LEADER 05461nam 22006735 450 001 9910299398503321 005 20200701020052.0 010 $a3-319-59695-0 024 7 $a10.1007/978-3-319-59695-2 035 $a(CKB)3710000001631226 035 $a(DE-He213)978-3-319-59695-2 035 $a(MiAaPQ)EBC4987589 035 $a(PPN)203851293 035 $a(EXLCZ)993710000001631226 100 $a20170829d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aVariational Formulation of Fluid and Geophysical Fluid Dynamics $eMechanics, Symmetries and Conservation Laws /$fby Gualtiero Badin, Fulvio Crisciani 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XVIII, 218 p.) 225 1 $aAdvances in Geophysical and Environmental Mechanics and Mathematics,$x1866-8348 311 $a3-319-59694-2 327 $aDedication -- 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. 330 $aThis book describes the derivation of the equations of motion of fluids as well as the dynamics of ocean and atmospheric currents on both large and small scales through the use of variational methods. In this way the equations of Fluid and Geophysical Fluid Dynamics are re-derived making use of a unifying principle, that is Hamilton?s Principle of Least Action. The equations are analyzed within the framework of Lagrangian and Hamiltonian mechanics for continuous systems. The analysis of the equations? symmetries and the resulting conservation laws, from Noether?s Theorem, represent the core of the description. Central to this work is the analysis of particle relabeling symmetry, which is unique for fluid dynamics and results in the conservation of potential vorticity. Different special approximations and relations, ranging from the semi-geostrophic approximation to the conservation of wave activity, are derived and analyzed. Thanks to a complete derivation of all relationships, this book is accessible for students at both undergraduate and graduate levels, as well for researchers. Students of theoretical physics and applied mathematics will recognize the existence of theoretical challenges behind the applied field of Geophysical Fluid Dynamics, while students of applied physics, meteorology and oceanography will be able to find and appreciate the fundamental relationships behind equations in this field. 410 0$aAdvances in Geophysical and Environmental Mechanics and Mathematics,$x1866-8348 606 $aFluids 606 $aAtmospheric sciences 606 $aGeophysics 606 $aMeteorology 606 $aEnvironmental sciences 606 $aFluid- and Aerodynamics$3https://scigraph.springernature.com/ontologies/product-market-codes/P21026 606 $aAtmospheric Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/G36000 606 $aGeophysics/Geodesy$3https://scigraph.springernature.com/ontologies/product-market-codes/G18009 606 $aMeteorology$3https://scigraph.springernature.com/ontologies/product-market-codes/312000 606 $aMath. Appl. in Environmental Science$3https://scigraph.springernature.com/ontologies/product-market-codes/U24005 606 $aGeophysics and Environmental Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P32000 615 0$aFluids. 615 0$aAtmospheric sciences. 615 0$aGeophysics. 615 0$aMeteorology. 615 0$aEnvironmental sciences. 615 14$aFluid- and Aerodynamics. 615 24$aAtmospheric Sciences. 615 24$aGeophysics/Geodesy. 615 24$aMeteorology. 615 24$aMath. Appl. in Environmental Science. 615 24$aGeophysics and Environmental Physics. 676 $a532 676 $a533.62 700 $aBadin$b Gualtiero$4aut$4http://id.loc.gov/vocabulary/relators/aut$01060347 702 $aCrisciani$b Fulvio$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910299398503321 996 $aVariational Formulation of Fluid and Geophysical Fluid Dynamics$92512572 997 $aUNINA