Wave–vortex decomposition of one-dimensional ship and aircraft observations

Distinguishing between geostrophic motion and inertia–gravity waves is fundamental to interpreting observations of flow in both the ocean and the atmosphere. Typically, observations that span a wide range of scales are available in one spatial dimension only, i.e. along ship or aircraft tracks. We present a method that decomposes the observed energy spectra in two steps: (1) a Helmholtz decomposition splits the kinetic energy spectrum into its rotational and divergent components and (2) the polarization and dispersion relations of linear inertia–gravity waves are used to diagnose the wave components of the kinetic and potential energy spectra. We apply this method to oceanographic and atmospheric data. Both geophysical fluids display a similar transition from turbulent geostrophic motion at large scales to quasi-linear inertia–gravity waves at small scales. This suggests important similarities in the dynamics of the atmosphere and ocean. In particular, the decomposition suggests that the transition in spectral slope in the atmospheric energy spectrum at about 500 km, as first observed by Nastrom and Gage, is due to inertia–gravity waves.