invoking some form of Alfvén limiter.

Another feature evident in Figure \[fig:Fz\] is increasing acoustic and magnetic flux with increasing $k_h$ in each case. This is due to the velocity power distribution in the stochastic driver, which is uniform in ${{\bmath{k}}}_h$. That leads to RMS power in $p$ and ${{{\bmath{b}}}}$ that increases linearly with wavenumber, and hence to a similar trend in flux.

![Representative examples of vertical wave energy fluxes (full curve: acoustic; dashed curve: magnetic; dotted curve: total) as a function of height. The top frame pertains to $\theta=60^\circ$, $\phi=80^\circ$, $B_0=1$ kG, and $k_h=1$ $\rm Mm^{-1}$ at 5 mHz, for which significant fast-to-Alfvén conversion is expected (see Figure \[fig:Fz\]). The bottom frame is for the corresponding vertical field case $\theta=0^\circ$ (for which $\phi$ is irrelevant). The full vertical lines indicates the location of the $a=c$ equipartition height, and the vertical dashed line shows the position of the stochastic driving plane.[]{data-label="fig:FzVz"}](figures/fz_th60ph80_5mHz_1kG "fig:"){width=".75\hsize"}\
![Representative examples of vertical wave energy fluxes (full curve: acoustic; dashed curve: magnetic; dotted curve: total) as a function of height. The top frame pertains to $\theta=60^\circ$, $\phi=80^\circ$, $B_0=1$ kG, and $k_h=1$ $\rm Mm^{-1}$ at 5 mHz, for which significant fast-to-Alfvén conversion is expected (see Figure \[fig:Fz\]). The 