Diffusion of Lagrangian invariants in the Navier-Stokes equations

Research output: Chapter in Book/Report/Conference proceedingChapter


The incompressible Euler equations can be written as the active vector system (∂tgt; + u. ∇) A = 0 where u = W[A] is given by the Weber formula W[A] = P{(∇A)*v} in terms of the gradient of A and the passive field v = u0 (A). (P is the projector on the divergence-free part.) The initial data is A(x,0)= x, so for short times this is a distortion of the identity map. After a short time one obtains a new u and starts again from the identity map, using the new u instead of uo in the Weber formula. The viscous Navier-Stokes equations admit the same representation, with a diffusive back-to-labels map A and a v that is no longer passive.

Original languageEnglish (US)
Title of host publicationTubes, Sheets and Singularities in Fluid Dynamics
PublisherKluwer Academic Publishers
Number of pages10
ISBN (Print)1402009801, 9781402009808
StatePublished - 2004

Publication series

NameFluid Mechanics and its Applications
ISSN (Print)0926-5112

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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