• Corpus ID: 119143040

Variational Lagrangian formulation of the Euler equations for incompressible flow: A simple derivation

  title={Variational Lagrangian formulation of the Euler equations for incompressible flow: A simple derivation},
  author={Mohammad Farazmand and Mattia Serra},
  journal={arXiv: Fluid Dynamics},
In 1966, Arnold [1] showed that the Lagrangian flow of ideal incompressible fluids (described by Euler equations) coincide with the geodesic flow on the manifold of volume preserving diffeomorphisms of the fluid domain. Arnold's proof and the subsequent work on this topic rely heavily on the properties of Lie groups and Lie algebras which remain unfamiliar to most fluid dynamicists. In this note, we provide a simple derivation of Arnold's result which only uses the classical methods of calculus… 
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