ON THE LINEAR-STABILITY OF A COMPRESSIBLE INVISCID PARALLEL SHEAR-FLOW

By applying an approach similar to that used in the Miles-Howard theor y [1], [2] we derive simple constraints on the phase speed c(r) of th e neutral three-dimensional (3-D) monochromatic disturbances in an inv iscid compressible parallel two-dimensional (2-D) shear flow. It is sh own that for a boundary layer flow [a0(y*)]2 - [U0*(y*) - c(r)*]2 mus t have a zero in [y1, y2*) for the neutral 2-D modes whose phase spee d c(r) does not belong to the range of U0*(y*). For the unstable wave s the argument of Chimonas [3] applies leading to the Howard semi-circ le theorem. Here U0(y*) and a0*(y*) are the dimensional base velocity and local sonic speed respectively. It is suggested that hypersonic f lows possess vertically highly undulated unstable normal modes.