|
課
|
主題
|
講稿
|
|
1
|
導師簡介
分發動力學的講義.
審閱班級描述和課程大綱
就流體對外加作用力的反應模式而言，定義流體。並嘗試描述什麼構成了流體動力學研究的內容艱苦的／有挑戰性的／有趣的。
Introduced the Instructor.
Gave handout on kinematics (英PDF).
Went over the class description and the course syllabus.
Defined a fluid with respect to its mode of resistance to applied forces and made an effort to demonstrate what makes the study of fluid dynamics hard/challenging/interesting.
|
(英PDF)
|
|
|
數學入門
簡要的介紹向量和張量符號，向量和張量代數，波的運動，特徵向量／值，向量分析，以及尺度分析。
分發來自於Jim Price的向量分析材料
Maths primer
Briefly covered vector and tensor notation, vector and tensor algebra, wave kinematics, eigenvectors/values, dimensional analysis, and scale analysis.
Handout on dimensional analysis from Jim Price (英PDF - 1.5 MB).
|
(英PDF)
|
|
2
|
來自於Jim Price新的流體動力學。
介紹拉各朗日與歐拉架構，並介紹其優缺點。
推導隨體導數（在歐拉架構下的流體的時間變率）。介紹軌跡，紋線以及流線。
使用技術手段來做兩個演示（一段mpeg格式的影片和一段影片）。
New Kinematics of Fluid Flow from Jim Price (英PDF - 2.6 MB).
Introduced Lagrangian and Eulerian frameworks giving pros and cons for each.
Derived the material derivative (time rate of change following the flow in an Eulerian context). Introduced trajectories, streaklines, and streamlines.
Technology conspired to foil two demos (one mpeg movie and one video).
|
(英PDF)
|
|
3
|
介紹分解定理。
量化流體運動，分解為平移，扭曲和剛體旋轉。
定義線性應變速率，剪切應變速率，剛體旋轉速度。
藉由選擇特殊的起始軸，顯示當去掉剪切應變速率，僅保留扭曲和剛性旋轉的數學上的影響。
Introduced the Cauchy-Stokes decomposition theorem.
Quantified how fluid motion may be broken down into translation, dialation, and rigid rotation.
Defined the linear strain rate, the shear strain rate, and the rigid rotation rate.
Showed that by a special choice of initial axes, the mathematical impact of shear strain rate is removed, and only dialation and rigid rotation remain.
|
(英PDF)
|
|
4
|
簡要的回顧拉格朗日和歐拉相關的隨體導數和應變速率（處於粘性關係中），以及Cauchy-Stokes分解定理。
定義速度梯度張量，並說明如何將它表示為應變速率張量與轉動率張量的。
給出一些動力學的例子來演示速度梯度張量的各個部分是如何使流體液滴變形的。(G=[4 4;2 8], G=[-1 6;1 -1], G=[-1 6;6 -1], G=[-3 6;-6 -1], 以下是壓縮過的英PDF文檔)。
給出一個關於岩石中的剪切形變的實例
介紹線性不確定傳播子，推導其如何得到起始時刻的方向，並且這個方向會演變成最終時刻橢圓的主要軸的方向。證明起始時刻的方向構成了標準正交基底。用一些圓演變成橢圓的圖像來探究其中的數學。
引入奇異值分解作為捷徑來得到MM' 和M'M特徵向量和特徵值。
Briefly reviewed Lagrangian vs. Eulerian, the material derivative, rates of strain (in the context of viscosity), and the Cauchy-Stokes decomposition theorem.
Defined the velocity gradient tensor and showed how it can be broken down into the sum of the strain rate tensor and the rotation rate tensor.
Gave some kinematic examples of how each component of the velocity gradient tensor deforms fluid blobs (G=[4 4;2 8] (ZIP), G=[-1 6;1 -1] (ZIP), G=[-1 6;6 -1] (ZIP), G=[-3 6;-6 -1] (ZIP), these are zipped pdf files).
Gave a real-world example of shear in a rock.
Introduced the linear uncertainty propagator and derived how one finds the directions at initial time that evolve into the directions of the principal axes of the final time ellipse, and proved that the initial time directions form an orthonormal basis. Followed up the maths with some pictures of circles evolving into ellipses.
