Atmospheric variables (temperature, velocity, etc.) are often decomposed into balanced and unbalanced components that represent, respectively, low-frequency variability and high-frequency dispersive waves.
For theory and forecasting, it is important to assess the influence of the fast waves on the slowly varying flow component. Traditionally, fast-slow decompositions do not account for phase changes of water since the latter create a piecewise operator that changes across phase boundaries (dry versus cloudy air). Here we demonstrate how a balanced--unbalanced decomposition can be performed in the presence of phase changes, and we analyze nonlinear coupling between dispersive waves and slow dynamics within the framework of fast-wave-averaging, along with simulations of Boussinesq dynamics.