Upper: amplitudes of resonant wave for l = 50 Mm (blue) and l = 100 Mm (red). Dashed lines show prediction from Eq. (13) and solid lines are results from numerical simulations. Lower: cross-field phase mixing profile for l = 50 Mm at t = 475 s (blue) and l = 100 Mm (red) at t = 950 s (red). The thin black line corresponds to a simulation with shear in the background field and is discussed in Sect. 3.4.