Stability of a Two-Dimensional Stagnation Flow

Abstract

The longitudinal vortices in a two-dimensional stagnation region of a cylindrical blunt body are expressed as a perturbation with respect to the mean motion in terms of the amplitude and the reciprocal of the square root of Reynolds number, in order to theoretically analyze their stability up to the second order of magnitude. As a result, a specific point can be determined where the integration of the kinetic energy involved in the vortices becomes minimum and the first and second orders of the magnitude of disturbances would never diverge at a considerable distance from the wall, and further, the damping factor of -α takes the minimum value. Moreover, the wave number for α=0 and the minimum kinetic energy reasonably agree with observations.