Invariants, diffusion and topological change in incompressible Navier-Stokes equations

Peter Constantin, Koji Ohkitani

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

Abstract

We discuss the effect that the presence of a small viscosity has on the evolution of fields that are transported unchanged in the absence of viscosity. We employ a diffusive Lagrangian formulation and show that the Cauchy invariant, the helicity density, the Jacobian determinant, and the virtual velocity obey parabolic equations that are well-behaved as long as the diffusive transformations are invertible. We call such quantities diffusive Lagrangian. We showby numerical calculations that the loss of invertibility of the diffusive transformation can occur, and that the time scale on which it does can be short even when the viscosity is small. We present quantitative evidence relating the loss of invertibility to the physicalphenomenon of vortex reconnection.

Original languageEnglish (US)
Title of host publicationIUTAM Symposium on Elementary Vortices and Coherent Structures
Subtitle of host publicationSignificance in Turbulence Dynamicsa
PublisherKluwer Academic Publishers
Pages303-317
Number of pages15
ISBN (Print)9781402041808
DOIs
StatePublished - Jan 1 2006

Publication series

NameFluid Mechanics and its Applications
Volume79
ISSN (Print)0926-5112

All Science Journal Classification (ASJC) codes

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

Keywords

  • Anomalous dissipation
  • Diffusive Lagrangian transformation
  • Vortex reconnection

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    Constantin, P., & Ohkitani, K. (2006). Invariants, diffusion and topological change in incompressible Navier-Stokes equations. In IUTAM Symposium on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamicsa (pp. 303-317). (Fluid Mechanics and its Applications; Vol. 79). Kluwer Academic Publishers. https://doi.org/10.1007/1-4020-4181-0_35