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E-grāmata: Waves and Mean Flows

(New York University)
  • Formāts: EPUB+DRM
  • Sērija : Cambridge Monographs on Mechanics
  • Izdošanas datums: 20-Aug-2009
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781139637442
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  • Formāts: EPUB+DRM
  • Sērija : Cambridge Monographs on Mechanics
  • Izdošanas datums: 20-Aug-2009
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781139637442
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A modern account of the nonlinear interactions between waves and mean flows such as shear flows and vortices.

Interactions between waves and mean flows play a crucial role in understanding the long-term aspects of atmospheric and oceanographic modeling. Indeed, our ability to predict climate change hinges on our ability to model waves accurately. This book gives a modern account of the nonlinear interactions between waves and mean flows such as shear flows and vortices. A detailed account of the theory of linear dispersive waves in moving media is followed by a thorough introduction to classical wave-mean interaction theory. The author then extends the scope of the classical theory and lifts its restriction to zonally symmetric mean flows. The book is a fundamental reference for graduate students and researchers in fluid mechanics, and can be used as a text for advanced courses; it will also be appreciated by geophysicists and physicists who need an introduction to this important area in fundamental fluid dynamics and atmosphere-ocean science.

Recenzijas

'Bühler's well-organized textbook is excellent in all the most important ways Waves and Mean Flows presents its readers with a clearly written text that is comfortable to read.' Physics Today ' this text is the best existing source for a comprehensive introduction to the GLM theory. Many important concepts, such as the development of Lagrangian-mean divergence in divergence-free Eulerian flows, are explained with clarity, often through the use of elegant examples.' R. M. Samelson, Oregon State University

