Weakly nonlinear internal gravity wavepackets

Horizontally periodic, vertically localized internal gravity wavepackets induce a horizontal mean flow in a manner analogous to the Stokes drift for surface waves. Unlike the the Stokes drift, however, the wave-induced mean flow of nonhydrostatic internal waves non-negligibly interacts with the waves themselves if they are moderately large amplitude: that is, if their maximum vertical displacement is larger than approximately one percent of the horizontal wavelength. Using Hamiltonian fluid dynamics to write the wave-induced mean flow in terms of the correlation of the vertical displacement and vorticity fields, a nonlinear Schroedinger equation is derived and, through comparison with fully nonlinear numerical simulations, this is shown to portray accurately the initial evolution of internal gravity wavepackets. The work is extended to examine the evolution in non-uniform flows of anelastic internal waves as they grow to large amplitude. The impact of internal waves passing through the middle atmosphere is discussed.