Testing Lagrangian theories of internal wave spectra

Our incomplete understanding of physical dissipation processes within an internal gravity wave field impacts on questions of mixing in both the atmosphere and ocean, with enormous dynamical ramifications in the case of the middle atmosphere. Efforts to solve the puzzle have centered on nonlinear interactions among internal waves, but the inherent complexity has hindered progress. There is a growing body of literature which maintains that this complexity can be circumvented by using a Lagrangian, rather than Eulerian, formulation. We have investigated this proposition with a Lagrangian wave model and wave fields typical of the middle atmosphere; the results have important consequences for certain Lagrangian theories of wave spectra, specifically those advanced by Hines and Allen and Joseph. They also have implications for Hines' Doppler spread parameterization, which has been employed in several middle atmosphere GCMs.