Introduced singular value decomposition as a shortcut to finding the eigenvectors and values of MM' and M'M.
|
(英PDF)
|
|
5
|
花一點時間在奇異向量上，引出流體圓點發展成流體橢圓點和狀態空間的圓點發展成狀態空間的橢圓點之間的類比關係。
討論內含與外延性質，推導雷諾運輸定理的不同形式來表達在歐拉架構下的外延性質的拉各朗日變率。
假推導出散度定理。用雷諾運輸定理來一般的推導連續性方程。
Spent a little more time on singular vectors, drawing the analogy between circular blobs of fluid evolving into elliptical blobs of fluid, and circular blobs of state space evolving into elliptical blobs of state space.
Discussed extensive and intensive properties, derived various forms of the Reynolds Transport Theorem to express Lagrangian rates of change of extensive properties in an Eulerian framework.
Pseudo-derived the divergence theorem. Trivially derived the continuity equation using the Reynolds Transport Theorem.
|
(英PDF)
|
|
6
|
花費一些章節來推導普通流的線性不確定傳播子。
簡要的回顧我們花費很多時間在圓演變成橢圓的問題上的動機（來幫助我們更好的理解推導以及我們將要推導的不同方程中的摩擦項的解釋）。
介紹對於連續性方程的Boussinesq和anelastic近似，表明Boussinesq可以導致質量守恆定律運算式成為一種體積守恆。Anelastic近似解釋起來有點困難，而且似乎可以看成是一些質量和一些體積的守恆。
向質量守恆方程的拉各朗日運算式中引入雷諾運輸定理，來推導動量方程。在右手邊的合力變成物體力（重力）和表面力（應力）。
應用散度定理，將通量應力的面積積分轉換成應力散度的體積積分。
Distributed notes deriving the linear uncertainty propagator for a generic flow.
Briefly reviewed the motivation for spending all that time on circles evolving into ellipses (essentially to help us better understand the derivation and interpretation of frictional terms in various equations we will derive).
Introduced the Boussinesq and anelastic approximations for the continuity equation, Showed that Boussinesq results in changing the expression of conservation of mass to one of conservation of volume. The anelastic approximation is a bit more difficult to interpret, and seems to boil down to conserving some mass and some volume.
Started the derivation of the momentum equations by applying the Reynolds Transport Theorem to the Lagrangian expression for conservation of mass. The sum of the forces on the right hand side become the body force (gravity) and the surface force (stress).
Using the divergence theorem, converted the area integral of the flux of stress for the surface force to a volume integral of the divergence of stress.
|
(英PDF)
|
|
7
|
假推導出簡化的線性斯托克斯本構方程，並對其中的每一項作出解釋說明其含義以及嘗試來解釋方程中的每一項。
向動量方程中引入作為結果的應力張量，並且它的散度產生了Navier-Stokes方程。
假設平均密度遠遠大於擾動的平均值，忽略粘性並作Boussinesq近似，來獲得歐拉方程。
Pseudo-derived the simple, linear constitutive equation of Stokes and provided interpretations and implications for each term.
Plugged the resulting stress tensor into the momentum equations and its divergence resulted in the production of the Navier-Stokes equations.
Attempted to interpret each of the terms in the equation.
Obtained the Euler equations by ignoring viscosity and the Boussinesq approximation by assuming the mean density is much greater than perturbations to the mean.
|
(英PDF)
|
|
8
|
概述前一周所講的內容，重點在Boussinesq近似和Navier-Stokes的引出。
從拉各朗日形式開始推導能量守恆方程。
使用在左邊的變化形式，並將右邊的做功率和加熱率擴展成體積積分和面積積分。然後利用散度定理將面積積分轉換成體積積分。在這其中，內能是減去機械能項的，並根據溫度來表達內能。對得出的熱方程做Boussinesq近似。
一些筆記（和一些打字搞）可以下載以下英語檔案。
Recap of the previous week, focusing on the Boussinesq approximation and the derivation of the Navier-Stokes equations.
Derived the energy conservation equations starting from the Lagrangian form.
Used the RTT on the LHS and expanded the work rate and heating rate terms of the RHS into volume and area integrals. Then used the divergence theorem to turn the area integrals into volume integrals. Obtained an expression for internal energy by subtracting off the mechanical energy terms, and expressed the internal energy in terms of temperature. Applied the Boussinesq approximation to the resulting heat equation.
