Brusch Lutz, Torcini Alessandro, Bär Markus
MPI for Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.
Phys Rev Lett. 2003 Sep 5;91(10):108302. doi: 10.1103/PhysRevLett.91.108302.
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.
研究了从移动源发出的非线性波。反应扩散介质中的蜿蜒螺旋提供了一个例子，其中波源自一个在径向方向上做往复运动的源。源的周期性运动引发了多普勒效应，导致波的波长和振幅发生调制（“超螺旋”）。通过直接模拟以及复金兹堡 - 朗道方程中的数值非线性分析，我们表明，受对流埃克豪斯不稳定性影响的波，根据扰动频率，可呈现单调增长或衰减以及这些调制的饱和状态。我们的研究结果阐明了最近关于超螺旋及其向时空混沌衰减的实验观测结果。
