Variational formulation of fluid and geophysical fluid dynamics : mechanics, symmetries and conservation laws /: mechanics, symmetries and conservation laws. (2017)

• Record Type: Book
• Further Information: Note: Gualtiero Badin, Fulvio Crisciani.
• Authors: Badin, Gualtiero; Crisciani, Fulvio
• Contents: Foreword; Preface; Acknowledgements; Contents; 1 Fundamental Equations of Fluid and Geophysical Fluid Dynamics; 1.1 Introduction; 1.2 The Continuum Hypothesis; 1.3 Derivation of the Equations of Motion; 1.3.1 Conservation of Mass; 1.3.2 Incompressibility and Density Conservation; 1.3.3 Momentum Equation in an Inertial Frame of Reference; 1.4 Elementary Symmetries of the Euler's Equation; 1.4.1 Continuous Symmetries; 1.4.2 Discrete Symmetries; 1.4.3 Role of Gravity in Breaking the Symmetries of the Euler's Equation; 1.5 Momentum Equation in a Uniformly Rotating Frame of Reference 1.9.3 Energy and Enstrophy Conservation for the Quasi-geostrophic Shallow Water Model1.9.4 Quasi-geostrophic Model of a Density Conserving Ocean; 1.9.5 Quasi-geostrophic Model of a Potential Temperature-Conserving Atmosphere; 1.9.6 Conservation of Pseudo-Enstrophy in a Baroclinic Quasi-geostrophic Model; 1.9.7 Surface Quasi-geostrophic Dynamics; 1.10 Bibliographical Note; References; 2 Mechanics, Symmetries and Noether's Theorem; 2.1 Introduction; 2.2 Hamilton's Principle of Least Action; 2.3 Lagrangian Function, Euler -- Lagrange Equations and D'Alembert's Principle 2.4 Covariance of the Lagrangian with Respect to Generalized Coordinates2.5 Role of Constraints; 2.6 Canonical Variables and Hamiltonian Function; 2.7 Hamilton's Equations; 2.8 Canonical Transformations and Generating Functions; 2.8.1 Phase Space Volume as Canonical Invariant: Liouville's Theorem and Poisson Brackets; 2.8.2 Casimir Invariants and Invertible Systems; 2.9 Noether's Theorem for Point Particles; 2.9.1 Mathematical Preliminary; 2.9.2 Symmetry Transformations and Proof of the Theorem; 2.9.3 Some Examples 2.10 Lagrangian Formulation for Fields: Lagrangian Depending on a Scalar Function2.10.1 Hamiltonian for Scalar Fields; 2.11 Noether's Theorem for Fields with the Lagrangian Depending on a Scalar Function; 2.11.1 Mathematical Preliminary; 2.11.2 Linking Back to the Physics; 2.12 Lagrangian Formulation for Fields: Lagrangian Density #x83;; 2.12.1 Hamilton's Equations for Vector Fields; 2.12.2 Canonical Transformations and Generating Functionals for Vector Fields; 2.13 Noether's Theorem for Fields: Lagrangian Density Dependent on Vector Functions; 2.14 Bibliographical Note; References
• Publisher Details: New York, NY : Springer Berlin Heidelberg
• Publication Date: 2017
• Extent: 1 online resource
• Subjects: 550; Physics; Geophysics; Fluid dynamics -- Mathematical models; Oceanography -- Mathematical models; Geophysics -- Fluid models; Vortex-motion; Fluid mechanics; Physical geography; Environmental sciences; SCIENCE / Earth Sciences / General; SCIENCE / Physics / Geophysics; Fluid dynamics -- Mathematical models; Fluid mechanics; Geophysics; Geophysics -- Fluid models; Oceanography -- Mathematical models; Vortex-motion; Science -- Earth Sciences -- Meteorology & Climatology; Science -- Geophysics; Science -- Environmental Science; Earth sciences; Geophysics; The environment; Science -- Mechanics -- Dynamics -- Fluid Dynamics; Fluid mechanics; Electronic books
• Languages: English
• ISBNs: 9783319596952; 3319596950; 9783319596945; 3319596942
• Notes: Note: Includes bibliographical references.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.