Notes (with some typos) are available for download (英PDF).
|
(英PDF)
|
|
9
|
回到與能量相關的Boussinesq問題。證明壓力修正項在Boussinesq近似下不應該被略去，引出位溫作為巧妙解決這個問題的方法。推出熱量方程的位溫形式。參照KC04的第二熱力學定律的推導。總結我們對連續性，動量，能量，和熵對於以下問題的推導。
1．無近似
2．Boussinesq近似，以及
3．歐拉（Euler）流
Returned to Boussinesq arguments about the energy equation. Demonstrated that the pressure correction term need not be negligible under Boussinesq, and derived potential temperature as a means to circumvent the problem. Produced the potential temperature form of the heat equation. Followed the KC04 derivation of the second law of thermodynamics. Summarized our derivations of continuity, momentum, energy, and entropy for
no approximation,
Boussinesq approximation, and
Euler fluid
|
(英PDF)
|
|
10
|
客座講者：Jon Moskaitis
推導柏努利公式，在此過程中我們注意到，如果假定密度是常數，重力物體力可以表述成勢能，或者只有壓力的作用，則氣壓梯度力也可以表述成勢能。說明穩流、穩定不旋轉流和不旋轉流的結果。定義速度勢並給出速度勢和／或流函數，遵循拉普拉斯方程。
Guest lecture by Jon Moskaitis.
Derived the Bernoulli form by noting that the gravity body force can be written in terms of a potential and that if we assume that density is constant or only a function of pressure, then the pressure gradient force can also be written as a potential. Showed results for steady flow, steady irrotational flow, and irrotational flow. Defined the velocity potential and gave situations in which the velocity potential and/or the stream function obey Laplace's equation.
|
(英PDF)
|
|
11
|
Jon Moskaitis的另一次客座演講。
藉由分析有旋轉和無旋轉的渦來介紹渦度。
定義環流，介紹Stokes定理，並用動作來演示。對於一個旋轉的渦旋，渦度是常量並也因此環流與其半徑（渦旋範圍內的區域）成比例。對於一個無旋的渦，除了在渦旋的中心（渦度是無限的），渦度在每一處都是零。對於限制在渦旋中心的區域，其和渦旋相關的環流是不變的，而在渦旋中心之外的任何區域都是零。
Another guest lecture by Jon Moskaitis.
Introduced vorticity by analyzing a rotational vortex and an irrotational vortex.
Defined circulation, introduced Stokes theorem, and gave an arm waving proof for Stokes theorem. Showed that for a rotational vortex, vorticity is constant and therefore circulation scales with radius (for an area that bounds the vortex). For an irrotational vortex, vorticity is zero everywhere except at the center of the vortex (where vorticity is infinite). The circulation associated with the vortex is constant for an area that bounds the center of the vortex, but zero for any area that does not bound the center of the vortex.
|
(英PDF)
|
|
12
|
會用很長時間來討論如何模擬點渦的相互作用。推導出開爾文（Kelvin）環流定理。討論當作出如下假設時這個定理如何分解：
1. 無粘性的
2. 正壓的
3. 物體力不守恆
Long discussion on how to model interacting point vortices. Derived Kelvin's Circulation Theorem. Discussed how the theorem breaks down if the assumptions of
inviscid,
barotropic, and
conservative body forces break down
|
(英PDF)
|
|
13
|
介紹亥姆霍茲渦旋定理並用動作來演示。
在動量方程中引入旋度，推導不可壓縮、正壓（和斜壓）渦度方程。
解釋拉伸項和傾斜項。
說明在平面和無粘性的情況下，渦度是常量作為附加的約束條件。
Introduced the Helmholtz vortex theorems and provided arm waving proofs.
Derived the incompressible, barotropic (and baroclinic) vorticity equations by taking the curl of the associated momentum equation.
Explained the stretching and tilting terms.
Showed that vorticity is constant for the additional constraints of 2d and inviscid.
|
(英PDF)
|
|
14
|
說明如何在旋轉和慣性系中轉換向量。
使用轉換來求出適應地球旋轉的動量方程。
描述因離心力的作用使地球的形狀變形，離心力的分量和重力的分量相平衡，所以重力被重新定義為重力與離心力之和。引入寇里奧利力並藉由一系列的影片和驗證來介紹它。
以下英語檔案是Jim Price對寇里奧利力很精彩的論述。
Showed how to transform vectors between rotating and inertial frames. Used the transformation to alter the momentum equations to account for the earth's rotation.
