An example vortex V with its center P. A point M is randomly chosen within the vortex V, with rotation speed v_rM, expansion speed v_eM, and speed vector v_M. The region S is used to calculate Γ₁ and Γ₂ values at the center P. The average rotation speed v_r, expansion speed v_e, and speed vector v of all points in S, centered on point P, are also shown. The quantity $sin\overline{\theta }$ is defined as the average value of sin(θ_M) for all points M within the region S.