Feng Peihua, Zhang Jiazhong, Wang Wei
School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China.
Chaos. 2016 Jun;26(6):063104. doi: 10.1063/1.4953015.
Nonlinear waves produced in an incompressible boundary layer driven by a travelling wave are investigated, with damping considered as well. As one of the typical nonlinear waves, the spike-like wave is governed by the driven-damped Benjamin-Ono equation. The wave field enters a completely irregular state beyond a critical time, increasing the amplitude of the driving wave continuously. On the other hand, the number of spikes of solitary waves increases through multiplication of the wave pattern. The wave energy grows in a sequence of sharp steps, and hysteresis loops are found in the system. The wave energy jumps to different levels with multiplication of the wave, which is described by winding number bifurcation of phase trajectories. Also, the phenomenon of multiplication and hysteresis steps is found when varying the speed of driving wave as well. Moreover, the nature of the change of wave pattern and its energy is the stability loss of the wave caused by saddle-node bifurcation.
研究了由行波驱动的不可压缩边界层中产生的非线性波，并考虑了阻尼。作为典型的非线性波之一，尖峰状波由受驱动阻尼的本杰明-奥诺方程控制。在超过临界时间后，波场进入完全不规则状态，同时持续增加驱动波的振幅。另一方面，孤立波的尖峰数量通过波型的倍增而增加。波能量以一系列急剧的步骤增长，并且在系统中发现了滞后回线。随着波的倍增，波能量跳跃到不同水平，这由相轨迹的缠绕数分岔来描述。此外，当改变驱动波的速度时，也会发现倍增和滞后步骤的现象。而且，波型及其能量变化的本质是由鞍结分岔导致的波的稳定性丧失。
