Complex-space singularities of 2D Euler flow in Lagrangian coordinates

Abstract

We show that, for two-dimensional space-periodic incompressible flow, the solution can be evaluated numerically in Lagrangian coordinates with the same accuracy 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.

5 pages, 2 figures, submitted to Physica D

References in corpus (4)

• Burgers Turbulence
• Nature of complex singularities for the 2D Euler equation
• The analytic structure of 2D Euler flow at short times
• Lagrangian singularities of steady two-dimensional flow

Cited by in corpus (7)

• Singularity formation for Prandtl's equations
• On the analyticity and Gevrey class regularity up to the boundary for the Euler Equations
• Maximum Palinstrophy Growth in 2D Incompressible Flows
• Systematic Search For Extreme and Singular Behavior in Some Fundamental Models of Fluid Mechanics
• Searching for Singularities in Navier-Stokes Flows Based on the Ladyzhenskaya-Prodi-Serrin Conditions
• Systematic search for singularities in 3D Euler flows
• Alignments of Triad Phases in 1D Burgers and 3D Navier-Stokes Flows