流體動力學穩(wěn)定性

內(nèi)容概要

　　《流體動力學穩(wěn)定性
第2版》是一部全面流體動力學穩(wěn)定性的專著。首先詳細介紹了這個領域的三大主題：流體穩(wěn)定性、熱對流、旋轉(zhuǎn)和彎曲流和平行切變流；接著講述平行切變流的數(shù)學理論、大量的線性理論應用、分層理論和不穩(wěn)定性。《流體動力學穩(wěn)定性
第2版》盡可能多地囊括涉及到的試驗和數(shù)值理論，重點強調(diào)用到的物理方法和技巧以及書中得到的結(jié)果。本書的最大特點是包括了大量的習題，這些習題不僅能夠很好的掌握書中的內(nèi)容，而且也是書中一些疑難知識的更具體解答。目次：導論；熱力不穩(wěn)定性；離心不穩(wěn)定性；平行切變流；一致漸進逼近；更多有關線性穩(wěn)定理論；非線性穩(wěn)定性；附錄：廣義airy函數(shù)。
　　《流體動力學穩(wěn)定性 第2版》讀者對象：物理、力學專業(yè)的研究生、教師和相關的科研人員。

作者簡介

作者：（英國）德拉津（P.G.Drazin）

書籍目錄

foreword by john miles
preface
1 introduction
1 introduction
2 mechanisms of instability
3 fundamental concepts of hydrodynamic stability
4 kelvin-helmholtz instability
5 break-up of a liquid jet in air
problems for chapter 1
2 thermal instability
6 introduction
7 the equations of motion
the exact equations, 34; the boussinesq equations,35
8 the stability problem
the linearized equations, 37; the boundary condi-tions, 40; normal
modes, 42
9 general stability characteristics
exchange of stabilities, 44; a variational principle,45
10 particular stability characteristics
free-free boundaries, 50; rigid-rigid boundaries,51; free-rigid
boundaries, 52
11 the cells
12 experimental results
13 some applications
problems for chapter 2
3 centrifugal instability
14 introduction
15 instability of an inviscid fluid
three-dimensional disturbances, 73; axisymmetric disturbances, 77,
two-dimensional disturbances, 80
16 instability of couette flow of an inviscid fluid
17 the taylor problem
axisymmetric disturbances, 90; two-dimensional disturbances, 103;
three-dimensional disturbances,104; some experimental results,
104
18 the dean problem
the dean problem, 108; the taylor-dean prob-lem, 113
19 the g6rtler problem
problems for chapter 3
4 parallel shear flows
20 introduction
the inviscid theory
21 the governing equations
22 general criteria for instability
23 flows with piecewise-linear velocity profiles
unbounded vortex sheet, 145; unbounded shear layer, 146; bounded
shear layer, 147
24 the initial-value problem
the viscous theory
25 the governing equations
26 the eigenvalue spectrum for small reynolds numbers
a perturbation expansion, 159; sufficient conditions for stability,
161
27 heuristic methods of approximation
the reduced equation and the inviscid approxima-tions, 165; the
boundary-layer approximation near a rigid wa!l, 167; the wkbj
approximations,167; the local turning-point approximations,171; the
truncated equation and tollmien's improved viscous approximations,
175; the viscous
correction to the singular inviscid solution, 177
28 approximations to the eigenvalue relation
symmetrical flows in a channel, 181; flows of the boundary-layer
type, 183; the boundary-layer approximation to φ3(z), 184; the wkbj
approxi-mation to φ3(z), 185; the local turning-point approximation
to φ3(z), 188; tollmien's improved approximation to φ3(z),
191
29 the long-wave approximation for unbounded flows
30 numerical methods of solution
expansions in orthogonal functions, 203; finite-difference methods,
206; initial-value methods (shooting), 207
31 stability characteristics of various basic flows
plane couette flow, 212; poiseuiile flow in a circular pipe, 216;
plane poiseuille flow, 221; combined plane couette and plane
poiseuille flow, 223; the blasius boundary-layer profile, 224; the
asymptotic suction boundary-layer profile, 227; boundary layers at
separation, 229; the falkner-skan profiles, 231; the bickley jet,
233; the hyper- bolic-tangent shear layer, 237
32 experimental results
problems for chapter 4
5 uniform asymptotic approximations
33 introduction
plane couette flow
34 the integral representations of the solutions
35 the differential,equation method
general velocity profiles
36 a preliminary transformation
37 the inner and outer expansions
