Author(s)

R. Mallier

Abstract

Using a nonlinear critical layer analysis, we derive a set of nonlinear in- tegrodifferential equations governing the temporal growth of a disturbance consisting of both an axisymmetric wave and a pair of helical waves with the same streamwise wavenumber as the axisymmetric wave superimposed on a circular jet. This is a model of Klebanoff-type transition. We consider the stage of evolution in which the growth first becomes nonlinear, with the nonlinearity appearing inside the critical layer. We find that the evolution equations are of integrodifferential form with a cubic nonlinearity and of the same general form as those for a mixing layer [1]. Numerical solutions to these equations develop a singularity at a finite time, which is confirmed by asymptotic analysis. 1 Introduction One of the questions of interest to researchers working o

Keywords