Format:
xviii, 719 Seiten
,
Illustrationen
Edition:
First published
ISBN:
052100666X
,
0-521-00666-X
Note:
MAB0014.001: AWI A6-04-0010
,
Contents
Preface
Part 1 Mathematical tools
M 1 Algebra of vectors
M 1.1 Basic concepts and definitions
M 1.2 Reference frames
M 1.3 Vector multiplication
M 1.4 Reciprocal coordinate systems
M 1.5 Vector representations
M 1.6 Products of vectors in general coordinate systems
M 1.7 Problems
M 2 Vector functions
M 2.1 Basic definitions and operations
M 2.2 Special dyadics
M 2.3 Principal-axis transformation of symmetric tensors
M 2.4 Invariants of a dyadic
M 2.5 Tensor algebra
M 2.6 Problems
M 3 Differential relations
M 3.1 Differentiation of extensive functions
M 3.2 The Hamilton operator in generalized coordinate systems
M 3.3 The spatial derivative of the basis vectors
M 3.4 Differential invariants in generalized coordinate systems
M 3.5 Additional applications
M 3.6 Problems
M 4 Coordinate transformations
M 4.1 Transformation relations of time-independent coordinate systems
M 4.2 Transformation relations of time-dependent coordinate systems
M 4.3 Problems
M 5 The method of covariant differentiation
M 5.1 Spatial differentiation of vectors and dyadics
M 5.2 Time differentiation of vectors and dyadics
M 5.3 The local dyadic of vP
M 5.4 Problems
M 6 Integral operations
M 6.1 Curves, surfaces, and volumes in the general qi system
M 6.2 Line integrals, surface integrals, and volume integrals
M 6.3 Integral theorems
M 6.4 Fluid lines, surfaces, and volumes
M 6.5 Time differentiation of fluid integrals
M 6.6 The general form of the budget equation
M 6.7 Gauss' theorem and the Dirac delta function
M 6.8 Solution of Poisson's differential equation
M 6.9 Appendix: Remarks on Euclidian and Riemannian spaces
M 6.10 Problems
M 7 Introduction to the concepts of nonlinear dynamics
M 7.1 One-dimensional flow
M 7.2 Two-dimensional flow
Part 2 Dynamics of the atmosphere
1 The laws of atmospheric motion
1.1 The equation of absolute motion
1.2 The energy budget in the absolute reference system
1.3 The geographical coordinate system
1.4 The equation of relative motion
1.5 The energy budget of the general relative system
1.6 The decomposition of the equation of motion
1.7 Problems
2 Scale analysis
2.1 An outline of the method
2.2 Practical formulation of the dimensionless flow numbers
2.3 Scale analysis of large-scale frictionless motion
2.4 The geostrophic wind and the Euier wind
2.5 The equation of motion on a tangential plane
2.6 Problems
3 The material and the local description of flow
3.1 The description of Lagrange
3.2 Lagrange's version of the continuity equation
3.3 An example of the use of Lagrangian coordinates
3.4 The local description of Euler
3.5 Transformation from the Eulerian to the Lagrangian system
3.6 Problems
4 Atmospheric flow fields
4.1 The velocity dyadic
4.2 The deformation of the continuum
4.3 Individual changes with time of geometric fluid configurations
4.4 Problems
5 The Navier-Stokes stress tensor
5.1 The general stress tensor
5.2 Equilibrium conditions in the stress field
5.3 Symmetry of the stress tensor
5.4 The frictional stress tensor and the deformation dyadic
5.5 Problems
6 The Helmholtz theorem
6.1 The three-dimensional Helmholtz theorem
6.2 The two-dimensional Helmholtz theorem
6.3 Problems
7 Kinematics of two-dimensional flow
7.1 Atmospheric flow fields
7.2 Two-dimensional streamlines and normals
7.3 Streamlines in a drifting coordinate system
7.4 Problems
8 Natural coordinates
8.1 Introduction
8.2 Differential definitions of the coordinate lines
8.3 Metric relationships
8.4 Blaton's equation
8.5 Individual and local time derivatives of the velocity
8.6 Differential invariants
8.7 The equation of motion for frictionless horizontal flow
8.8 The gradient wind relation
8.9 Problems
9 Boundary surfaces and boundary conditions
9.1 Introduction
9.2 Differential operations at discontinuity surfaces
9.3 Particle invariance at boundary surfaces, displacement velocities
9.4 The kinematic boundary-surface condition
9.5 The dynamic boundary-surface condition
9.6 The zeroth-order discontinuity surface
