  We present three-dimensional direct numerical simulations of internal waves
excited by turbulent convection in a self-consistent, Boussinesq and Cartesian
model of convective--stably-stratified fluids. We demonstrate that in the limit
of large Rayleigh number ($Ra\in [4\times 10^7,10^9]$) and large stratification
(Brunt-V\"{a}is\"{a}l\"{a} frequencies $f_N \gg f_c$, where $f_c$ is the
convective frequency), simulations are in good agreement with a theory that
assumes waves are generated by Reynolds stresses due to eddies in the turbulent
region (Lecoanet \& Quataert 2013 MNRAS 430 (3) 2363-2376). Specifically, we
demonstrate that the wave energy flux spectrum scales like
$k_{\perp}^4f^{-13/2}$ for weakly-damped waves (with $k_{\perp}$ and $f$ the
waves' horizontal wavenumbers and frequencies), and that the total wave energy
flux decays with $z$, the distance from the convective region, like
$z^{-13/8}$.
