论文标题
波群的演变和相互作用
Wave group evolution and interaction
论文作者
论文摘要
该论文涉及流体动力实验室中确定性怪胎波产生的数学和物理方面。我们采用非线性schrödinger（NLS）方程作为表面重力波包包封的演化的数学模型。正如本杰明和费尔（Benjamin and Feir，1967）在实验中预测的，在侧带调制下，深水上的斯托克斯波不稳定。 NLS方程的平面波解，代表Stokes波的基本组成部分，在线性扰动理论下经历了类似的模量不稳定性。 Soliton家族在有限的背景（SFB）上给出了这种扰动波的非线性延伸，在该家族中，可以通过几种技术进行分析得出确切的表达。我们讨论了SFB家族作为怪胎波事件的主要候选人的特征。相应的物理波场表现出波前错位和相奇异性的有趣现象。
This thesis deals with mathematical and physical aspects of deterministic freak wave generation in a hydrodynamic laboratory. We adopt the nonlinear Schrödinger (NLS) equation as a mathematical model for the evolution of the surface gravity wave packet envelopes. As predicted theoretically and observed experimentally by Benjamin and Feir (1967), Stokes waves on deep water are unstable under a sideband modulation. The plane-wave solution of the NLS equation, which represents the fundamental component of the Stokes wave, experiences a similar modulational instability under the linear perturbation theory. A nonlinear extension for this perturbed wave is given by the family of Soliton on Finite Background (SFB), where an exact expression is available and can be derived analytically by several techniques. We discuss the characteristics of the SFB family as a prime candidate for freak wave events. The corresponding physical wave field exhibits intriguing phenomena of wavefront dislocation and phase singularity.
