Cauchy invariants for the 3D incompressible Euler equations and the time-analyticity of Lagrangian trajectories

2018/09/14 Fri 15:00 - 16:30
Uriel Frisch 氏
Laboratoire Lagrange, Observatoire and Universite Cote d'Azur, Nice, France

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 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.

場所:京大 理学研究科 物理学教室(理5号館) 401号室