Doppler Effect of Nonlinear Waves and Superspirals in Oscillatory Media

TL;DR

This paper investigates how nonlinear waves emitted from a moving source in oscillatory media exhibit Doppler effects, leading to superspirals with modulated wavelengths and amplitudes, analyzed through the complex Ginzburg-Landau equation.

Contribution

It introduces a theoretical framework for understanding Doppler effects in nonlinear wave sources and explains the formation and decay of superspirals in reaction-diffusion systems.

Findings

Doppler-induced modulations depend on source motion and perturbation frequency.

Waves can grow, decay, or saturate depending on convective Eckhaus instability.

Results interpret recent experimental observations of superspirals and chaos.

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.