Doppler effect of nonlinear waves and superspirals in oscillatory media

Year: 2003

Authors: Brusch L., Torcini A., Bar M.

Autors Affiliation: MPI for Physics of Complex Systems, Nothnitzer Strasse 38, 01187 Dresden, Germany;
Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy

Abstract: Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example in which waves originate from a source exhibiting a back-and-forth movement in a 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 direct simulations as well as numerical nonlinear analysis within the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonic growth or decay as well as saturation of these modulations depending on the perturbation frequency. Our findings elucidate recent experimental observations concerning superspirals and their decay to spatiotemporal chaos.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 91 (10)      Pages from: 108302-1  to: 108302-4

KeyWords: Modulated Amplitude Waves; Ginzburg-landau Equation; Rotating Spiral Waves; Convective Instability; Eckhaus Instability; Excitable Media; Dynamics; Transition; Model; Breakup
DOI: 10.1103/PhysRevLett.91.108302

Citations: 22
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