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 o f approximate momentum balance, the simplest form of which is geostrop hy. Furthermore, balanced models have often been shown to be quite acc urate 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 a coustic, gravitational, and inertial oscillations. However, this behav ior is not universal, and here we investigate the fluid dynamics on on e of the margins of this regime. We solve for linearized, inviscid flu ctuations about a horizontal shear flow with spatially uniform vortici ty and strain rate in a rotating, stratified, incompressible fluid, wi thout making any balanced approximations. In both parallel and ellipti cal shear flows, we find that a significant increase occurs in the gro wth of unbalanced fluctuations near the violation of a necessary condi tion for the time integrability of the balance equations. This conditi on is that the absolute vertical vorticity everywhere exceeds the modu lus 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-m anifold'' evolutionary behavior. (C) 1998 American Institute of Physic s.