課程資訊
課程名稱
基本流體穩定學及應用
BASIC HYDRODYNAMIC STABILITY THEORY WITH APPLICATIONS 
開課學期
97-1 
授課對象
工學院  水利工程組  
授課教師
楊德良 
課號
CIE5074 
課程識別碼
521 U8760 
班次
 
學分
全/半年
半年 
必/選修
選修 
上課時間
星期二2,3,4(9:10~12:10) 
上課地點
土220 
備註
總人數上限:50人 
 
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課程概述

(1) Introduction to Hydrodynamic Instability in Nature
a. Gravity currents in the atmosphere, rivers, and oceans, avalanches, pyroclastic flows, and finger instability of gravity currents on a slope
b. The surface-heated and double-diffusive convections (e.g. thermal and salinity stratifications in oceans)
c. Wind-ocean interaction (Kelvin-Helmholtz instability)
d. Surface and internal waves
d. Spatial instability (e.g., smoke, plume, boundary layer, wake, jet)

(2) Basic Concepts and Preliminaries
a. The matrix theory (eAt, Jordan normal form, matricant, 2-norm, normal matrix, Floquet theory)
b. The Fluid Mechanics—e.g., deriving the linearized perturbation equation and base-state solution of plane-Couette flow

(3) The Thermal Instability of a Fluid Layer Heated from Below
a. The equations of continuity, motion, and energy
b. The Boussinesq approximation
c. Non-dimensionalization (Rayleigh, Grashof and Prandtl number)
d. The base-state solution and linearized perturbation equation
e. The free-free and rigid-rigid boundary conditions
f. The Fourier transform and spectral method
g. Long-wave approximation (e.g., layering mode)
h. Solving the dynamical system
i. Stable, unstable, and neutrally stable
j. The marginal stability curve and stationary/oscillatory onset
k. Drawing the flow pattern at the instability onset—the critical-state stream function
l. The kinetic energy equation of perturbations
m. The transient instability for distinct and repeated eigenvalues
n. Three-dimensional analysis
o. Time-periodic heating at boundaries: the time-periodic basic state and perturbation equations, Floquet theory and numerical methods for obtaining the Floquet exponent, Mathieu’s equation, what if there are repeated eigenvalues ?
p. Special lecture: oscillating box—resonance in a gravity-modulated instability (a brief introduction).

(4) The Double-Diffusive Instability
a. Introduction to ‘double-diffusive’
b. The governing equations and Boussinesq approximation
c. The Rayleigh numbers for temperature and solute stratifications
d. The base-state solution and linearized perturbation equation
e. The boundary conditions for the ‘diffusive’ and ‘finger’ regimes
f. The stability diagram
g. Oscillatory/stationary onset
h. The formation of diffusive- and finger- regime layers
i. Related observations in oceans

(5) The Instability of Newtonian Fluids on an Inclined Plane
a. The governing equations for perturbations
b. The linearization of dynamic and kinematic boundary conditions
c. The Orr-Sommerfeld equation
d. First and second long-wave approximations
e. Approximation for small Reynolds number
f. The shallow-water equation
g. The instability induced by one-D wavy bottom—Floquet theory
h. Whether there can be a theory of ‘Band-gap’ in a Newtonian, mud, granular, or debris flow on a slope with two-D wavy bottom

(6) Perturbations in Plane-Sheared Dense Granular Flows (DGF)
a. The visco-plastic constitutive law
b. The inertial number
c. The base-state solution and perturbation equations

(7) Advanced Topic—Secondary Instability Theory
 

課程目標
流體穩定學研究的問題很多,其中包括大家都耳熟能詳的—流體如
何從層流演變成亂流, 而近代的流體穩定學的應用,已經包括了:航太,機械,化工,材料科學,土木,水力,海洋,大氣.
廣義地說,它的理論背景主要是建構在動力系統穩定學 (Stability of Dynamical Systems). 而動力系統穩定學並不只限用於流體, 它以豐富的數學理論來研究許多大自然現象,包括生態的研究, 可以說這是一門探索大自然科學的重要知識.
這門課是以幾種不同的流場為媒介,來介紹基本的流體穩定學,並進而引導學生進入初階的動力系統穩定學. 對有興趣研究連體力學的學生,這是有幫助的專業領域.
 
課程要求
8. 限修對象:大學部3,4年級及碩士班學生。 
預期每週課後學習時數
 
Office Hours
 
參考書目
隨堂發論文(Journal articles)或講義資料(Lecture notes). 
指定閱讀
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
期中考 
40% 
 
2. 
期末論文報告 
60% 
 
 
課程進度
週次
日期
單元主題