Frisch, Uriel (Author)
Villone, Barbara (Author)
Two prized papers, one by Augustin Cauchy in 1815, presented to the French Academy and the other by Hermann Hankel in 1861, presented to Göttingen University, contain major discoveries on vorticity dynamics whose impact is now quickly increasing. Cauchy found a Lagrangian formulation of 3D ideal incompressible flow in terms of three invariants that generalize to three dimensions the now well-known law of conservation of vorticity along fluid particle trajectories for two-dimensional flow. This has very recently been used to prove analyticity in time of fluid particle trajectories for 3D incompressible Euler flow and can be extended to compressible flow, in particular to cosmological dark matter. Hankel showed that Cauchy's formulation gives a very simple Lagrangian derivation of the Helmholtz vorticity-flux invariants and, in the middle of the proof, derived an intermediate result which is the conservation of the circulation of the velocity around a closed contour moving with the fluid. This circulation theorem was to be rediscovered independently by William Thomson (Kelvin) in 1869. Cauchy's invariants were only occasionally cited in the 19th century -- besides Hankel, foremost by George Stokes and Maurice Lévy -- and even less so in the 20th until they were rediscovered via Emmy Noether's theorem in the late 1960, but reattributed to Cauchy only at the end of the 20th century by Russian scientists.
...More
Article
Frisch, Uriel;
Villone, Barbara;
(2014)
Cauchy's Almost Forgotten Lagrangian Formulation of the Euler Equation for 3D Incompressible Flow
(/isis/citation/CBB001451853/)
Article
Eckert, Michael;
(2002)
Euler and the Fountains of Sanssouci
(/isis/citation/CBB000300069/)
Article
Delcourt, Jean;
(2011)
Analyse et géométrie, histoire des courbes gauches De Clairaut à Darboux
(/isis/citation/CBB001034291/)
Article
Lubet, Jean-Pierre;
(2010)
Calcul symbolique et calcul intégral de Lagrange à Cauchy
(/isis/citation/CBB001033635/)
Thesis
Walker, Helen E.;
(1983)
Taylor's theorem with remainder: The legacy of Lagrange, Ampère, and Cauchy
(/isis/citation/CBB001563379/)
Thesis
Hepburn, Brian S.;
(2007)
Equilibrium and Explanation in 18th-Century Mechanics
(/isis/citation/CBB001560501/)
Article
Elisa Patergnani;
Luigi Pepe;
(2021)
Les mathématiciens français et italiens du «siècle long»: 1700-1814
(/isis/citation/CBB124027972/)
Article
Craik, Alex D. D.;
(2013)
“Continuity and Change”: Representing Mass Conservation in Fluid Mechanics
(/isis/citation/CBB001211054/)
Article
Caroline Stalker;
Richard Morgan;
Roger I. Tanner;
(2016)
Raymond John Stalker 1930–2014
(/isis/citation/CBB086586319/)
Thesis
Daugherty, Debra;
(2007)
Elaborating the Crystal Concept: Scientific Modeling and Ordered States ofMatter
(/isis/citation/CBB001560882/)
Book
Taub, Liba Chaia;
Willmoth, Frances;
(2006)
The Whipple Museum of the History of Science: Instruments and Interpretations, to Celebrate the 60th Anniversary of R. S. Whipple's Gift to the University of Cambridge
(/isis/citation/CBB000773371/)
Article
Bloor, David;
(2008)
Sichtbarmachung, Common Sense and Construction in Fluid Mechanics: The Cases of Hele-Shaw and Ludwig Prandtl
(/isis/citation/CBB000931143/)
Article
Capecchi, Danilo;
Ruta, Giuseppe;
Trovalusci, Patrizia;
(2010)
From Classical to Voigt's Molecular Models in Elasticity
(/isis/citation/CBB001022006/)
Article
Rowlinson, J. S.;
(2003)
The Work of Thomas Andrews and James Thomson on the Liquefaction of Gases
(/isis/citation/CBB000470288/)
Article
Thomas William Barrett;
(2015)
On the Structure of Classical Mechanics
(/isis/citation/CBB188856810/)
Article
Gallavotti, Giovanni;
(2013)
Aspects of Lagrange's Mechanics and their Legacy
(/isis/citation/CBB001320790/)
Article
Martínez-Torregrosa, Joaquín;
López-Gay, Rafael;
Gras-Martí, Albert;
(2006)
Mathematics in Physics Education: Scanning Historical Evolution of the Differential to Find a More Appropriate Model for Teaching Differential Calculus in Physics
(/isis/citation/CBB000671077/)
Article
Capecchi, Danilo;
Ruta, Giuseppe C.;
(2007)
Piola's Contribution to Continuum Mechanics
(/isis/citation/CBB000772558/)
Article
Mukherji, Purabi;
Bhattacharjee, Mala;
(2014)
Bengal School of Fluid Mechanics: Nineteenth and Twentieth Century
(/isis/citation/CBB001451540/)
Article
Meo, M.;
(2004)
The Mathematical Life of Cauchy's Group Theorem
(/isis/citation/CBB000410846/)
Be the first to comment!