Complex-space singularities of 2D Euler flow in Lagrangian coordinates
Matsumoto, T., Bec, J. and Frisch, U

Sunday 28 November 2010 by Ponty Yannick

 

We show that, for 2D space-periodic incompressible flow, the solution can be evaluated numerically in Lagrangian coordinates with the same accuracy that is achieved in standard Eulerian spectral methods. This allows the determination of complex-space Lagrangian singularities. Lagrangian singularities are found to be closer to the real domain than Eulerian singularities and seem to correspond to fluid particles which escape to (complex) infinity by the current time. Various mathematical conjectures regarding Eulerian/Lagrangian singularities are presented.

Keywords: Complex singularities; Euler equation; Lagrangian frame; Analyticity strip method

 

 Matsumoto, T., Bec, J. and Frisch, U., "Complex-space singularities of 2D Euler flow in Lagrangian coordinates", Physica D Nonlinear Phenomena, 237, pp. 1951-1955 (2008) (doi:10.1016/j.physd.2007.11.007)