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1.

図書

図書
C. Foias ... [et al.]
出版情報: Cambridge, [Eng.] ; New York : Cambridge University Press, 2001  xiv, 347 p. ; 25 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 83
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目次情報: 続きを見る
Preface
Acknowledgments
Introduction and Overview of Turbulence / Chapter I:
Introduction
Viscous Fluids. The Navier-Stokes Equations / 1.:
Turbulence: Where the Interests of Engineers and Mathematicians Overlap / 2.:
Elements of the Theories of Turbulence of Kolmogorov and Kraichnan / 3.:
Function Spaces, Functional Inequalities, and Dimensional Analysis / 4.:
Elements of the Mathematical Theory of the Navier-Stokes Equations / Chapter II:
Energy and Enstrophy
Boundary Value Problems
Helmholtz-Leray Decomposition of Vector Fields
Weak Formulation of the Navier-Stokes Equations
Function Spaces / 5.:
The Stokes Operator / 6.:
Existence and Uniqueness of Solutions: The Main Results / 7.:
Analyticity in Time / 8.:
Gevrey Class Regularity and the Decay of the Fourier Coefficients / 9.:
Function Spaces for the Whole-Space Case / 10.:
The No-Slip Case with Moving Boundaries / 11.:
Dissipation Rate of Flows / 12.:
Nondimensional Estimates and the Grashof Number / 13.:
Mathematical Complements / Appendix A.:
Proofs of Technical Results in Chapter II / Appendix B.:
Finite Dimensionality of Flows / Chapter III:
Determining Modes
Determining Nodes
Attractors and Their Fractal Dimension
Approximate Inertial Manifolds
Proofs of Technical Results in Chapter III
Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors / Chapter IV:
Mathematical Framework, Definition of Stationary Statistical Solutions, and Banach Generalized Limits
Invariant Measures and Stationary Statistical Solutions in Dimension 2
Stationary Statistical Solutions in Dimension 3
Attractors and Stationary Statistical Solutions
Average Transfer of Energy and the Cascades in Turbulent Flows
New Concepts and Results Used in Chapter IV
Proofs of Technical Results in Chapter IV
A Mathematical Complement: The Accretivity Property in Dimension 3 / Appendix C.:
Time-Dependent Statistical Solutions of the Navier-Stokes Equations and Fully Developed Turbulence / Chapter V:
Time-Dependent Statistical Solutions on Bounded Domains
Homogeneous Statistical Solutions
Reynolds Equation for the Average Flow
Self-Similar Homogeneous Statistical Solutions
Relation with and Application to the Conventional Theory of Turbulence
Some Concluding Remarks
Proofs of Technical Results in Chapter V
References
Index
Preface
Acknowledgments
Introduction and Overview of Turbulence / Chapter I:
2.

図書

図書
Albert Gyr, Wolfgang Kinzelbach, Arkady Tsinober, editors
出版情報: Basel : Birkhauser, c1999  viii, 480 p. ; 24 cm
シリーズ名: Trends in mathematics
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3.

図書

図書
by G. K. Batchelor
出版情報: Cambridge : Cambridge University Press, 1953  xi, 197 p. ; 22 cm
シリーズ名: Cambridge monographs on mechanics and applied mathematics
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4.

図書

図書
[by] D.C. Leslie
出版情報: Oxford : Clarendon Press, c1973  xix, 368 p. ; 24 cm
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5.

図書

図書
V.E. Zakharov, editor ; [translation edited by A.B. Sossinsky]
出版情報: Providence, R.I. : American Mathematical Society, c1998  x, 197 p. ; 27 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 182 . Advances in the mathematical sciences : (Formerly Advances in Soviet mathematics) / [editoral committee, V.I. Arnold, S.G. Gindikin, V.P. Maslov] ; 36
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Invariants of wave systems and web geometry / A. M. Balk ; E. V. Ferapontov
Stability of weak-turbulence Kolmogorov spectra / V. E. Zakharov
Energy transfer in the spectrum of surface gravity waves by resonance five wave-wave interactions / V. A. Kalmykov
Wave resonances in systems with discrete spectra / E. Kartashova
Hamiltonian formalism for Rossby waves / L. I. Piterbarg
Weakly nonlinear waves on the surface of an ideal finite depth fluid
Invariants of wave systems and web geometry / A. M. Balk ; E. V. Ferapontov
Stability of weak-turbulence Kolmogorov spectra / V. E. Zakharov
Energy transfer in the spectrum of surface gravity waves by resonance five wave-wave interactions / V. A. Kalmykov
6.

図書

図書
Jean Mathieu, Julian Scott
出版情報: New York : Cambridge University press, 2000  x, 374 p. ; 26 cm
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7.

図書

図書
Herman Branover ... [et al.]
出版情報: San Diego, Calif. ; London : Academic Press, c1999  xv, 270 p. ; 24 cm
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8.

図書

図書
M.T. Landahl, E. Mollo-Christensen
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1986  vi, 154 p. ; 24 cm
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Preface to the second edition
Preface to the first edition
Introduction with historical notes / 1:
Characteristic scales and nondimensional parameters / 2:
Basic equations / 3:
Equations of motion
Averaged equations
Stability and turbulent energy
Statistical tools for description of turbulence / 4:
Ensemble averages
Joint moment, covariance
Stationary random functions
Properties of the time autocovariances
Joint covariance
Spectra and cross spectra
Space-time covariances
Response of linear systems to random excitation
Impulse response and superposition
Response to a random input
Examples of response calculations
Distribution function and probability density
Characteristic function
Joint distributions, conditional probability
Central limit theorem
The lognormal distribution
Flows that are homogeneous in more than one spatial dimension / 5:
Some spatially homogeneous fields
Isotropic turbulence
Waves / 6:
Kinematic wave theory
Effects of weak nonlinearity
Modulational instability
Soliton behavior
Surface gravity waves
Discussion
Instability and transition to turbulence / 7:
Instability to small disturbances
Universality in transition to chaos
Shear flow turbulence structure / 8:
Boundary layer turbulence structure
Theoretical model for wall layer bursting
Structure of free-shear layers
Turbulence modeling and closure schemes / 9:
Some turbulence models
Closure schemes for spectral theories
Aerodynamic noise / 10:
A linear acoustic field excited by turbulent fluctuations
The far-field sound
Similarity analysis for the emitted sound
Effects of source motion and sound advection
Effects of a nonuniform flow
Instability of a supersonic jet, overreflection
Instability of an isolated shear layer
Convective transport / 11:
Nondimensional parameters characterizing convective transport
Thermal convection without mean shear
Numerical simulation of turbulence / 12:
Numerical techniques
Some results from numerical simulation
References
Index
Preface to the second edition
Preface to the first edition
Introduction with historical notes / 1:
9.

図書

図書
by S. Panchev
出版情報: Oxford ; New York : Pergamon Press, c1971  xiii, 444 p ; 26 cm
シリーズ名: International series of monographs in natural philosophy ; v.32
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10.

図書

図書
edited by P. Bradshaw ; with contributions by P. Bradshaw ... [et al.]
出版情報: Berlin ; New York : Springer-Verlag, 1976  x, 335 p. ; 24 cm
シリーズ名: Topics in applied physics ; 12
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