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.