Excitation of Internal Gravity Waves by Adjacent Convection

In nature, regions of convecting fluid are often bounded by a stably stratified region. This include's the Earth's atmosphere (at the tropopause), the Earth's oceans (at the thermocline), the Sun (at the tachocline), and possibly the Earth's outer liquid core. The stably-stratified regions support internal gravity waves, which can be excited by convection. Here, we present three-dimensional direct numerical simulations (DNS) of a Boussinesq fluid which self-consistently organizes into a lower convective region, and an upper stably-stratified region. The turbulent convective motions excite a spectrum of waves in the stably-stratified region. We compare the spectrum of excited waves to a theoretical model based on the coupling of Reynolds stresses from convective eddies to waves. The model predicts the wave energy flux to increase with wavenumber like k⁴ up to a threshold wavenumber; decrease with frequency like ϖ^-13/2; and decrease with height like z^-13/8. We verify each of these scaling exponents in our DNS. Using this model, one can predict the amplitude of internal gravity waves in stars, as well as any possible MAC waves in the Earth's core.