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The large-scale dynamics of the mid-latitude atmosphere and ocean is characterised 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 focusses on the small-Rossby-number regime 1 corresponding to strong rotation. Theoretical arguments indicate that spontaneous generation is then exponentially small in for smooth flows. They are complemented by numerical simulations which identify specific generation mechanisms.

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The exponential decay of the variance of a passive scalar released in a homogeneous random two-dimensional flow is examined. Two classes of flows are considered: short-correlation-time ͑Kraichnan͒ flows, and renewing flows, with complete decorrelation after a finite time. For these two classes, a closed evolution equation can be derived for the concentration covariance, and the variance decay rate ␥ 2 is found as the eigenvalue of a linear operator. By analyzing the eigenvalue problem asymptotically in the limit of small diffusivity , we establish that ␥ 2 is either controlled ͑i͒ locally, by the stretching characteristics of the flow, or ͑ii͒ globally, by the large-scale transport properties of the flow and by the domain geometry. We relate the eigenvalue problem for ␥ 2 to the Cramer function encoding the large-deviation statistics of the stretching rates; hence we show that the Lagrangian stretching theories developed by Antonsen et al. ͓Phys. Fluids 8, 3094 ͑1996͔͒ and others provide a correct estimate for ␥ 2 as → 0 in regime ͑i͒. However, they fail in regime ͑ii͒, which is always the relevant one if the domain scale is significantly larger than the flow scale. Mathematically, the two types of controls are distinguished by the limiting behavior as → 0 of the eigenvalue identified with ␥ 2 : in the local case ͑i͒ it coincides with the lower limit of a continuous spectrum, while in the global case ͑ii͒ it is an isolated discrete eigenvalue. The diffusive correction to ␥ 2 differs between the two regimes, scaling like 1 / log 2 in regime ͑i͒, and like for some 0 Ͻ Ͻ 1 in regime ͑ii͒. We confirm our theoretical results numerically both for Kraichnan and renewing flows.