Fluctuation growth and instability associated with a singularity of the balance equations

Large-scale flows in the atmosphere and ocean are usually in a state of approximate momentum balance, the simplest form of which is geostrophy. Furthermore, balanced models have often been shown to be quite accurate in this regime, with the quasigeostrophic equations the simplest such model and the balance equations a more accurate one, even though such models exclude the rapidly oscillatory, unbalanced dynamics of acoustic, gravitational, and inertial oscillations. However, this behavior is not universal, and here we investigate the fluid dynamics on one of the margins of this regime. We solve for linearized, inviscid fluctuations about a horizontal shear flow with spatially uniform vorticity and strain rate in a rotating, stratified, incompressible fluid, without making any balanced approximations. In both parallel and elliptical shear flows, we find that a significant increase occurs in the growth of unbalanced fluctuations near the violation of a necessary condition for the time integrability of the balance equations. This condition is that the absolute vertical vorticity everywhere exceeds the modulus of the horizontal strain rate. Thus, we seemingly have found a new boundary to the regime of large-scale dynamics, with its approximate gradient-wind balance, anisotropic velocity field, and mostly "slow-manifold" evolutionary behavior. (C) 1998 American Institute of Physics.