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Fine-scale structure of thin vortical layers

Published online by Cambridge University Press:  10 June 1998

TAKASHI ISHIHARA
Affiliation:
Department of Mathematics, Faculty of Science, Toyama University, Gofuku, Toyama 930, Japan Present address: Department of Computational Science and Engineering, School of Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan.
YUKIO KANEDA
Affiliation:
Department of Computational Science and Engineering, School of Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan

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.

Type
Research Article
Copyright
© 1998 Cambridge University Press

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