the inner expansions, 268; the outer expansions,271; the central
matching problem, 276; com- posite approximations, 278
38 uniform approximations
the solution of well-balanced type, 280; the solu- tions of
balanced type, 280; the solutions of dominant-recessive type,
283
39 a comparison with lin's theory
40 preliminary simplification of the eigenvalue relation
41 the uniform approximation to the eigenvalue relation
a computational form of the first approximation to the eigenvalue
relation, 299; results for plane poiseuille flow, 301
42 a comparision with the heuristic approximations to the
eigenvalue relation
the local turning-point approximation to φ3(z), 305;tolimien's
improved approximation to φ3(z), 306;the uniform approximation to
φ3(z) based on the truncated equation, 308; the uniform
approxima-tion to φ3(z) based on the orr-sommerfeld
equation,3o9
43 a numerical treatment of the orr-sommerfeld problem using
compound matrices
symmetrical flows in a channel, 315; boundary-layer flows,
316
problems for chapter 5
6 additional topics in linear stability theory
44 instability of parallel flow of a stratified fluid
introduction, 320; internal gravity waves and ray-leigh-taylor
instability, 324; kelvin-helmholtz instability, 325
45 baroclinic instability
46 instability of the pinch
47 development of linear instability in time and space
initial-value problems, 345; spatially growing modes, 349
48 instability of unsteady flows
introduction, 353; instability of periodic flows, 354;instability
of other unsteady basic flows, 361
problems for chapter 6
7 nonlinear stability
49 introduction
landau's theory, 370; discussion, 376
so the derivation of ordinary differential systems governing
stability
sl resonant wave interactions
internal resonance of a double pendulum, 387;resonant wave
interactions, 392
s2 fundamental concepts of nonlinear stability
introduction to ordinary differential equations, 398;introduction
to bifurcation theory, 402; structural stability, 407; spatial
development of nonlinear stability, 416; critical layers in
parallel flow, 420
s3 additional fundamental concepts of nonlinear stability
the energy method, 424; maximum and minimum energy in vortex
motion, 432; application of boun-dary-layer theory to cellular
instability, 434
s4 some applications of the nonlinear theory
benard convection, 435; couette flow, 442;parallel shear flows,
450
problems for chapter 7
appendix. a class of generalized airy functions
a1 the airy functions ak(z)
a2 the functions an(z, p), bo(z, p) and bk(z, p)
a3 the functions ak(z, p, q) and bk(z, p, q)
a4 the zeros of at(z,p)
addendum: weakly non-parallel theories for the blasius boundary
layer
solutions
bibliography and author index
motion picture index
subject index

章節(jié)摘錄

版權頁：   插圖：   An important limitation of Landau's theory is due to the assump-tion that the interaction of only one mode and its harmonics need be considered. This assumption is plausible if the igenfunctions of the linearized problem are discrete and simple, so that when the flow is slightly unstable only one normal mode is unstable and all the others decay. When the flow is in an unbounded domain, however, the eigenfunctions depend continuously on a real wavenumber. Then a wavepacket of modes is unstable when the flow is slightly unstable. This in fact occurs for most of the cases we have treated. For example, Fig. 2.2(a) shows that, when a fluid at rest between infinite horizontal planes is heated from below and the Rayleigh number R is slightly supercritical, there is a small band of unstable waves, say a1(R)

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《流體動力學穩(wěn)定性(第2版)(英文版)》是一部全面流體動力學穩(wěn)定性的專著。《流體動力學穩(wěn)定性(第2版)(英文版)》適用于物理、力學專業(yè)的研究生、教師和相關的科研人員。

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