Noise-sustained structures due to convective instability in finite domains

In large aspect ratio systems with broken reflection symmetry the onset of instability is closely related to the threshold for absolute instability in the corresponding unbounded system. The upstream boundary (with respect to the group velocity) plays a crucial part in fixing the frequency of the no nlinear wavetrain that results, and hence its stability properties. In cont rast in the convectively unstable regime all perturbations decay, although persistent structures can be maintained by the addition of small amplitude noise. The upstream boundary, however distant, continues to play an essenti al role in frequency selection, with the result that the structures induced by noise are of universal form. A general theory is developed that predict s the selected frequency and wave number for both primary and secondary con vective instabilities, and the results illustrated using the complex Ginzbu rg-Landau equation and a mean-field dynamo model of magnetic field generati on in the Sun. (C) 2000 Elsevier Science B.V. All rights reserved.