| Abstract: | Cauchy's invariants for 3D incompressible Euler flow, recently rediscovered after 200 years, give us a powerful tool for investigating the Lagrangian structure of such flow. Among the topics we shall discuss: how the Cauchy invariants relate to the Lie-transport (pullback) invariance of the vorticity 2-form; how they can be generalized to higher-order forms and to Euler flow on Riemann manifolds; how they generate recursion relations - resembling those of the Lagrangian perturbation theory in cosmology - giving a constructive hold on time-analyticity of the Lagrangian map and thereby allowing the development of Cauchy-Lagrange numerical schemes that can be orders of magnitude faster than the usual Eulerian schemes. |
