Internal gravity waves in a time-varying stratification

The influence of slow time variations of the Brun-Väisälä frequency N upon the energy of internal gravity waves is investigated. It is found that, when time variations in N are produced by a mean deformation field (reversible mean state), the wave energy can vary in either direct or inverse proportion, depending on the wavenumber orientation. When N changes owing to a certain type of irreversible process, the wave energy varies with only inverse proportionality. The nocturnal planetary boundary layer (NPBL) provides an example where N = N(z, t). The full initial/boundary-value problem for an N(z, t) similar to the climatological mean for the NPBL is solved.