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Lagrangian Fluid Dynamics

ISBN-10: 0521853109

ISBN-13: 9780521853101

Edition: 2005

Authors: Andrew Bennett, C. G. Batchelor (Deceased), M. J. Ablowitz, S. H. Davis, E. J. Hinch

List price: $150.00
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Description:

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 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.
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Book details

List price: $150.00
Copyright year: 2005
Publisher: Cambridge University Press
Publication date: 3/9/2006
Binding: Hardcover
Pages: 310
Size: 6.00" wide x 9.00" long x 1.00" tall
Weight: 1.342
Language: English

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