稳态共振波及非线性波流相互作用研究

发布时间：2018-04-25 14:39

本文选题：表面重力波 + 波浪共振　；参考：《上海交通大学》2015年博士论文

【摘要】：非线性波波共振作用和非线性波流相互作用是导致波浪场能量谱发生变化的重要因素,相关问题广泛存在于工程实际问题中,已有的大量研究工作主要从初边值问题角度研究这两种因素对波浪场能量谱随时间演化的影响。本论文尝试从边值问题角度出发寻求对应的稳态解现象,以理论分析为主,辅以试验验证的方式分析了稳态共振波的存在性并揭示了其能量分布特性,此外提出了非线性波流相互作用模型并考虑了涡量对频率(相速度)的影响。本文主要研究了如下六个问题,分别描述如下:1.从已有的特殊四波共振开始,研究了一般的四波共振,多个波分量耦合的四波共振及由高阶波波作用形成的六波共振。在以上三种情况中,我们发现稳态共振均存在且有多解,此外当参加共振的波分量个数增加时稳态共振波多解的个数有增加的趋势。2.以特殊的四波共振和六波共振为例,研究了当参数变化时稳态共振波的能量分布情况。确认了能量分布在参数空间内的连续变化,当波形从二维趋向一维或当波系中各波分量幅值增加(总能量增加)时,近似共振分量将包含越来越多的能量。3.通过线性稳定性分析发现当扰动不与任何未扰动波分量发生共振作用时,稳态共振波是稳定的。考虑到小振幅的初始扰动需要足够长的时间发展才有可能影响到波系能量分布,因此至少理论上讲,稳态共振波可能是亚稳定的,这为实验观测提供了可能性。4.为消除了稳态共振波必须满足Phillips线性共振条件的限制,在同伦分析方法框架中提出了分段的线性算子。通过此分段线性算子,得到了仅满足非线性共振条件的稳态共振波,扩展了稳态共振波的存在空间,且发现当波系中波分量幅值增加(总能量增加)时稳态共振波的存在区域随之扩大。5.在物理实验误差允许范围内,通过对照组实验的定量对比讨论了稳态共振波的存在性。观察到了由主波分量间的相位差而产生的对称组和非对称组波形。此外,定性对比上实测数据和理论结果吻合良好。6.考虑了无来流时双色波中基波相速度受非线性波波作用的影响,给出了考虑波波作用时相速度的高阶近似。分析了有旋来流对基波相速度的影响,发现来流(平均涡量)对非线性波波作用的影响由来流特征斜率决定,而来流表面速度大小则增强或减弱此效应。
[Abstract]:Nonlinear wave resonance and nonlinear wave-current interaction are important factors leading to the variation of wave field energy spectrum, and the related problems are widely used in engineering practice. The influence of these two factors on the evolution of wave energy spectrum with time is studied from the point of view of initial boundary value problem. In this paper, we try to find the corresponding steady-state solution from the point of view of boundary value problem, and analyze the existence of steady-state resonance wave and reveal its energy distribution characteristics by means of theoretical analysis and experimental verification. In addition, a nonlinear wave-current interaction model is proposed and the effect of vorticity on the frequency (phase velocity) is considered. In this paper, we mainly study the following six problems, which are described as follows: 1. Starting from the existing special four-wave resonance, the general four-wave resonance, the four-wave resonance coupled with multiple wave components and the six-wave resonance formed by the interaction of high-order waves are studied. In the above three cases, we find that the steady-state resonance exists and has multiple solutions. In addition, when the number of wave components participating in the resonance increases, the number of the steady-state resonance wave has an increasing trend. Taking the special four-wave resonance and six-wave resonance as examples, the energy distribution of the steady-state resonance wave is studied when the parameters change. The continuous variation of energy distribution in parameter space is confirmed. When the waveform tends from two dimensions to one dimension or when the amplitude of each wave component in the wave system increases (total energy increase), the approximate resonance component will contain more and more energy. By linear stability analysis, it is found that the steady resonance wave is stable when the disturbance does not resonate with any undisturbed wave component. Considering that the initial disturbance of small amplitude needs long enough development to affect the energy distribution of the wave system, at least theoretically, the steady state resonance wave may be metastable, which provides the possibility for experimental observation. In order to eliminate the limitation that the steady-state resonance wave must satisfy the Phillips linear resonance condition, a piecewise linear operator is proposed in the framework of homotopy analysis method. By using this piecewise linear operator, the stable resonance wave satisfying the nonlinear resonance condition is obtained, and the existence space of the steady state resonance wave is extended. It is also found that when the amplitude of wave component (total energy) increases in the wave system, the region of existence of the steady-state resonance wave expands with the increase of the total energy. The existence of steady-state resonance waves is discussed by quantitative comparison of the control group experiments within the allowable error of physical experiments. The symmetrical and asymmetric waveforms generated by the phase difference between the main wave components are observed. In addition, the measured data are in good agreement with the theoretical results in qualitative comparison. Considering the effect of nonlinear wave on the phase velocity of the fundamental wave in a bicolor wave without incoming current, the high order approximation of the phase velocity is given when the wave action is considered. The influence of swirl flow on the phase velocity of the fundamental wave is analyzed. It is found that the effect of the flow (average vorticity) on the nonlinear wave is determined by the characteristic slope of the flow, while the velocity on the surface of the flow increases or weakens the effect.
【学位授予单位】：上海交通大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：P731.22;P75

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