Radial profile of the horizontally averaged luminosity associated with the waves for the four simulations ref (top left), boost1d1 (top right), boost1d2 (bottom left), and boost1d4 (bottom right) at six different frequencies. The power spectra are normalised by their value at the convective boundary, L_wave(r_conv). The horizontal solid black line indicates the radiative–convective boundary as defined by the Schwarzschild criterion for the initial model. The horizontal dashed green and dotted blue lines indicate the radii r = r_conv − l_bulk and r = r_conv − l_max, respectively. The horizontal average, ⟨.⟩_𝒮, is defined in Eq. (10).