ABSOLUTE AND CONVECTIVE INSTABILITIES IN NONLINEAR-SYSTEMS

The concepts of absolute and convective instability are extended to nonlinear systems with broken Galilean invariance. As an illustrative model we describe the behavior of a flow, homogeneous in a semi-infinite domain, which undergoes a subcritical pitchfork bifurcation. The classical bifurcation phenomenology is shown to be nontrivially affected by the presence of a nonremovable advection term. In particular the existence of a hysteresis loop is shown to be restricted to the nonlinear absolute instability range. A qualitative description of the possible scenarios likely to arise in subcritically bifurcating open flows is outlined and a practical test is suggested to determine the nature of the bifurcation.