The breakdown of large-scale flows in rotating, stratified fluids

Flows under the influences of environmental rotation and stable density stratification often exhibit an approximate force balance and a consequently slow rate of evolution at large Reynolds number. Such flows are typically anisotropic in their velocity field. This regime is relevant to large-scale motions in the Earth's atmosphere and ocean, as well as many other planetary and astrophysical systems. The Balance Equations are usually an accurate approximate model for this regime. However, they have solvability limits associated with a change of type in their time-integration operator. In this paper we derive these limiting conditions for the conservative Balance Equations in isentropic coordinates, show that the least familiar of these conditions coincides with loss of convexity of the streamfunction for horizontal velocity in the inertial reference frame, and identify these conditions with the general conditions for symmetric loss of stability for circular and parallel flows as well as for the three-dimensional loss of stability for elliptical hows. We then conjecture that the identified limits of balance coincide generally with the boundary between the distinctive nonlinear dynamical behaviors (i.e., their turbulent cascade and dissipation rates) associated with the large- and small-scale regimes in geophysical and astrophysical hows. (C) 1998 American Institute of Physics. [S1070-6631(98)02412-X].