本文關(guān)鍵詞： 非齊次KdV-Burgers方程 β效應(yīng) 緩變地形 耗散 熱外源　出處：《內(nèi)蒙古大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

【摘要】：Rossby孤立波是大氣與海洋運(yùn)動的主要波動之一,本文在層結(jié)流體準(zhǔn)地轉(zhuǎn)位渦方程,以及含有緩變地形下邊界條件的基礎(chǔ)上,用攝動方法與時(shí)空伸長變化得到層結(jié)流體中Rossby孤立波振幅滿足的非線性方程.本文首先在直角坐標(biāo)系下導(dǎo)出了推廣的β效應(yīng)(即Rossby參數(shù)β是緯度變量y的函數(shù))的層結(jié)流體準(zhǔn)地轉(zhuǎn)位渦方程與帶有緩變地形hB1(t)的下邊界條件,進(jìn)行無量綱化處理,得到無量綱化的控制方程與邊界條件,然后引入G-M(Gardner-Morikawa)變換濾去快變量x,t；利用小參數(shù)展開得到各階攝動方程；用正交模方法討論各階問題,最后利用消奇異條件討論Rossby孤立波在緩變地形、耗散與熱源作用下Rossby孤立波振幅在慢變量ξ,τ下的演變規(guī)律.在準(zhǔn)地轉(zhuǎn)位渦方程的基礎(chǔ)上,對地球流體中Rossby孤立波含有緩變地形、耗散與熱源做了一些研究,主要內(nèi)容如下：第一章介紹了地球流體中有關(guān)Rossby波的研究現(xiàn)狀、研究方法與選題背景.第二章給出了有關(guān)處理地球流體的一些近似模式,并推導(dǎo)了推廣的β平面近似下的正壓模式、層結(jié)模式下地球流體的準(zhǔn)地轉(zhuǎn)方程以及帶有緩變地形的下邊界條件.第三章采用推廣的β-平面近似模式,將β平面近似f=f_0+β_0y(β_0是常數(shù)),進(jìn)一步化為f=f0+β0(y)y這里β0(y)是緯度變量y的非線性函數(shù),這樣的近似可以更好的描述大氣與海洋的運(yùn)動,尤其在中高緯度地區(qū).在下邊界條件中考慮有緩變地形存在并利用擾動展開與時(shí)空伸長變化推導(dǎo)了Rossby孤立波振幅滿足的Kortewege-de Vries-Burgers(KdV-Burgers)方程與Modify Kortewege-de Vries(mKdV)方程的結(jié)論.第四章對本文所做工作的總結(jié)與展望.
[Abstract]:Rossby solitary wave is one of the main waves of atmospheric and oceanic motion. This paper is based on the quasi geostrophic vorticity equation of stratified fluid and the boundary conditions under slowly varying terrain. The nonlinear equation of Rossby solitary wave amplitude in stratified fluid is obtained by using perturbation method and space-time elongation variation. In this paper, the generalized 尾 effect (that is, Rossby parameter 尾 is a function of latitude variable y) is derived in a rectangular coordinate system. The quasi-geostrophic vorticity equation of stratified fluid and the lower boundary conditions with slowly varying terrain hb1. The dimensionless governing equation and boundary condition are obtained by dimensionless treatment, and then G-Me Gardner-Morikawa-transform is introduced to filter the fast variable xt; the perturbation equation of each order is obtained by using small parameter expansion; and the problems of each order are discussed by orthogonal mode method. Finally, the evolution law of the amplitude of Rossby solitary wave under slowly changing topography, dissipation and heat source is discussed by using the condition of eliminating singularity. On the basis of quasi geostrophic vorticity equation, the Rossby solitary wave in earth fluid contains slowly varying topography. Some studies on dissipative and heat sources are carried out. The main contents are as follows: in Chapter 1, the current research situation, research methods and background of Rossby wave in earth fluid are introduced. In chapter 2, some approximate models for dealing with earth fluid are given. The barotropic model under the generalized 尾 plane approximation, the quasi geostrophic equation of the earth fluid under the stratified model and the lower boundary conditions with slowly changing terrain are derived. In chapter 3, the generalized 尾-plane approximation model is adopted. If the 尾 plane is approximated to ff0 尾 0yth (尾 _ S _ 0 is a constant, further reduced to f _ f _ 0 尾 _ 0y) is a nonlinear function of the latitude variable y, such an approximation can better describe the motion of the atmosphere and the ocean. Especially in the middle and high latitudes, the existence of slowly varying terrain is taken into account in the lower boundary conditions, and the conclusions of Kortewege-de Vries-Burgersn KdV-Burgers equation and Modify Kortewege-de VriesmKdV) equation satisfying the amplitude of Rossby solitary wave are derived by using perturbation expansion and space-time elongation variation. In chapter 4th, the results of the Kortewege-de Vries-Burgersberg equation and the Modify Kortewege-de VriesmKdV equation are derived. Summary and prospect of the work done in this paper.
【學(xué)位授予單位】：內(nèi)蒙古大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：O175.29

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