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 φ3z, 184; the wkbj
approxi-mation to φ3z, 185; the local turning-point approximation
to φ3z, 188; tollmien''s improved approximation to φ3z,
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 φ3z, 305;tolimien''s
improved approximation to φ3z, 306;the uniform approximation to
φ3z based on the truncated equation, 308; the uniform
approxima-tion to φ3z 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 akz
a2 the functions anz, p, boz, p and bkz, p
a3 the functions akz, p, q and bkz, p, q
a4 the zeros of atz,p
addendum: weakly non-parallel theories for the blasius boundary
layer
solutions
bibliography and author index
motion picture index
subject index
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