Fine-scale structure of thin vortical layers

Takashi Ishihara, Yukio Kaneda

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A class of exact solutions of the Navier-Stokes equations is derived. Each of them represents the velocity field v = U + u of a thin vortical layer (a planar jet) under a uniform strain velocity field U in three-dimensional infinite space, and provides a simple flow model in which nonlinear coupling between small eddies plays a key role in small-scale vortex dynamics. The small-scale structure of the velocity field is studied by numerically analysing the Fourier spectrum of u. It is shown that the Fourier spectrum of u falls off exponentially with wavenumber k for large k. The Taylor expansion in powers of the coordinate (say y) in the direction perpendicular to the vortical layer suggests that the solution may be well approximated by a function with certain poles in the complex y-plane. The Fourier spectrum based on the singularities is in good agreement with that obtained numerically, where the exponential decay rate is given by the distance of the poles from the real axis of y.

Original languageEnglish
Pages (from-to)297-318
Number of pages22
JournalJournal of Fluid Mechanics
Volume364
DOIs
Publication statusPublished - Jun 10 1998
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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