Papildus informācija

A modern account of the nonlinear interactions between waves and mean flows such as shear flows and vortices.
Preface xv
Part I Fluid Dynamics and Waves
1(94)
Elements of fluid dynamics
3(18)
Flow kinematics
3(5)
Mass, momentum and velocity
3(2)
Material trajectories and derivatives
5(1)
Lagrangian and Eulerian variables
6(1)
Evolution of material elements
6(2)
Perfect fluid dynamics
8(3)
Euler's equation
8(1)
Constitutive relations
9(1)
The polytropic fluid model
10(1)
Conservation laws and energy
11(1)
Circulation and vorticity
12(4)
Circulation theorem
12(2)
Vorticity and potential vorticity
14(2)
Rotating frames of reference
16(2)
Shallow-water system
18(2)
Available potential energy
19(1)
Notes on the literature
20(1)
Linear waves
21(17)
Linear dynamics
22(15)
Particle displacements and the virial theorem
23(1)
Vortical and wave modes
24(1)
Kinematics of plane waves
25(2)
Shallow-water plane waves
27(3)
Refraction
30(2)
WKB theory for slowly varying wavetrains
32(4)
Related wave equations and adiabatic invariance
36(1)
Notes on the literature
37(1)
Geometric wave theory
38(15)
Two-dimensional refraction
39(5)
Characteristics and Fermat's theorem
39(2)
Ocean acoustic tomography
41(1)
Ray tubes
42(2)
Caustics
44(8)
Green's function representation
44(1)
High-wavenumber boundary-value problem
45(1)
Stationary phase approximation
46(2)
Curved wave fronts and focusing
48(1)
The phase shift across caustics
49(1)
Solution directly on the caustic
50(1)
Non-smooth wavemakers and diffraction
51(1)
Notes on the literature
52(1)
Dispersive waves and ray tracing
53(42)
Facets of group velocity
53(11)
Beat waves
54(1)
Boundary forcing and radiation condition
54(2)
Asympotic solution to initial-value problem
56(4)
Asymptotic wave energy dynamics
60(2)
The case of equal-and-opposite frequencies
62(2)
Examples of dispersive waves
64(6)
Rotating shallow water
64(3)
Two-dimensional Rossby waves
67(3)
Ray tracing for dispersive wavetrains
70(7)
Model example
72(2)
Generic ray-tracing equations
74(2)
Symmetries and ray invariants
76(1)
A note on the asymptotic phase in ray tracing
77(1)
Ray tracing in moving media
77(8)
Doppler shifting and the intrinsic frequency
78(1)
Refraction by the basic flow
79(1)
Fermat's principle for dispersive wavetrains
80(3)
Wave action conservation and amplitude prediction
83(2)
Wave activity conservation laws
85(8)
Ensemble conservation law in discrete mechanics
86(1)
Ensemble conservation law for linear waves
87(1)
Pseudomomentum and pseudoenergy
88(2)
Wave action for slowly varying wavetrains
90(1)
Moving media and several dimensions
91(2)
Notes on the literature
93(2)
Part II Wave---Mean Interaction Theory
95(164)
Zonally symmetric wave---mean interaction theory
97(6)
Basic assumptions
98(5)
Small-amplitude wave-mean interactions
98(2)
Simple geometry
100(1)
Zonal averaging
101(2)
Internal gravity waves
103(39)
Boussinesq system and stable stratification
103(3)
Momentum, energy and circulation
105(1)
Linear Boussinesq dynamics
106(5)
Vortical mode
107(1)
Plane internal gravity waves
107(3)
Spatial structure of time-periodic waves
110(1)
Two-dimensional vertical slice model
111(1)
Zonal pseudomomentum of internal waves
111(5)
Lagrangian and Eulerian pseudomomentum
112(3)
Forcing and dissipation of pseudomomentum
115(1)
Mountain lee waves and drag force
116(9)
Linear lee waves in two dimensions
117(4)
Hydrostatic solution using Hilbert transforms
121(1)
Drag force and momentum flux
122(3)
Mean-flow response
125(8)
Eulerian-mean equations
125(1)
Mean buoyancy and pressure response
126(3)
Zonal mean-flow response
129(1)
Mass, momentum and energy budgets
130(3)
Wave dissipation
133(4)
Radiative damping and secular mean-flow growth
134(1)
Non-acceleration and the pseudomomentum rule
135(2)
Extension to variable stratification and density
137(4)
Variable stratification and wave reflection
138(1)
Density decay and amplitude growth
139(2)
Notes on the literature
141(1)
Shear flows
142(29)
Linear Boussinesq dynamics with shear
143(5)
Wave activity measures with shear
144(1)
Energy changes for a sheared wavetrain
145(1)
Rayleigh's theorem for shear instability
146(1)
Ray tracing in a shear flow
147(1)
Critical layers
148(12)
Validity of ray tracing in critical layers
149(1)
Failure of steady linear theory for critical layers
150(2)
Causal linear theory for critical layers
152(2)
Singular wave absorption by dissipation
154(2)
Strongly nonlinear critical layers
156(2)
Numerical simulations and drag parametrization
158(1)
Saturation parametrization of critical layers
158(2)
Joint evolution of waves and the mean shear flow
