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Nonlinear Transition to a Global Mode for Traveling-Wave Instability in a Finite box.

Using hydrothermal waves in a long narrow channel as an ideal supercritical nonlinear wave system, we study the critical behavior at onset for a finite cell with poorly reflecting boundaries. We observe a spatially nonuniform global eigenmode localized near the end of the cell and associated with a wave front invading the cell. The onset of this mode-corresponding to the absolute instability transition-is shifted above the value corresponding to convective instability, measured in an annular channel with periodic boundary conditions. Experimental critical exponents are discussed in the framework of existing theoretical descriptions and quantitative comparison with the complex Ginzburg-Landau model is attempted.