<p>In open-channel flows, a notably higher spanwise vortex density near the free surface compared to other wall-bounded turbulent flows has been observed, termed the additional vortex phenomenon. Two hypotheses explain this phenomenon: The free-surface accumulation hypothesis, suggesting slower vortex dissipation in open-channel flows leading to vortex accumulation in the outer region, and the free-surface generation hypothesis, proposing that free surface restrictions on vertical motions enhance vortex generation, increasing vortex density near the surface. To elucidate the dominant origin mechanism of the additional vortex phenomenon, this study conducts direct numerical simulation (DNS) of open-channel flows and closed-channel flows at a friction Reynolds number <i>Re</i>_<i>τ</i> = 500. Using the <i>λ</i>_ci - criterion, the spanwise, streamwise, and vertical vortex densities variations with distance from the wall are identified and quantified for both flows, and the presence of the additional vortex phenomenon near the free surface in the open-channel DNS data is confirmed again. Furthermore, the vortex birth-death density is defined to elucidate the dominant origin mechanism of the additional vortex phenomenon. Through the analysis of the vortex birth-death density profiles, the exact birth location of the additional vortices can be pinpointed. The result reveals significant positive values for spanwise and streamwise vortices near the wall and free surface in open-channel flow, indicating substantial vortex generation, while small negative values in the central region suggest vortex dissipation. The results of the vortex birth-death density analysis support the free-surface generation hypothesis for the additional vortex phenomenon in open-channel flows.</p>