= Internal-wave momentum deposition
{title2=$\overline u=(k/\omega)\mathcal E$}
A slowly established upward <plane internal gravity wave> has $\overline{u'w'}=-m|a|^2/(2k)$. The mean horizontal <conservation of momentum> equation gives $\overline u_t=-\partial_z\overline{u'w'}$. Using envelope transport and an initially vanishing mean gives $\overline u=-m|a|^2/(2kc_{gz})$. Its <energy density> per unit mass is $\mathcal E=(k^2+m^2)|a|^2/(2k^2)$, so $\overline u=(k/\omega)\mathcal E$. This is the mean flow left behind the advancing wave envelope, rather than a claim that an established uniform wavetrain has nonzero local stress divergence.
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