矩形谐振器中非传播重力-表面张力孤波的理论研究

INVESTIGATIONS ON NONPROPAGATING GRAVITY-SURFACE TENSION SOLITON

本文用多重尺度微扰方法研究了外加驱动下,计及表面张力时矩形谐振器中有限深流体重力-表面张力驻波模的弱非线性调制。对吴君汝等人所发现的非传播表面孤波现象进行了较为详细的分析计算,修正和发展了Larraza,Putterman和Miles的非传播孤波理论,得到了正确的二次谐波共振条件。在σ-kd图上对非传播表面孤波的存在区域进行了仔细的理论分析,发现除静态液面深度外,流体的表面张力是产生和控制非传播表面孤波的另一重要参数。最后讨论了矩形谐振器的非线性共振曲线特性,并与实验进行了比较。

In this paper, the method of multiple-scales is used to investigate the weak nonlinear self-modulation of the gravity-surface tension standing wave mode in a finite deep fluid which is filled in a rectangular resonator. The detailed analysis and calculations about the nonpropaga-ting soliton discovered by Wu et al. are made when external driving and damping of the surface wave are considered. The nonpropagating soliton theory established by Larraza, Put-terman and Miles is revised and developed. The correct second harmonic resonace condition about gravity-surface tension wave in the rectangular trough is obtained. The stabilities of propagating soliton are analyzed in detail according toδ-kd diagram. It is found, in addition to the static depth d, that the surface-tension of fluid is an important parameter which may control the formation of nonpropagating soliton. Finally, the nonlinear tuning curves of the surface wave resonator are discussed and compared with experimental results.