Abstract
Locality properties are formulated for short-wave length disturbances in the problem of hydrodynamic stability, which together with global flow stability enable us to study the stability of particular sections of the stream, e.g., the flow core or the zone next to the wall. The locality properties are illustrated in the spectrum of small perturbations of plane Poiseuille flow and flows which are obtained by deforming a small section of the Poiseuille parabola. Such a deformation produces points of inflection which lead to the appearance of growing perturbations with wavelength of the order of the deformation zone. It is shown that discontinuities in the velocity profile leads to the loss of stability for high enough Reynolds' numbers.
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