Upward energy leakage in the dry atmosphere

In the classical theory of linear dispersive waves, the concept of group velocity is limited to waves with real wavenumbers and frequencies. However, semi-open dispersive systems also allow exponentially blowing up or decaying solutions. In this talk I will address the question of how to extend the classical dispersive wave theory to understand the energy propagation for exponential waves. This can be used to derive radiation boundary conditions for semi-open dispersive systems. I will present an application of this theory to the dry atmosphere, where the leakage of gravity waves from the troposphere to the stratosphere is a significant physical effect that cannot be ignored in toy models with a finite atmosphere.