Lagrangian Fluid Dynamics

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Hardcover | 9 March 2006

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310 Pages

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22.86 x 15.24 x 1.91

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The emergence of observing systems such as acoustically-tracked floats in the deep ocean, and surface drifters navigating by satellite has seen renewed interest in Lagrangian fluid dynamics. Starting from the foundations of elementary kinematics and assuming some familiarity of Eulerian fluid dynamics, this 2006 book reviews the classical and new exact solutions of the Lagrangian framework, and then addresses the general solvability of the resulting general equations of motion. A unified account of turbulent diffusion and dispersion is offered, with applications among others to plankton patchiness in the ocean. Written at graduate level, the book provides the first detailed and comprehensive analytical development of the Lagrangian formulation of fluid dynamics, of interest not only to applied mathematicians but also oceanographers, meteorologists, mechanical engineers, astrophysicists and indeed all investigators of the dynamics of fluids.

Industry Reviews

"...the first book devoted to providing a unified exposition of dynamics in the Lagrangian frame. The treatment is comprehensive, making the book valuable to all fluid dynamicists seeking to expand their backgrounds in the Lagrangian perspective..." --Russ Davis, Research Oceanographer; Scripps Institution of Oceanography, University of California, San Diego, CA, USA.
...A superb collection of well-written survey materials, covering the state-of-the-art in the theoretical aspects of problems arising in Lagrangian hydrodynamics...On the whole, this is an indispensable and obligatory book for anyone seriously interested in Lagrangian Fluid Dynamics...Also, this book will be of interest to applied mathematicians, particularly those interested in mathematical aspects of environmental fluid dynamics." -Andrzej Icha, Institute of Mathematics, Pomeranian Academy in Slupsk, Poland.

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Non-Fiction Science Physics Classical Mathematics Fluid Mechanics Mathematics Calculus & Mathematical Analysis Science in General Maths for Scientists Applied Mathematics

Preface	p. xiii
Acknowledgments	p. xxi
The Lagrangian Formulation	p. 1
Lagrangian kinematics	p. 5
Conservation of particle identity	p. 5
Streaklines, streamlines and steady flow	p. 11
Local kinematics	p. 13
Lagrangian statistics	p. 16
Single-particle, single-time statistics	p. 16
Single-particle, two-time statistics	p. 20
Two-particle, two-time statistics	p. 21
The Eulerian-Lagrangian problem: path integrals	p. 21
Lagrangian dynamics	p. 25
Conservation of mass	p. 25
Conservation of momentum	p. 26
Conservation of energy	p. 30
Variational principle	p. 32
Bernoulli's theorem	p. 33
Kelvin's theorem	p. 34
Cauchy-Weber integrals	p. 36
First integrals	p. 36
Matrix formulation	p. 39
Cauchy-Weber integrals and Clebsch potentials	p. 40
Potential flow and a Riemannian metric	p. 41
Boundary conditions	p. 43
Rigid boundaries	p. 43
Comoving boundaries	p. 43
Comoving boundary conditions	p. 44
Adjacent Lagrangian coordinates	p. 48
Local dynamics	p. 48
Relabeling symmetry	p. 50
Historical note	p. 55
Coordinates	p. 56
Independent variables	p. 56
Dependent space variables	p. 57
Rotational symmetry	p. 59
Globally uniform rotations	p. 59
Time-varying rotations	p. 59
Real fluids	p. 62
Viscous stresses and heat conduction	p. 62
Navier-Stokes equations for incompressible flow	p. 62
Matrix formulation for viscous incompressible flow	p. 64
Boundary conditions	p. 65
Lagrangian Flows	p. 67
Some analytical Lagrangian solutions	p. 71
Flow around a cylinder	p. 71
Gerstner's trochoidal wave	p. 72
One-dimensional gas dynamics	p. 76
One-dimensional traveling waves	p. 76
Riemann invariants	p. 77
Arbitrary one-dimensional flow	p. 77
Plane Poiseuille flow	p. 78
Sound waves, shear instabilities, Rossby waves and Ptolemaic vortices	p. 79
Sound waves	p. 79
Hydrodynamic stability	p. 80
Rossby waves	p. 82
Hamiltonian dynamics of Rossby waves	p. 87
Plane Ptolemaic vortices	p. 88
Sheared Ptolemaic vortices	p. 91
Viscous incompressible flow	p. 94
Simple shear flow	p. 94
The suddenly accelerated plane wall: Stokes' first problem	p. 95
Flow near an oscillating flat plate: Stokes' second problem	p. 96
The boundary layer along a flat plate	p. 97
General solvability	p. 99
Kinematics	p. 99
Incompressible dynamics (1)	p. 99
Incompressible dynamics (2)	p. 102
Incompressible dynamics (3)	p. 103
Compressible dynamics	p. 105
Labeling singularities	p. 107
Phenomenology	p. 108
Viscous incompressible flow	p. 110
Equations of motion	p. 111
Picard iteration	p. 112
A priori bounds	p. 113
The viscous operator	p. 113
The elliptic operator	p. 115
Diffusion	p. 117
Absolute dispersion	p. 123
Displacement: first and second moments	p. 123
Displacement pdf	p. 125
Forward closure, boundary conditions	p. 127
Backward closure, scalar concentrations	p. 131
Reversibility for incompressible flow; the Markov property, Corrsin's hypotheses	p. 133
Scalar concentrations in compressible flow; floats, surface drifters and balloons	p. 137
Corrections	p. 138
Random flight models and plankton dynamics	p. 141
Annual plankton patchiness	p. 143
Relative dispersion	p. 146
Joint displacement of a pair of particles	p. 146
Separation of a pair of particles	p. 150
Richardson's self-similar asymptotic solution	p. 153
Lundgren's log normal solution	p. 155
Observations of dispersion	p. 158
Kinetic energy subranges	p. 162
Kinetic energy spectra and structure functions	p. 167
Kinetic energy spectra and longitudinal diffusivities	p. 170
Convective subranges of the scalar variance spectrum	p. 177
Scalar covariance	p. 177
Reversibility	p. 179
Power spectra	p. 179
Enstrophy inertia convective subrange	p. 181
Energy inertia convective subrange	p. 182
Viscous convective subrange	p. 185
Transition	p. 186
Relative dispersion and plankton patchiness	p. 188
Diffusion	p. 191
Scalar diffusion: An approximate general solution	p. 191
Variance spectrum	p. 194
Enstrophy inertia diffusive subrange	p. 196
Energy inertia diffusive subrange	p. 198
Viscous diffusive subrange	p. 200
Lagrangian Data	p. 207
Observing systems	p. 211
The laboratory	p. 211
The atmosphere	p. 212
The ocean surface	p. 212
The deep ocean	p. 214
Data analysis: the single particle	p. 216
Time series analysis: the single particle	p. 216
Polarization of Lagrangian velocities	p. 216
Diffusivities from floats	p. 221
Assimilation: the single particle	p. 228
Lagrangian measurement functionals	p. 229
Lagrangian assimilation: first steps	p. 232
Data analysis: particle clusters	p. 238
Time series analysis: the particle pair	p. 238
Assimilation: particle clusters	p. 241
Eulerian kinematical analysis	p. 241
Lagrangian dynamical analysis: shallow-water theory	p. 246
Lagrangian dynamical analysis: Boussinesq theory	p. 253
Least-squares estimator	p. 257
References	p. 259
Subject Index	p. 271
Author Index	p. 283
Table of Contents provided by Ingram. All Rights Reserved.

Lagrangian Fluid Dynamics

At a Glance

Hardcover

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