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000824122 1001_ $$aBadin, Gualtiero,$$eauthor.
000824122 24510 $$aVariational formulation of fluid and geophysical fluid dynamics :$$bmechanics, symmetries and conservation laws /$$cGualtiero Badin, Fulvio Crisciani.
000824122 264_1 $$aNew York, NY :$$bSpringer Berlin Heidelberg,$$c2017.
000824122 300__ $$a1 online resource.
000824122 336__ $$atext$$2rdacontent
000824122 337__ $$acomputer$$2rdamedia
000824122 338__ $$aonline resource$$2rdacarrier
000824122 4901_ $$aAdvances in Geophysical and Environmental Mechanics and Mathematics,$$x1866-8348
000824122 504__ $$aIncludes bibliographical references.
000824122 5050_ $$aForeword; Preface; Acknowledgements; Contents; 1 Fundamental Equations of Fluid and Geophysical Fluid Dynamics; 1.1 Introduction; 1.2 The Continuum Hypothesis; 1.3 Derivation of the Equations of Motion; 1.3.1 Conservation of Mass; 1.3.2 Incompressibility and Density Conservation; 1.3.3 Momentum Equation in an Inertial Frame of Reference; 1.4 Elementary Symmetries of the Euler's Equation; 1.4.1 Continuous Symmetries; 1.4.2 Discrete Symmetries; 1.4.3 Role of Gravity in Breaking the Symmetries of the Euler's Equation; 1.5 Momentum Equation in a Uniformly Rotating Frame of Reference
000824122 5058_ $$a1.9.3 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
000824122 5058_ $$a2.4 Covariance of the Lagrangian with Respect to Generalized Coordinates2.5 Role of Constraints; 2.6 Canonical Variables and Hamiltonian Function; 2.7 Hamilton's Equations; 2.8 Canonical Transformations and Generating Functions; 2.8.1 Phase Space Volume as Canonical Invariant: Liouville's Theorem and Poisson Brackets; 2.8.2 Casimir Invariants and Invertible Systems; 2.9 Noether's Theorem for Point Particles; 2.9.1 Mathematical Preliminary; 2.9.2 Symmetry Transformations and Proof of the Theorem; 2.9.3 Some Examples
000824122 5058_ $$a2.10 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
000824122 506__ $$aAccess limited to authorized users.
000824122 520__ $$aThis book describes the derivation of the equations of motion of fluids as well as the dynamics of ocean and atmospheric currents on both large and small scales through the use of variational methods. In this way the equations of Fluid and Geophysical Fluid Dynamics are re-derived making use of a unifying principle, that is Hamilton's Principle of Least Action. The equations are analyzed within the framework of Lagrangian and Hamiltonian mechanics for continuous systems. The analysis of the equations' symmetries and the resulting conservation laws, from Noether's Theorem, represent the core of the description. Central to this work is the analysis of particle relabeling symmetry, which is unique for fluid dynamics and results in the conservation of potential vorticity. Different special approximations and relations, ranging from the semi-geostrophic approximation to the conservation of wave activity, are derived and analyzed. Thanks to a complete derivation of all relationships, this book is accessible for students at both undergraduate and graduate levels, as well for researchers. Students of theoretical physics and applied mathematics will recognize the existence of theoretical challenges behind the applied field of Geophysical Fluid Dynamics, while students of applied physics, meteorology and oceanography will be able to find and appreciate the fundamental relationships behind equations in this field.
000824122 650_0 $$aGeophysics.
000824122 650_0 $$aFluid dynamics$$xMathematical models.
000824122 650_0 $$aOceanography$$xMathematical models.
000824122 650_0 $$aGeophysics$$xFluid models.
000824122 650_0 $$aVortex-motion.
000824122 650_0 $$aFluid mechanics.
000824122 7001_ $$aCrisciani, Fulvio,$$eauthor.
000824122 77608 $$iPrint version: $$z9783319596945$$z3319596942$$w(OCoLC)985082219
000824122 830_0 $$aAdvances in geophysical and environmental mechanics and mathematics.
000824122 852__ $$bebk
000824122 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-59695-2$$zOnline Access$$91397441.1
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