Solid: cumulative Poynting flux injected through the lower z boundary by the imposed wave driver averaged along y for various values of x. Dashed: estimated energy requirements in typical Quiet Sun conditions. The losses shown by the red dashed line are delayed to show that the mean Poynting flux for x = 0.3 Mm is sufficient to balance expected Quiet Sun losses once the Kelvin-Helmholtz instability forms. Conversely, the green dashed line shows that the mean Poynting flux for x = 0.6 Mm is not sufficient even once the instability has developed.