發(fā)布時(shí)間：2018-03-22 22:34

  本文選題：Zakharov方程　切入點(diǎn)：波群　出處：《大連理工大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：波群的非線性演化研究是波浪理論中重要的研究課題之一。近年來(lái),水波的非線性理論發(fā)展很快。一方面,Phillips (1960)[1]對(duì)此做出了奠基性的工作,提出了共振機(jī)制理論。該理論認(rèn)為當(dāng)四個(gè)波的波數(shù)與波頻滿足一定條件(即共振)時(shí),它們之間就會(huì)緩慢互相傳遞能量。目前普遍認(rèn)為共振機(jī)理是海洋中波浪的波能傳遞的重要原因。另一方面,BenjaminFeir (1967)[2]提出只要有微小的邊帶擾動(dòng),Stokes波將是不穩(wěn)定的。該擾動(dòng)就是波浪緩慢調(diào)制的最根本的原因。從那時(shí)起,波群在短時(shí)間和長(zhǎng)時(shí)間范圍內(nèi)非線性穩(wěn)定問(wèn)題的擴(kuò)展性研究工作(包括理論和實(shí)驗(yàn)工作)得到了大量的開(kāi)展。 基于水波控制方程,Zakharov (1968)[3]推導(dǎo)了適用于深水情況下的波浪非線性演化研究的積分方程。該方程即是著名的Zakharov方程。隨后StiassnieShemer (1984)[4]推導(dǎo)了在有限水深情況下的Zakharov方程,并用該方程研究了波浪的線性穩(wěn)定性,所得結(jié)果與McLean (1982)[5]吻合。Shemer et al.(2001)[6]將Zakharov方程由時(shí)域轉(zhuǎn)化為空間域,從而可模擬單向波群沿水槽演化。他們將模擬結(jié)果與實(shí)驗(yàn)結(jié)果定性與定量對(duì)比,吻合良好。 但是,該空間域方程只適用于常水深情況。本文針對(duì)該方程的不足,添加了與水深梯度成正比的項(xiàng),從而使改進(jìn)后的方程能適用于一般變水深的情況。改進(jìn)的方程非線性近似到三階,適用于任意譜寬的波群,是Zakharov方程的擴(kuò)展。 應(yīng)用Zakharov方程研究了兩類問(wèn)題,一是考慮了水深與波陡對(duì)波浪第一類不穩(wěn)定性的影響,二是討論了坡度、周期與波幅對(duì)波群的演化的影響。
[Abstract]:The study of nonlinear evolution of wave groups is one of the most important research topics in wave theory. In recent years, the nonlinear theory of water waves has developed rapidly. The theory of resonance mechanism is put forward, which holds that when the wave number and frequency of four waves satisfy certain conditions (i.e. resonance), At present, it is generally believed that resonance mechanism is an important reason for wave energy transfer in the ocean. On the other hand, Benjamin Feir (1967) [2] suggests that the Stokes wave will be unstable as long as there is a small side-band disturbance. Disturbance is the fundamental reason for the slow modulation of waves. From then on, The research on the expansibility of wave groups in the short and long time range of nonlinear stability problems has been carried out extensively, both in theory and in experiment. Based on the water wave control equation Zakharov (1968) [3], an integral equation for the study of the nonlinear evolution of waves in deep water is derived. This equation is known as the Zakharov equation. [4] subsequently, the Zakharov equation in the case of limited water depth is derived. The linear stability of waves is studied by using this equation. The results are in good agreement with that of McLean's 1982) [5] .Shemer et al. [6] [6] the Zakharov equation is transformed from time domain to spatial domain. Thus, the evolution of unidirectional wave group along the flume can be simulated, and the qualitative and quantitative comparison between the simulation results and the experimental results shows that the simulation results are in good agreement with each other. However, the space domain equation is only suitable for the case of constant water depth. In this paper, a term proportional to the gradient of water depth is added to the equation. The improved equation is an extension of the Zakharov equation, which is approximate to the third order and suitable for wave groups of arbitrary spectral width. Two kinds of problems are studied by using Zakharov equation. One is to consider the influence of water depth and wave steepness on the first kind of wave instability, the other is to discuss the influence of slope, period and amplitude on the evolution of wave group.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TV139.2

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 張耀光,劉巖,李春平,董麗晶;中國(guó)海洋油氣資源開(kāi)發(fā)與國(guó)家石油安全戰(zhàn)略對(duì)策[J];地理研究;2003年03期

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本文編號(hào)：1650741