A wave-vortex decomposition for rotating Boussinesq flows in bounded domains

A rotating Boussinesq model bounded in the vertical and periodic in the horizontal is shown to be exactly separable into its linear wave and vortex solutions using the horizontal velocities and density anomaly at any given moment in time. The decomposition extends the familiar wave-vortex decomposition for triply periodic, constant stratification cases to vertically bounded flows with arbitrary stratification.