05461nam 22006735 450 991029939850332120200701020052.03-319-59695-010.1007/978-3-319-59695-2(CKB)3710000001631226(DE-He213)978-3-319-59695-2(MiAaPQ)EBC4987589(PPN)203851293(EXLCZ)99371000000163122620170829d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierVariational Formulation of Fluid and Geophysical Fluid Dynamics Mechanics, Symmetries and Conservation Laws /by Gualtiero Badin, Fulvio Crisciani1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XVIII, 218 p.) Advances in Geophysical and Environmental Mechanics and Mathematics,1866-83483-319-59694-2 Dedication -- Foreword by Geoffrey K. Vallis -- Preface -- Acknowledgements -- Fundamental Equations of Fluid and Geophysical Fluid Dynamics -- Mechanics, Symmetries and Noether’s Theorem -- Variational Principles in Fluid Dynamics, Symmetries and Conservation Laws -- Variational Principles in Geophysical Fluid Dynamics and Approximated Equations -- Appendix A - Derivation of Equation (1.2) -- Appendix B - Derivation of the Conservation of Potential Vorticity from Kelvin’s Circulation Theorem -- Appendix C - Some Simple Mathematical Properties of the Legendre Transformation -- Appendix D - Derivation of Equation (2.114) -- Appendix E - Invariance of the Equations of Motion (2.116) under a Divergence Transformation -- Appendix E - Invariance of the Equations of Motion (2.190) under a Divergence Transformation -- Appendix F - Functional Derivatives -- Appendix G - Derivation of Equation (2.229) -- Appendix H - Invariance of the Equations of Motion (2.217) under a Divergence Transformation -- Appendix I - Proofs of the Algebraic Properties of the Poisson Bracket -- Appendix J - Some Identities concerning the Jacobi Determinant -- Appendix K - Derivation of (3.131) -- Appendix L - Scaling the Rotating Shallow Water Lagrangian Density.This 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.Advances in Geophysical and Environmental Mechanics and Mathematics,1866-8348FluidsAtmospheric sciencesGeophysicsMeteorologyEnvironmental sciencesFluid- and Aerodynamicshttps://scigraph.springernature.com/ontologies/product-market-codes/P21026Atmospheric Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/G36000Geophysics/Geodesyhttps://scigraph.springernature.com/ontologies/product-market-codes/G18009Meteorologyhttps://scigraph.springernature.com/ontologies/product-market-codes/312000Math. Appl. in Environmental Sciencehttps://scigraph.springernature.com/ontologies/product-market-codes/U24005Geophysics and Environmental Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P32000Fluids.Atmospheric sciences.Geophysics.Meteorology.Environmental sciences.Fluid- and Aerodynamics.Atmospheric Sciences.Geophysics/Geodesy.Meteorology.Math. Appl. in Environmental Science.Geophysics and Environmental Physics.532533.62Badin Gualtieroauthttp://id.loc.gov/vocabulary/relators/aut1060347Crisciani Fulvioauthttp://id.loc.gov/vocabulary/relators/autBOOK9910299398503321Variational Formulation of Fluid and Geophysical Fluid Dynamics2512572UNINA