Daniel Lecoanet, Eliot Quataert
We calculate the flux of internal gravity waves (IGWs) generated by turbulent convection in stars. We solve for the IGW eigenfunctions analytically near the radiative-convective interface in a local, Boussinesq, and cartesian domain. We consider both discontinuous and smooth transitions between the radiative and convective regions and derive Green's functions to solve for the IGWs in the radiative region. We find that if the radiative-convective transition is smooth, the IGW flux ~ F_conv (d/H), where F_conv is the flux carried by the convective motions, d is the width of the transition region, and H is the pressure scale height. This can be much larger than the standard result in the literature for a discontinuous radiative-convective transition, which gives a wave flux ~ F_conv M, where M is the convective Mach number. However, in the smooth transition case, the most efficiently excited perturbations will break immediately when they enter the radiative region. The flux of IGWs which do not break and are able to propagate in the radiative region is ~ F_conv M^(5/8) (d/H)^(3/8), larger than the discontinuous transition result by (M H/d)^(-3/8). The transition region in the Sun is smooth for the energy-bearing waves; as a result, we predict that the IGW flux is about five times larger than previous estimates. We discuss the implications of our results for several astrophysical applications, including IGW driven mass loss and the detectability of convectively excited IGWs in main sequence stars.
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http://arxiv.org/abs/1210.4547
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