Harmonic modulation instability and spatiotemporal chaos

摘要

Patterns may he formed by the harmonic modes excited by the spatially modulational master mode. If only the master pattern exists, the system is in spatiotem- poral coherent state or in TC and SPC state depending on the modulation wave number. The pattern selection leads to the number of the formed harmonic patterns to be less than that of the unstable harmonic modes. As a few harmonic patterns coexist with the master pattern, the system is still in in TC and SPC. However, as many harmonic patterns occur, in the early phase, the system may experience the SPC state. With the lapse of time collision and fusion among patterns in stochastic motion may frequently take place to reform a few new incoherent patterns, the system enters the STC state, and the energy is extends to stable high-harmonic modes with shorter wavelengths and transport occurs in the system. In addition, the more the patterns formed, the faster the dynamic transition to STC. This implies that the unstable excitation of a large number spatially harmonic modulation lengths is the essentially initial condition to cause STC. The above features may contribute to comprehend the onset of weak turbulence.