The Weakly Nonlinear Stability of the Two-Dimensional Jet and Wake

The nonlinear stability of the two-dimensional jet and wake in slightly supercritical states is investigated by making use of the weakly nonlinear theory. Accurate values of the coefficients in the Stewartson-Stuart equation are calculated numerically. Both flows are shown to have supercritical equilibrium states. The side-band instability of the equilibrium solutions in the form of plane wave is examined, and they are shown to be unstable. But in numerical solution simulating an access to the equilibrium from smoothly localized initial values, any instability and chaotic behaviour have not been detected.