Wave energy flux (light purple line) for the four simulations ref (top left), boost1d1(top right), boost1d2 (bottom left), and boost1d4 (bottom right). The spectra are computed at r = r_conv − l_max (i.e. at a distance l_max from the convective boundary) and for angular degree ℓ = 10. The grey vertical lines indicate the convective turnover frequency, ω_conv, and the blue, red, and orange lines correspond to functions with slope ω^−13/2, ω^−41/6, and ω^−15/2, respectively. The dashed curves represents two Gaussian spectra with characteristic frequencies ω_conv (cyan) and (black). The dark purple line is a running 25th percentile of the flux over 100 frequency bins.