Extending Group Velocity Concept to Waves That Leak and Its Applications to Amtospheric Dynamics

We will present new analytical tools that one can use in linear dispersive systems with leakage. When a system loses energy through radiating waves, one must work with exponential waves with complex wave number and frequency. Unfortunately, classical linear wave theory and the concept of group velocity can no longer be applied. This setup, however, is ubiquitous in AOFD; for example, where there is leakage of energy through wave radiation from the troposphere to the stratosphere. We will demonstrate the new techniques to resolve this problem in general, and demonstrate their efficacy on atmospheric dynamics applications.