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Doppler Effect of Nonlinear Waves and Superspirals in Oscillatory Media

Lutz Brusch·Alessandro Torcini·Markus Baer
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Abstract

Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example, where waves originate from a source exhibiting a back-and-forth movement in radial direction. The periodic motion of the source induces a Doppler effect that causes a modulation in wavelength and amplitude of the waves (``superspiral''). Using the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonous growth or decay as well as saturation of these modulations away from the source depending on the perturbation frequency. Our findings allow a consistent interpretation of recent experimental observations concerning superspirals and their decay to spatio-temporal chaos.

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Lutz Brusch, Alessandro Torcini, Markus Baer. 2003-02-12. Doppler Effect of Nonlinear Waves and Superspirals in Oscillatory Media. https://doi.org/10.1103/physrevlett.91.108302

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