Described that the centrifugal force acts to deform the shape of the earth so that the tangential component of the centrifugal force balances the tangential component of gravity. Gravity is redefined as the sum of gravity and the centrifugal force. The coriolis force is introduced and the impact of the coriolis force is demonstrated in a series of movies and demonstrations.
A nice writeup on the Coriolis force from Jim Price (英PDF - 2.2 MB).
|
(英PDF)
|
|
15
|
開始先推導慣性圓周期，並與旋轉架構的週期做比較。
介紹局笛卡兒坐標系並討論曲率項的內容。
寫出在旋轉球體中區域笛卡兒座標系(直角座標系)下的動量方程。
考慮到地球的旋轉，對前半節獲得的渦度方程作出修正。並以行星渦度中的拉伸／傾斜項作為結束。
考慮到地球的旋轉，修正開爾文環流定理。也在其中表述了絕對渦度守恆。
Began by deriving the period of inertial circles and comparing it with the period of the rotating frame.
Introduced the locally Cartesian coordinate system and discussed the inclusion of the curvature terms.
Wrote down the momentum equations on a rotating sphere is the locally Cartesian coordinate system.
Modified the vorticity equation obtained in the first half of the class to include the earth's rotation. Ended up with a stretching/tilting term for planetary vorticity.
Modified Kelvin's circulation theorem to include the earth's rotation. An expression for conservation of absolute vorticity is obtained.
|
(英PDF)
|
|
16
|
概述旋轉架構下的動量和渦度方程。
對動量方程做一些尺度分析，使其變成更加易用的形式。
開始討論模式的約束條件和渦旋尺度混合影響參數化的必要性，並且馬上重新引入水平粘性到簡化的動量方程中。始終對粘性有所擔心，我們忽略掉粘性實為了觀察在簡化的動量方程中的一些平衡關係。
以再次討論慣性振盪為開始，然後討論地轉。
說明被證明的地轉平衡需要小的羅斯貝數。
Recapped the momentum and vorticity equations in the rotating frame.
Did some scaling on the momentum equations to put them in a more friendly form.
Started talking about modeling constraints and the necessity of parameterizing the impact of eddy-scale mixing, and promptly reinserted horizontal "viscosity" back into our simplified momentum equations. After all that worrying about viscosity, we ignored it in order to start looking at some balances in the simplified momentum equations.
Started by revisiting the inertial oscillation, and then moved on to geostrophy.
Showed that one needed a small Rossby number in order for the geostrophic balance to be justified.
|
(英PDF)
|
|
17
|
推導出地轉速度方程的高度梯度形式，藉由觀察500百帕高度地圖舉出很多地轉的例子。
推導出梯度風方程並在500毫八高度地圖中舉出梯度風的例子（以及它與地轉風的不同之處）。求解梯度風方程（一個二次方程），並根據羅斯貝數和無因次壓力梯度項的作用來劃分這些解。
藉由數學和受力圖來證明方程各種不同的解（以及無解）。最後介紹旋轉流。
Produced the height-gradient form of the geostrophic velocity equations and provided many examples of geostrophy by looking at 500mb height maps.
Produced the gradient wind equation and showed examples of gradient wind (and its difference from the geostrophic wind) in 500mb height maps.
Solved the gradient wind equation (a quadratic equation), and plotted solutions as a function of "Rossby number" and a non-dimensional pressure gradient term.
Demonstrated in maths and force diagrams the various solutions (and non-solutions) to the equation. Ended with cyclostrophic flow.
|
(英PDF)
|
|
18
|
概述慣性圓，地轉，梯度風，旋轉風。
接下來介紹等壓風（在急流入口和出口區域發現的非地轉風），並給出一些觀測的實例。
引入摩擦，介紹埃克曼數，並討論埃克曼平衡（一種處於氣壓梯度力，寇里奧利力，以及摩擦力中的平衡）。展示觀測實例。
轉向渦度方程，並藉由假設無粘性，正壓，小羅絲貝數的流動，推導出Taylor-Proudman定理。
在兩段電影中展示旋轉流體的垂直剛性的例子。
討論泰勒柱的形成原因，並播放一段電影
Recapped inertial circles, geostrophy, gradient wind, and cyclostrophic wind.
Next introduced the isallobaric wind (ageostrophic wind found at the entrance and exit regions of jets) and gave some observation examples.
