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| Preface | |
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| Acknowledgments | |
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| The Lagrangian Formulation | |
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| Lagrangian kinematics | |
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| Conservation of particle identity | |
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| Streaklines, streamlines and steady flow | |
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| Local kinematics | |
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| Lagrangian statistics | |
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| Single-particle, single-time statistics | |
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| Single-particle, two-time statistics | |
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| Two-particle, two-time statistics | |
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| The Eulerian-Lagrangian problem: path integrals | |
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| Lagrangian dynamics | |
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| Conservation of mass | |
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| Conservation of momentum | |
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| Conservation of energy | |
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| Variational principle | |
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| Bernoulli's theorem | |
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| Kelvin's theorem | |
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| Cauchy-Weber integrals | |
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| First integrals | |
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| Matrix formulation | |
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| Cauchy-Weber integrals and Clebsch potentials | |
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| Potential flow and a Riemannian metric | |
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| Boundary conditions | |
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| Rigid boundaries | |
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| Comoving boundaries | |
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| Comoving boundary conditions | |
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| Adjacent Lagrangian coordinates | |
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| Local dynamics | |
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| Relabeling symmetry | |
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| Historical note | |
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| Coordinates | |
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| Independent variables | |
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| Dependent space variables | |
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| Rotational symmetry | |
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| Globally uniform rotations | |
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| Time-varying rotations | |
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| Real fluids | |
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| Viscous stresses and heat conduction | |
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| Navier-Stokes equations for incompressible flow | |
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| Matrix formulation for viscous incompressible flow | |
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| Boundary conditions | |
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| Lagrangian Flows | |
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| Some analytical Lagrangian solutions | |
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| Flow around a cylinder | |
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| Gerstner's trochoidal wave | |
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| One-dimensional gas dynamics | |
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| One-dimensional traveling waves | |
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| Riemann invariants | |
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| Arbitrary one-dimensional flow | |
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| Plane Poiseuille flow | |
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| Sound waves, shear instabilities, Rossby waves and Ptolemaic vortices | |
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| Sound waves | |
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| Hydrodynamic stability | |
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| Rossby waves | |
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| Hamiltonian dynamics of Rossby waves | |
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| Plane Ptolemaic vortices | |
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| Sheared Ptolemaic vortices | |
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| Viscous incompressible flow | |
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| Simple shear flow | |
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| The suddenly accelerated plane wall: Stokes' first problem | |
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| Flow near an oscillating flat plate: Stokes' second problem | |
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| The boundary layer along a flat plate | |
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| General solvability | |
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| Kinematics | |
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| Incompressible dynamics (1) | |
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| Incompressible dynamics (2) | |
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| Incompressible dynamics (3) | |
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| Compressible dynamics | |
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| Labeling singularities | |
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| Phenomenology | |
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| Viscous incompressible flow | |
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| Equations of motion | |
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| Picard iteration | |
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| A priori bounds | |
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| The viscous operator | |
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| The elliptic operator | |
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| Diffusion | |
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| Absolute dispersion | |
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| Displacement: first and second moments | |
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| Displacement pdf | |
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| Forward closure, boundary conditions | |
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| Backward closure, scalar concentrations | |
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| Reversibility for incompressible flow; the Markov property, Corrsin's hypotheses | |
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| Scalar concentrations in compressible flow; floats, surface drifters and balloons | |
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| Corrections | |
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| Random flight models and plankton dynamics | |
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| Annual plankton patchiness | |
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| Relative dispersion | |
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| Joint displacement of a pair of particles | |
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| Separation of a pair of particles | |
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| Richardson's self-similar asymptotic solution | |
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| Lundgren's log normal solution | |
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| Observations of dispersion | |
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| Kinetic energy subranges | |
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| Kinetic energy spectra and structure functions | |
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| Kinetic energy spectra and longitudinal diffusivities | |
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| Convective subranges of the scalar variance spectrum | |
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| Scalar covariance | |
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| Reversibility | |
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| Power spectra | |
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| Enstrophy inertia convective subrange | |
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| Energy inertia convective subrange | |
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| Viscous convective subrange | |
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| Transition | |
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| Relative dispersion and plankton patchiness | |
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| Diffusion | |
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| Scalar diffusion: An approximate general solution | |
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| Variance spectrum | |
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| Enstrophy inertia diffusive subrange | |
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| Energy inertia diffusive subrange | |
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| Viscous diffusive subrange | |
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| Lagrangian Data | |
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| Observing systems | |
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| The laboratory | |
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| The atmosphere | |
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| The ocean surface | |
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| The deep ocean | |
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| Data analysis: the single particle | |
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| Time series analysis: the single particle | |
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| Polarization of Lagrangian velocities | |
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| Diffusivities from floats | |
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| Assimilation: the single particle | |
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| Lagrangian measurement functionals | |
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| Lagrangian assimilation: first steps | |
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| Data analysis: particle clusters | |
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| Time series analysis: the particle pair | |
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| Assimilation: particle clusters | |
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| Eulerian kinematical analysis | |
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| Lagrangian dynamical analysis: shallow-water theory | |
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| Lagrangian dynamical analysis: Boussinesq theory | |
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| Least-squares estimator | |
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| References | |
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| Subject Index | |
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| Author Index | |