9.7 An example of a first-order discontinuity surface
9.8 Problems
10 Circulation and vorticity theorems
10.1 ErteFs form of the continuity equation
10.2 The baroclinic Weber transformation
10.3 The baroclinic Ertel-Rossby invariant
10.4 Circulation and vorticity theorems for frictionless baroclinic flow
10.5 Circulation and vorticity theorems for frictionless barotropic flow
10.6 Problems
11 Turbulent systems
11.1 Simple averages and fluctuations
11.2 Weighted averages and fluctuations
11.3 Averaging the individual time derivative and the budget operator
11.4 Integral means
11.5 Budget equations of the turbulent system
11.6 The energy budget of the turbulent system
11.7 Diagnostic and prognostic equations of turbulent systems
11.8 Production of entropy in the microturbulent system
11.9 Problems
12 An excursion into spectral turbulence theory
12.1 Fourier Representation of the continuity equation and the equation of motion
12.2 The budget equation for the amplitude of the kinetic energy
12.3 Isotropie conditions, the transition to the continuous wavenumber space
12.4 The Heisenberg spectrum
12.5 Relations for the Heisenberg exchange coefficient
12.6 A prognostic equation for the exchange coefficient
12.7 Concluding remarks on closure procedures
12.8 Problems
13 The atmospheric boundary layer
13.1 Introduction
13.2 Prandtl-layer theory
13.3 The Monin-Obukhov similarity theory of the neutral Prandtl layer
13.4 The Monin-Obukhov similarity theory of the diabatic Prandtl layer
13.5 Application of the Prandtl-layer theory in numerical prognostic models
13.6 The fluxes, the dissipation of energy, and the exchange coefficients
13.7 The interface condition at the earth's surface
13.8 The Ekman layer - the classical approach
13.9 The composite Ekman layer
13.10 Ekman pumping
13.11 Appendix A: Dimensional analysis
13.12 Appendix B: The mixing length
13.13 Problems
14 Wave motion in the atmosphere
14.1 The representation of waves
14.2 The group velocity
14.3 Perturbation theory
14.4 Pure sound waves
14.5 Sound waves and gravity waves
14.6 Lamb waves
14.7 Lee waves
14.8 Propagation of energy
14.9 External gravity waves
14.10 Internal gravity waves
14.11 Nonlinear waves in the atmosphere
14.12 Problems
15 The barotropic model
15.1 The basic assumptions of the barotropic model
15.2 The tinfiltered barotropic prediction model
15.3 The filtered barotropic model
15.4 Barotropic instability
15.5 The mechanism of barotropic development
15.6 Appendix
15.7 Problems
16 Rossby waves
16.1 One-and two-dimensional Rossby waves
16.2 Three-dimensional Rossby waves
16.3 Normal-mode considerations
16.4 Energy transport by Rossby waves
16.5 The influence of friction on the stationary Rossby wave
16.6 Barotropic equatorial waves
16.7 The principle of geostrophic adjustment
16.8 Appendix
16.9 Problems
17 Inertial and dynamic stability
17.1 Inertial motion in a horizontally homogeneous pressure field
17.2 Inertial motion in a homogeneous geostrophic wind field
17.3 Inertial motion in a geostrophic shear wind field
17.4 Derivation of the stability criteria in the geostrophic wind field
17.5 Sectorial stability and instability
17.6 Sectorial stability for normal atmospheric conditions
17.7 Sectorial stability and instability with permanent adaptation
17.8 Problems
18 The equation of motion in general coordinate systems
18.1 Introduction
18.2 The covariant equation of motion in general coordinate systems
18.3 The contravariant equation of motion in general
18.4 The equation of motion in orthogonal coordinate systems
18.5 Lagrange's equation of motion
18.6 Hamilton's equation of motion
18.7 Appendix
18.8 Problems
19 The geographical coordinate systems
19.1 The equation of motion
19.2 Application of Lagrange's equation of motion
19.3 The first metric simplification
19.4 The coordinate simplification
19.5 The continuity equation
19.6 Problems
20 The stereographic coordinate system
20.1 The stereographic projection
20.2 Metric forms in stereographic coordinates
20.
Language:
English
Keywords:
Lehrbuch
URL:
http://bvbr.bib-bvb.de:8991/exlibris/aleph/a23_1/apache_media/263NGTIMJICTAR59ADPLN2Q2T3F4JL.pdf