Applied Mathematics Seminar

Nearly inviscid 3-D Navier-Stokes flows are examined, with regard to how a viscous perturbation deforms distinguished manifolds of boundaryless 3-D steady Euler flows. A special Melnikov method is necessary in this analysis, given the lack of knowledge of the differentiability of the Navier-Stokes velocity with respect to the viscous parameter, and the fact that its closeness to the Euler velocity cannot be valid for infinite time. An explicit expression for the splitting of the manifold is obtained, and the consequences for viscous fluid transport in the 'bubble vortex' geometry discussed.