THE BREAKDOWN OF LARGE-SCALE FLOWS IN ROTATING, STRATIFIED FLUIDS

Flows under the influences of environmental rotation and stable densit y stratification often exhibit an approximate force balance and a cons equently slow rate of evolution at large Reynolds number. Such flows a re typically anisotropic in their velocity field. This regime is relev ant to large-scale motions in the Earth's atmosphere and ocean, as wel l as many other planetary and astrophysical systems. The Balance Equat ions are usually an accurate approximate model for this regime. Howeve r, they have solvability limits associated with a change of type in th eir time-integration operator. In this paper we derive these limiting conditions for the conservative Balance Equations in isentropic coordi nates, show that the least familiar of these conditions coincides with loss of convexity of the streamfunction for horizontal velocity in th e inertial reference frame, and identify these conditions with the gen eral conditions for symmetric loss of stability for circular and paral lel flows as well as for the three-dimensional loss of stability for e lliptical hows. We then conjecture that the identified limits of balan ce coincide generally with the boundary between the distinctive nonlin ear dynamical behaviors (i.e., their turbulent cascade and dissipation rates) associated with the large- and small-scale regimes in geophysi cal and astrophysical hows. (C) 1998 American Institute of Physics. [S 1070-6631(98)02412-X].