Nonlinearities and Linearities in Internal Gravity Waves of the Atmosphere and Oceans

The spectrum of internal gravity waves in the atmosphere and oceans is sufficiently intense that nonlinear interactions must occur, if these waves are analyzed in Eulerian coordinates as is usually done. As it happens, however, if these waves are analyzed in Lagrangian coordinates the most important nonlinearity can be entirely avoided: it is an Eulerian mathematical construct only, not a physical process. The mathematical basis for this assertion is developed here, and some of its consequences are discussed. Among the latter is a questioning of the validity of standard Eulerian eikonal methods of calculating ray paths and related functions in a multiwave environment, discussed in an appendix.