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Samelson R.M., Wiggins S. — Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach
Samelson R.M., Wiggins S. — Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach

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Название: Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach

Авторы: Samelson R.M., Wiggins S.

Аннотация:

This book provides an accessible introduction to a new set of methods for the analysis of Lagrangian motion in geophysical flows. These methods were originally developed in the abstract mathematical setting of dynamical systems theory, through a geometric approach to differential equations. Despite the recent developments in this field and the existence of a substantial body of work on geophysical fluid problems in the dynamical systems and geophysical literature, this is the first introductory text that presents these methods in the context of geophysical fluid flow. The book is organized into seven chapters; the first introduces the geophysical context and the mathematical models of geophysical fluid flow that are explored in subsequent chapters. The second and third cover the simplest case of steady flow, develop basic mathematical concepts and definitions, and touch on some important topics from the classical theory of Hamiltonian systems. The fundamental elements and methods of Lagrangian transport analysis in time-dependent flows that are the main subject of the book are described in the fourth, fifth, and sixth chapters. The seventh chapter gives a brief survey of some of the rapidly evolving research in geophysical fluid dynamics that makes use of this new approach. Related supplementary material, including a glossary and an introduction to numerical methods, is given in the appendices.

This book will prove useful to graduate students, research scientists, and educators in any branch of geophysical fluid science in which the motion and transport of fluid, and of materials carried by the fluid, is of interest. It will also prove interesting and useful to the appliedmathematicians who seek an introduction to an intriguing and rapidly developing area of geophysical fluid dynamics. The book was jointly authored by a geophysical fluid dynamicist, Roger M. Samelson of the College of Oceanic and Atmospheric Sciences at Oregon State University, USA and an applied mathematician, Stephen Wiggins of the School of Mathematics, University of Bristol, UK.


Язык: en

Рубрика: Науки о земле/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 150

Добавлена в каталог: 13.05.2008

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Предметный указатель
Action-angle variable      35
Advection      1 86
Advective transport      1
Amplitude      11
Asymptotic      26
Autonomous      6
Baroclinic      85
Baroclinic instability      92
Barotropic      85
Cellular flow      27
Centers      21
Chaos      39
Chaotic dynamical system      39
Chaotic invariant set      39
Chaotic motion      40
Closed material curve      32 34 37
Coherent structures      3
Comoving frame      11 17 89
Conservation properties      86
Convection      15
Convective transport      29
Coordinate transformation      34 106
Crests      8
Critical layer      12 87 90
Critical lines      12 89
Cross-jet exchange      92
Deep western boundary current      96
Diffusion      1
Diffusive transport      1
Diophantine condition      37
Divergence      5
Drifters      2
Dynamical balances      86
Dynamical models      85
Dynamical systems theory      2
Ekman transport      94
Ellipses      21
Elliptic point      21 31 32 34
Eulerian      1 3
Eulerian coordinates      4
Exponential dichotomy      49 50
floats      2
Flow regimes      25
Fluid density      5 126
Fundamental solution matrix      46
Geometric theory      28
Geophysical fluid dynamics      1 15
Geostrophic      6 85
Gulf Stream      3 8 89 91
Hamiltonian      1 86
Hamiltonian mechanics      36 38
Hessian matrix      128
Heteroclinic trajectory      26
Homoclinic trajectory      26
Hyperbola      21
Hyperbolic      21
Hyperbolic stagnation point      21
Hyperbolic trajectory      52
Incompressible      5
Incompressible flows      20
Instabilities      87
Integrability      86 Integrable
Invariant curve      25
Invariant manifold      25
Invariant tori      37
Jacobian matrix      5
jet      4 8 17
Kam theorem      35 36 38 41
KAM tori      37
Kinematic      8
Lagrangian      1
Lagrangian coordinates      4
Lagrangian fluid dynamics      15
Lagrangian label      6 29
Lagrangian transport      3
Level sets      8
Linear approximation      19
Linear velocity field      20
Linearization      19 86
Lobe dynamics      63
Lobe transport      88 90
Lobes      64 73
Lyapunov exponent      47
Mass conservation      5 126
Material conservation      30
Material curve      23 32
Material derivative      5 29
Material line      23
Material manifold      25
Material manifolds of hyperbolic trajectories      61
Matrix associated with the linearization      19 46
Method of characteristics      30
Morse lemma      25 128
Near-integrable      35
Nonautonomous      43
Nonlinear wave      12
Ordinary differential equations      5 105
Orientation-preserving      76
Oscillatory motion      23
Periodic trajectories      32 35
Persistence theorem for hyperbolic trajectories and stable and unstable manifolds      56
Phase speed      11 17 89
Poisson bracket      39
Polar vortex      3
Potential vorticity      85 86 90 94
Potential vorticity gradient      92
Primary intersection point      76
Projection      50
Quadratures      40
Quasigeostrophic      85
Quasiperiodic      36 37
Rate of change      29
Real Jordan canonical forms      20
Recirculation      96
Recirculation cells      13
Reconnection      13
Reduction to quadratures      33
Regime boundaries      10
Resonant      37
Rossby wave      87 90
Rotation      20
Saddle point      21 31
scalar      29
Scalar advection      29
Sea-surface temperature      8
Separatrix reconnection      92
Shear      20
Shear dispersion      31
Stable and unstable manifold theorem for hyperbolic stagnation points      28
Stable and unstable manifold theorem for hyperbolic trajectories      55
Stable and unstable manifolds      26 89 131
Stable material manifold      55
Stable subspace      24
Stagnation point      18 23
Steady      6
Stokes’s theorem      7
strain      20 32
Streamfunction      7 32
streamline      25
Thermocline      1
Trajectories      1 4 5
Translating frame      17
Transport      1
traveling wave      10
Troughs      8
Turbulent mixing      90
Turnstile lobe      79 81
Two-dimensional turbulence      40 86
Uniqueness      25
Unstable material manifold      55
Unstable subspace      24
Vector space      23
Velocity field      5
Velocity gradient tensor      19
Volume preservation      106
Vorticity      2 85
Wave      4 17
Wavenumber      11
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