permeability, and the angled brackets indicate averaging over time, or over $x$ and $y$. For the most part, only vertical components of these fluxes will be plotted. Three different horizontal wavenumbers are selected: $k_h=1.0$, 0.75, and 0.5 $\rm Mm^{-1}$, corresponding to phase speeds and skip distances set out in Table \[tab:skip\]. The overall flux normalization is arbitrary, but is consistent with the solar-like spectrum of the stochastic driving plane across the frequencies, *i.e.*, having maximum power in the range 2 – 5.5 mHz with peak at about 3.2 mHz.

The features in Figure \[fig:Fz\] are very much in accord with the simplified analyses of @CalGoo08aa and @KhoCal11aa. Specifically, there is negligible acoustic power at low field inclination because of the acoustic cutoff of a little over 5 mHz in the atmosphere. However, once $\omega > \omega_c\cos\theta$, acoustic waves may propagate upward (the ramp effect), and substantial flux is recorded at the top of the box. At 3 mHz, acoustic power peaks at $\theta=50^\circ$– $60^\circ$, whilst the peak is at around $30^\circ$ at 5 mHz. These peak powers may be understood in terms of the ‘attack angle’ $\alpha$ between the 3D wavevector and the magnetic field at the equipartition level [@Cal06aa; 