Numerical study of the Eulerian-Lagrangian formulation of the Navier-Stokes equations

An Euler-Lagrangian analysis of the Navier-Stokes equations is performed with use of numerical simulations. On this basis we propose a new method for capturing vortex reconnection. It is found that the diffusive Lagrangian map becomes noninvertible under time evolution and requires resetting for its calculation. This sets a time scale and its frequent resetting corresponds to vortex reconnection. Another time scale defined by the connection coefficients, responsible for noncommutativity of Euler and Euler-Lagrange derivatives, is shown to be on the same order during reconnection. This introduces a novel singular perturbation problem of connection anomaly underlying reconnection. (C) 2003 American Institute of Physics.