Balance and Spontaneous Wave Generation in Geophysical Flows

The large-scale dynamics of the mid-latitude atmosphere and ocean is characterized by a timescale separation between slow balanced motion and fast inertia-gravity waves. As a result of this separation, the two types of motion interact only weakly, and the dynamics can be approximated using balanced models, which filter out the fast waves completely. The separation is not complete, however: The evolution of well-balanced flows inevitably leads to the excitation of inertia-gravity waves through the process of spontaneous generation. Spontaneous generation has fundamental and practical implications: It limits the validity of balanced models and provides a source of inertia-gravity-wave activity. These two aspects are discussed in this review, which focuses on the small-Rossby-number regime ε≪1 corresponding to strong rotation. Theoretical arguments indicate that spontaneous generation is then exponentially small in ε for smooth flows. They are complemented by numerical simulations that identify specific generation mechanisms.