EFFECTS OF DISTANT BOUNDARIES ON PATTERN FORMING INSTABILITIES

The distinction between convective and absolute instability for an ins tability in the form of a traveling wave becomes important when the tr ansition takes place in a finite domain. When the instability takes th e form of waves traveling in one direction only, or the boundaries are perfectly absorbing, then the absolute stability criterion is the cor rect one for global modes to exist. When waves can travel equally easi ly in either direction, on the other hand, the convective criterion is the correct one. In this paper we show how the two results are linked by investigating a model system in which both left and right travelin g waves can be unstable, but in which there is no symmetry. Whether th e absolute instability boundary or some other boundary is the appropri ate one depends on the degree of asymmetry. Both linear and nonlinear aspects of the problem are discussed.