Instability and Frequency Selection of the Wake behind a Flat Plate

Abstract

The frequency of instability waves in a wake flow is uniquely determined by a logarithmic singularity of complex ray trajectories describing the propagation of a two-dimensional wave packet. Conditions for the singularity are given by simultaneous equations indicating that the group velocity and X-derivative of the complex dispersion relation for a given flow field are both equal to zero, where X is the downstream coordinate and the dispersion relation defines the complex frequency as a function of the complex wave number and X. Simple mathematical models are introduced to simulate spatial variations of the wake behind a moderately thin flat plate. Stability calculations of the model flow indicate that the logarithmic singularity is located in the vicinity of the real axis of the complex coordinate X.