Dynamics of Slowly Varying Wavetrains in Finite Geometry
The effect of distant endwalls on a Hopf bifurcation from a translation-invariant state is considered. The walls break the translation symmetry with the result that the initial bifurcation is to standing waves with a fixed phase. Travelling waves (TW) appear in a secondary pitchfork bifurcation. A new two-frequency state (MW) is present at small amplitude only. The theory is applied to systems, such as binary fluid convection, that are described by coupled complex Ginzburg-Landau equations. As a result the TW and MW are tentatively identified with the confined travelling wave states and the blinking states, respectively, observed both experimentally and numerically in systems with sufficiently large group velocity.
KeywordsRayleigh Number Hopf Bifurcation Standing Wave Bifurcation Diagram Travel Wave Solution
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