fields tend to lie perpendicular to the flow direction and separate nearby vortices. The shedding of vortices coincides with a ‘peel off’ process in the forward-time FTLE fields, in which a ridge connected to the cylinder splits into two strips, one of which moves downstream. Particular attention is given to the ‘wake breathing’ process, in which the streamwise motion of the cylinder causes both shear layers to roll up simultaneously and two vortices of opposite sign to be shed into the wake. In this case, the ridges in forward-time FTLE fields are shown to define ‘vortex cells’, in which the new vortices form, and the FTLE fields allow the wake to be decomposed into three distinct regions. Finally, the mixing associated with each wake mode is examined, and it is shown that cross-wake mixing is enhanced in the second response branch, while the symmetric shedding in the first branch does not induce stronger mixing relative to the von Karman vortex street observed behind near-stationary bodies