RELATION BETWEEN TEMPORAL AND SPATIAL STABILITY IN 3-DIMENSIONAL FLOWS

An analysis is presented of the stability of three-dimensional incompressible, isothermal boundary-layer flows. The method of multiple scales is used to derive partial-differential equations that describe the axial and crossflow variations of the disturbance amplitude, phase, and wavenumbers. This equation is used to derive the expressions that relate the temporal and spatial instabilities. These relations are functions of the complex group velocities. Moreover, this equation is used to derive the expression that relates the spatial amplification in any direction to a calculated amplification in any other direction. These relations are verified by numerical results obtained for two- and three-dimensional disturbances in two- and three-dimensional flows. © 1979 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.