Elinborg Ingunn Olafsdottir, University of Edinburgh
We consider particular solutions of the hydrostatic Boussinesq equations which describe the evolution of a three-dimensional vortex in a horizontal shear flow. This provides an analytically tractable example of spontaneous generation of inertia-gravity waves by slow balanced motion.
We derive the amplitude of the inertia-gravity waves in the limit of small Rossby number using the tools of exponential asymptotics, and we interpret the wave generation as a Stokes phenomenon. The analysis reduces the problem to the evaluation of a single integral which is computed numerically to provide a picture of the three-dimensional structure of the inertia-gravity waves.