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A growing body of literature has been built on the premise that kinematic advection produced by linear superpositions of sinusoidal Lagrangian gravity waves confined to lower vertical wavenumbers can provide an explanation for quasi-universal Eulerian spectral tails commonly found in the oceans and the atmosphere. Recently, Hines has established criteria delineating the circumstances in which Eulerian and Lagrangian spectra differ. For conditions in which Hines claims Lagrangian linearity and the production of quasi-universal Eulerian m-3 spectra, a kinematic advection model based on ensembles of seven nonstanding Lagrangian waves reveals the presence of gross violations of continuity and adiabaticity as well as severe departures from hydrostatic balance. Similar infractions are found for other seven-wave ensembles having a broad range of amplitudes and wavenumbers typical of saturated wave fields in the middle atmosphere. Furthermore, m-3 spectra are found only as the Lagrangian wave field approaches a singular state. The singularities in the Lagrangian to Eulerian transformation are induced by stretching deformation fields that form during the superposition of sinusoidal waves with nonparallel wave vectors. Such deformation fields are known to be unstable with respect to three-dimensional vortices. The results strongly suggest that saturated middle atmosphere wave fields are frequently accompanied by small-scale turbulent eddies. [ABSTRACT FROM AUTHOR]

The article comments on the gravity wave theory concerning dissipation induced by nonlinear effects. The Eulerian advective nonlinearity is capable of producing diffusion, instability and turbulence which is either absent from the nonlinear frequency-spreading theories or incorporated as an afterthought. Moreover, putative diffusivity of the W76 was inferred on improper mathematical developments and physical assumptions that implied for the modeling of the circulation of the middle atmosphere. Meanwhile, H02's derivations omitted the nonlinear complexity in the fluid subject to interacting fluctuations.

Presents information on a study which investigated the gravity wave focusing in the middle atmosphere using a time-dependent ray-tracing model. Model description; Description of wave backgrounds with multiple phase speeds; Background modulation effects; Conclusions.