Generalized equations of motion for the Weber-Clebsch potentials that
reproduce Navier-Stokes dynamics are derived. These depend on a new
parameter, with the dimension of time, and reduce to the Ohkitani and
Constantin equations in the singular special case where the new
parameter vanishes.
Let us recall that Ohkitani and Constantin found that the diffusive
Lagrangian map became noninvertible under time evolution and required
resetting for its calculation. They proposed that high frequency of
resetting was a diagnostic for vortex reconnection.
Direct numerical simulations of the generalized equations of motion are
performed. The Navier-Stokes dynamics is well reproduced at small enough
Reynolds number without resetting. Computation at higher Reynolds
numbers is achieved by performing resettings. The interval between
successive resettings is found to abruptly increase when the new
parameter is varied from zero to a value much smaller than the resetting
interval.