Comparison of the values of v_y of a simulation (+ symbols) and the derived eigenfunctions (dotted lines) on a cut perpendicular to the flow direction. For clarity, only a limited amount of simulated points is shown, The values of v_y are given in cm s^-1. The cut, taken at t = 3, only spans a small portion of the range along the y-axis, and is centred on the middle of the boundary layer. The distance from the centre is given in units of D. The dotted lines each represent a solution of the eigenfunction, the red line in the upper flow, teal in the middle layer, and blue in the lower flow. From the correspondence with the simulated values, it is clear that during the perpendicular velocity the linear phase evolves from the perturbation in Eq. (8) to the distribution expected from the analytical derivation of the eigenfunction.