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The role of absolute and convective instability in predicting the behavior of fluid systems. (English) Zbl 0705.76038
Summary: It is demonstrated, mainly by example, how local hydrodynamic stability properties of certain spatially-developing free shear flows can be used to anticipate the onset of self-sustained global oscillations. The terms “local” and “global” refer here to the stability of local velocity profiles and of the entire flow field, respectively. On the local level, temporal and spatial instability modes on parallel shear flows are briefly discussed and the concept of “absolute” and “convective” instability is introduced. The local concepts are then related to the global behavior of a fluid system. It is shown that systems, which contain regions of local absolute instability, may respond to external forcing by developing time-amplified global oscillations, which are generally intrinsic to the flow and fundamentally different from the response of a system that is convectively unstable everywhere. The usefulness of these concepts are illustrated by the Kármán vortex street behind a 2-dimensional bluff body, the breakup of a capillary jet into drops, and by the low-density (hot) jet.

76E15 Absolute and convective instability and stability in hydrodynamic stability