160(10)
Multi-scale expansion in wave amplitude
161(3)
Examples of joint wave-mean dynamics
164(4)
The quasi-biennial oscillation
168(2)
Notes on the literature
170(1)
Three-dimensional rotating flow
171(15)
Rotating Boussinesq equations on an f-plane
171(1)
Linear structure
172(8)
Balanced vortical mode and Rossby adjustment
172(3)
Internal inertia-gravity waves
175(3)
Rotating lee waves and mountain drag
178(2)
Mean-flow response and the vortical mode
180(3)
Leading-order response and the TEM equations
181(1)
Forcing of mean vortical mode
182(1)
Rotating vertical slice model
183(2)
Stratification and rotation symmetry
183(1)
Wave-mean interactions in the slice model
184(1)
Notes on the literature
185(1)
Rossby waves and balanced dynamics
186(18)
Quasi-geostrophic dynamics
186(7)
Governing equations
187(2)
Conservation properties
189(2)
Quasi-geostrophic β-plane
191(1)
Response to effective zonal mean force
192(1)
Small amplitude wave-mean interactions
193(3)
Rossby-wave pseudomomentum
194(1)
Localized forcing and dissipation
194(2)
Rossby waves and turbulence
196(7)
The Taylor identity for quasi-geostrophic dynamics
196(2)
Turbulent mixing of PV
198(2)
PV staircases and self-sharpening jets
200(3)
Notes on the literature
203(1)
Lagrangian-mean theory
204(45)
Lagrangian and Eulerian averaging
205(6)
Stokes corrections
207(2)
Stokes drift, pseudomomentum and bolus velocity
209(2)
Elements of GLM theory
211(18)
Lifting map and Lagrangian averaging
211(2)
The mean material derivative and trajectories
213(1)
Mean mass conservation
214(3)
Small-amplitude relations for the mass density
217(1)
The divergence effect
217(3)
Mean surface elements and conservation laws
220(3)
Circulation and pseudomomentum
223(2)
Why pseudomomentum is conserved
225(1)
Vorticity and potential vorticity
226(3)
Wave activity conservation in GLM theory
229(8)
General wave activity equation
230(2)
Pseudomomentum and pseudoenergy
232(2)
Non-barotropic flows
234(1)
Angular momentum and pseudomomentum
235(2)
Coriolis forces in GLM theory
237(8)
Rotating circulation and pseudomomentum
238(1)
Wave activity relations
239(1)
Angular momentum and pseudomomentum
240(1)
Gauged pseudomomentum and the β-plane
241(4)
Lagrangian-mean gas dynamics and radiation stress
245(3)
Radiation stress and pseudomomentum flux
246(2)
Notes on the literature
248(1)
Zonally symmetric GLM theory
249(10)
GLM theory for the Boussinesq equations
249(5)
Dissipative pseudomomentum rule
252(1)
Pseudomomentum with vertical shear
253(1)
Rotating Boussinesq equations on an f-plane
254(3)
Residual and Lagrangian-mean circulations
255(1)
EP flux in GLM theory
255(1)
Rotating vertical slice model in GLM theory
256(1)
Notes on the literature
257(2)
Part III Waves and Vortices
259(76)
A framework for local interactions
261(28)
A geometric singular perturbation
262(1)
Examples of mean pressure effects
263(11)
Mean-flow response to acoustic wavetrain
264(3)
Mean force on a wavemaker
267(3)
Large-scale return flow beneath surface waves
270(4)
Vortical mean-flow response
274(7)
Local interactions in shallow water
275(1)
Bretherton flow
276(2)
A wavepacket life cycle
278(2)
Strong interactions and potential vorticity
280(1)
Impulse and pseudomomentum conservation
281(7)
Classical impulse theory
281(4)
Impulse and pseudomomentum in GLM theory
285(3)
Notes on the literature
288(1)
Wave-driven vortex dynamics on beaches
289(28)
Wave-driven longshore currents
289(2)
Classic theory based on simple geometry
291(7)
Wave structure
292(2)
Mean-flow response
294(4)
Theory for inhomogeneous wavetrains
298(1)
Vorticity generation by wave breaking and shock formation
299(4)
Vortex dynamics on sloping beaches
303(8)
Impulse for one-dimensional topography
304(1)
Self-advection of vortices
305(3)
Mutual interaction of vortices and rip currents
308(1)
A statistical argument for vortex locations
309(2)
Barred beaches and current dislocation
311(4)
Current dislocation by vortex dynamics
313(1)
Bottom fricton and turbulence
314(1)
Notes on the literature
315(2)
Wave refraction by vortices
317(18)
Anatomy of wave refraction
318(3)
Refraction by a bath-tub vortex
320(1)
Remote recoil
321(3)
Wave capture of internal gravity waves
324(9)
Impulse and pseudomomentum for stratified flow
326(3)
Wavepacket and vortex dipole example
329(1)
Mean-flow response at the wavepacket
330(3)
Wave-vortex duality and dissipation
333(1)
Notes on the literature
334(1)
References 335(4)
Index 339
Oliver Bühler is an Associate Professor in the Department of Mathematics at the Courant Institute of Mathematical Sciences, New York University.