Mathematics of Climate Modeling - Rilegato

Dymnikov, Valentin P.; Filatov, Aleksander N.

Rilegato

ISBN 10: 0817639152 ISBN 13: 9780817639150

Casa editrice: Springer Basel AG, 1997

Riassunto

Providing an introduction to a branch of climate theory - the study of climate by means of the quality theory of partial differential equations, this text is oriented towards specialists and graduates in geophysical hydrodynamics and climate modelling. The first part of the book concentrates on current theory of infinite-dimensional and finite-dimensional nonlinear dissipative systems. Section two of the text contains the results of analysis of climate models of different complexity from barotropic models to models based on the full system of hydrothermodynamics equations.

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Contenuti

1. Dynamical Systems. Attractors, Invariant Measures.- 1.1 Metric Spaces. Compactness.- 1.2 Dynamical Systems. Main Properties.- 1.3 Invariant Sets.- 1.4 Classification of Motions.- 1.5 Recurrence of Domains.- 1.6 Measure. Krylov-Bogolyubov Theorem.- 1.7 Dynamical Systems with Invariant Measure.- 1.8 Nonlinear Dissipative Systems.- 1.9 Inertial Manifolds of Dissipative Systems.- 2. Non-Autonomous Dissipative Systems, their Attractor and Averaging.- 2.1 Introduction.- 2.2 Processes and their Attractors. Kernel of Processes, Section of Kernel.- 2.3 Families of Processes and their Attractors.- 2.4 Family of Processes and Semigroups.- 2.5 Averaging of Nonlinear Dissipative Systems. Closeness between Attractors of Original and Averaged Systems.- 2.6 On Closeness of Solutions of Original and Averaged Nonlinear Dissipative Systems on Infinite Time Interval.- 3. Analysis of Barotropic Model.- 3.1. Existence of Global Attractor.- 3.2 Estimate of Dimension of Attractor.- 3.3 Statistical Solutions and Invariant Measures on Attractor.- 3.4 Estimate of Attractor Dimension with Respect to Orography.- 3.5 Galerkin Approximations.- 3.6 Existence of Inertial Manifold.- 4. Discretization of Systems Possessing Attractor.- 4.1 Discretization of Systems Possessing Inertial Manifolds.- 4.2 Time-Space Discretization of Systems Possessing Attractor.- 4.3 Globally Stable Difference Schemes for Barotropic Vorticity Equation.- 5. Numerical Study of Structure of Attractor Generated by Barotropic Equations on Sphere.- 5.1 Equations and Parameters of Model. Methods of Solving of Stationary and Nonstationary Problems.- 5.2 Statistical Stationary Solution and Stationary Points.- 5.3 Lyapunov Exponents and Attractor Dimension.- 5.4 Analysis of Analytical Estimates of Attractor Dimension of Barotropic Atmospheric Equations.- 6. Two-Layer Baroclinic Model.- 6.1 Two-Layer Baroclinic Model.- 6.2 Estimate of Attractor Dimension.- 6.3 Numerical Investigation of Attractor. Characteristics of Two-Layer Baroclinic Model.- 7. Investigation of Structure of Climate Attractors by Observed Data Series.- 7.1. Correlation Dimension of Attractor.- 7.2. Calculation of Lyapunov Exponents.- 7.3 Statistically Independent Degrees of Freedom and Attractor Dimension.- 8. Regimes of Atmosphere Circulation.- 8.1 Definition of Atmosphere Circulation Regimes.- 8.2 Dynamical Theory of Two-Regime Barotropic Circulation.- 8.3. Statistical Theory of Two-Regime Barotropic Circulation.- 8.4 S-Regimes of Atmosphere Circulation.- 9. Solvability of Ocean and Atmosphere Models.- 9.1 Introduction.- 9.2 Solvability of Ocean and Atmosphere Models in Bounded Domains.- 9.3 Solvability of Ocean and Atmosphere Models on Sphere in p-System of Coordinates.

Product Description

Book by Dymnikov Valentin P Filatov Aleksander N

Dettagli dell'edizione

• Editore: Springer Basel AG
• Data di pubblicazione: 1997
• Lingua: Inglese
• ISBN 10: 0817639152
• ISBN 13: 9780817639150
• Rilegatura: Copertina rigida
• Numero di pagine: 284
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania