The upper rotor vortex center trajectories for locations A, B, and C were traced for all the cases. Figure 6 contains representative vortex trajectory plots for two test cases. For tracing the vortex trajectories, vortex centers were identified using the algorithm described by Graftieaux et al. [27]. The algorithm involves defining functions Γ_{1} and Γ_{2} which characterize the locations of the center and boundary of a large scale vortex by considering the topology of the velocity field. In Eqs. (2) and (3), *P* is a fixed point in the measurement domain, *S* is the area surrounding *P*, and *M* is a point in *S*. The functions effectively find sine of mean angle between position vectors of points neighboring *P* and flow velocities at those points. The point corresponding to local maximum or minimum of Γ_{2} (for counter-clockwise and clockwise rotating vortices, respectively) in the region of a vortex is the vortex center. The equations are in discretized form for application to PIV data. The PIV velocity fields were interpolated to increase the resolution threefolds before using the algorithm to identify vortex centers. The uncertainty in the identification of location of vortex centers is within 1 PIV data pixel (1.4 mm or about 1% or the rotor radius)
Display Formula

(2)$\Gamma 1(P)=1S\u2211M\u2208S(PM\u2227UM)\xb7z||PM||\xb7||UM||=1S\u2211M\u2208S\u2009sin(\theta M)$

Display Formula(3)$\Gamma 2(P)=1S\u2211M\u2208S(PM\u2227(UM\u2212U\u0303P))\xb7z||PM||\xb7||UM\u2212U\u0303P||$