Left panel: Normalised vertical profiles of the density perturbation $\delta \widehat{\rho }$ (Eqs. A.4 and A.15) with $H=h_{70\%}/\sqrt{2}$ for different values of the radial wave number k_R (solid curves), compared with the normalised unperturbed vertical density profile (Eq. 8; dashed curve). Right panel: Vertical profiles of the ratio between the density perturbation and the unperturbed density profile for the same values of k_R as in the left panel, assuming that $\delta \widehat{\rho }/\rho =0.01$ at z = 0. The plotted range in z encloses 90% of the mass per unit surface of the unperturbed distribution.