Brought back friction, introduced the Ekman number, and discussed the Ekman balance (a balance between the pressure gradient force, the Coriolis force, and the frictional force). Showed examples in observations.
Moved to the vorticity equations, and derived the Taylor-Proudman theorem by assuming inviscid, barotropic, small Rossby number flow.
Examples of the vertical rigidity of rotating fluids were given in two movies.
The Taylor column result was discussed, and a movie was provided.
|
(英PDF)
|
|
19
|
概述慣性圓，地轉，梯度風，旋轉風，埃克曼平衡Taylor-Proudman和泰勒柱。
假設小羅絲貝數，無粘性（但允許斜壓性），從渦度方程推導熱成風關係。
解釋當傾斜的密度面向水準轉變時，行星渦度平衡傾斜，渦度如何產生的。根據溫度梯度重新改變，並在大氣觀測和試驗中演示例子。
介紹邊界層，並演示在旋轉影響下，行星邊界層的厚度不隨時間增長。邊界層中渦度的擴散與行星渦度的傾斜平衡。
根據大氣風應力的作用，推導在海洋表面邊界層質量運輸的運算式。
Recapped inertial circles, geostrophy, gradient wind, cyclostrophic wind, isallobaric wind, Ekman balance, Taylor-Proudman, and Taylor columns.
Derived the thermal wind relationship from the vorticity equation assuming small Rossby number and no viscosity (but allowing for baroclinicity).
Explained how tilting of planetary vorticity balances the vorticity generated by sloping density surfaces trying to flatten out. Recast in terms of temperature gradient, and showed examples in atmospheric observations and in the lab (see hadley.mpeg).
Introduced boundary layers and showed that under the influence of rotation, the thickness of planetary boundary layers does not grow with time. The diffusion of vorticity in the boundary is balanced by the tilting of planetary vorticity.
Derived an expression for mass transport in the ocean's surface boundary layer in terms of the applied atmospheric wind stress.
|
(英PDF)
|
|
20
|
迅速的概述在埃克曼層中的質量運輸，並用動作來給出關於在埃克曼層中隨高度變化的速度結構的描述。在近似埃克曼平衡的情形下可以產生埃克曼螺旋。
赤道之外北半球風應力的特點導致了質量在中緯度的聚合，並在高緯度分散。連續性則引起了埃克曼抽吸並進入到埃克曼層。
舊有的開爾文環流定理，需要穩態解，這是有爭議的，認為反應地球內部的唯一方法是藉由向低行星渦度（向赤道方向的）流體的流動。計算Sverdrup運輸的量級是根據表面風應力的旋度。
Started with a quick recap of the mass transport in the Ekman layer, and provided an arm-waving description of the velocity structure with depth within the Ekman layer. An Ekman balance-like argument produced an Ekman spiral.
The wind stress patterns in the northern hemisphere outside of the tropics result in convergence of mass in the mid-latitudes, and divergence of mass in the high latitudes. Continuity results in Ekman pumping and suction out of and into the Ekman layer.
Used Kelvin's circulation theorem and a desire for a steady state solution, it was argued that the only way the ocean interior can respond is by moving fluid to an area of lower planetary vorticity (equatorward). The magnitude of this Sverdrup transport was quantified in terms of the curl of the surface wind stress.
|
(英PDF)
|
|
|
波動的初級知識
各種形式的波動方程，波數和頻率的定義，相速度和群速度的引入，以及一個關於色散關係的小討論。參閱waves.zip中的內容，其中有影片展示波數和頻率影響相速度和群速度的不同之處。還有入門知識的筆記和相關的圖示可以參照以下的英語檔案。
Waves Primer
Various forms of wave equations, definitions of wave number and frequency, derivations of phase speed and group velocity, and a quick discussion on dispersion relationships. See contents of waves.zip for movies showing how different wave numbers and frequencies impact phase and group speed. Primer notes and associated figures are available (Waves.pdf, wavefigs.pdf).
|
(英PDF)
|
|
21
|
從開爾文環流定理出發推導固定深度的、正壓、無粘性方程。為了解決色散關係，假設波動解（普通樣式），用雷諾平均方法線性化方程，根據流函數變換方程。
發現與平均緯向氣流相關的作為結果的羅斯貝相位速度是向西的。而群速度則根據波數向西或是向東。
回到控制方程的線性化形式，並設平均緯向速度依賴於y，這會導致假設的標準模式解的波幅也依賴於y。
Derived the fixed depth, barotropic, inviscid vorticity equation starting from Kelvin's circulation theorem. Linearized the equation using Reynold's averaging, put linearized equation in terms of streamfunction, assumed a wavy (normal mode) solution, and solved for the dispersion relation.
