We introduce the mixing parameter to analyze the \textit{in situ} measurements of a Kelvin-Helmholtz event observed by the Magnetospheric Multiscale mission. We define the mixing parameter, for both ions and electrons, using the well distinct particle energies which characterize the magnetosphere and magnetosheath plasmas. This parameter nicely identifies the different populations which are interacting at the Earth’s magnetopause and the boundaries of Kelvin-Helmholtz vortices. Thus, we analyze the crossing of each structure into a parameter-space defined as the space of the electron mixing versus the ion mixing, where specific shapes occur according to the evolutionary phase of the Kelvin-Helmholtz instability. All along the event, we observe three different types of shapes, namely a straight line, a simple loop, and a complex loop, which likely correspond to surface waves, vortices in the early nonlinear phase and rolled-up vortices in the fully nonlinear stage, respectively. The most complex shape (rolled-up vortex) is observed only at the end of the interval, owing to a fast growth of the instability which is connected to variations of the solar wind magnetic field orientation.