Found that the phase speed of the resulting Rossby waves is westward relative to the mean zonal flow, and that the group velocity could be westward or eastward depending upon the wave number.
Returned to the linearization of the governing equation and added a y-dependence to the mean zonal velocity, which resulted in a y-dependence in the wave amplitude of the assumed normal mode solution.
Began to discuss the stability implications.
|
(英PDF)
|
|
22
|
概述推導色散關係和進行穩定性分析的方法（鑒別方程，線性化，假設波動解，用代數學方法解析，分析結果）
在經向上變化的時間平均緯向氣流中，固定深度正壓渦度方程的條件下，討論不穩定分析。
描述緯度作用下的寇里奧利參數和觀測的平均渦度的分佈圖，並說明熱帶正壓不穩定的必要條件。
設定一種理想化的剪切流來展示擾動發展的機制，同時包含到普遍的切變不穩定和些斜壓不穩定。
以推導淺水波方程結束課程。
Began by recapping the "recipe" for producing dispersion relations and performing stability analysis (identify equations, linearize, assume a wavy solution, grind through the algebra, analyze results).
Discussed stability analysis in the context of the fixed depth, barotropic vorticity equations with a time mean zonal flow that varies in the meridional direction.
Sketched profiles of the coriolis parameter and observed mean relative vorticity as a function of latitude, and showed that the necessary condition for barotropic instability exists in the tropics.
Sketched an idealized shear flow to show the mechanisms by which the perturbations grow, and related to both generic shear instability and to baroclinic instability.
Ended class by deriving the shallow water equations.
|
(英PDF)
|
|
23
|
從淺水波動量方程和連續性方程出發推導淺水波位渦方程。
舉例說明相對渦度和寇里奧利參數之間是如何交換的，以及流體深度可以根據位元渦守恆或者絕對環流守恆來表述。
說明位勢渦度方程中的深度項可以用很多種解釋。
論證對於小擾動而言，西風氣流是穩定的。然後論證這種擾動可以由地形引發。
將給出一個實驗室的例子。藉由作出准地轉的假設來推導出淺水羅斯貝波的色散關係。最根本的不同在於淺水波色散關係下的羅斯貝形變半徑設定了空間尺度，並且不允許極大的快波。
Derived the shallow water potential vorticity equation from the shallow water momentum and continuity equations.
Provided some examples of how the trade-offs between relative vorticity, coriolis parameter, and fluid depth can be described in terms of potential vorticity conservation or absolution circulation conservation.
Made the point that the "depth" term in the potential vorticity equation can be interpreted in many ways.
Demonstrated that westerly flow is stable to small perturbations, and then demonstrated that such perturbations can be generated by topography.
A laboratory example was given in topo_beta.mpg. Derived the shallow water Rossby wave dispersion relation by making a quasi-geostrophic assumption, and showed that it is qualitatively identical to the fixed depth dispersion relation. The primary difference is that the Rossby radius of deformation that finds its way into the shallow water dispersion relation sets a spatial scale for the system and does not allow infinitely fast waves.
|
|
|
24
|
這一天講述重力波。從無旋的淺水重力波出發，引出重力波的色散關係，然後再把旋轉加入到潛水波方程中來引出慣性重力波色散關係。
討論分別在小的很大的波數限制下，龐加萊波怎樣表現的如同慣性振盪和無旋的重力波。
介紹開爾文波，推導出色散關係，然後將它代入假定的解，代入邊界條件，推導出開爾文波的運算式。
課程的最後討論關於厄爾尼諾-南方濤動的振盪模型中的滯後現象。
24 A day of gravity waves. Started from the shallow water equations sans rotation to produce the gravity wave dispersion relation, then added rotation back to the shallow water equations to produce the Poincare (or inertia-gravity) wave dispersion relation.
Discussed how the Poincare waves behave like inertial oscillations and like gravity waves without rotation in the limits of small and large wavenumbers, respectively.
Introduced the Kelvin wave, derived the dispersion relation, then plugged it back into the assumed solution and, along with boundary conditions, derived the form of the Kelvin wave.
Ended with a discussion of the delayed action oscillator model of ENSO.
|
(英PDF)
|
