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Development of mixing and isotropy in inviscid homogeneous turbulence

Published online by Cambridge University Press:  20 April 2006

Jon Lee
Jon Lee
Affiliation:
Flight Dynamics Laboratory, Wright-Patterson AFB, Ohio 43322, U.S.A.
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Abstract

We have investigated a sequence of dynamical systems corresponding to spherical truncations of the incompressible three-dimensional Navier-Stokes equations in Fourier space. For lower-order truncated systems up to the spherical truncation of wavenumber radius 4, it is concluded that the inviscid Navier-Stokes system will develop mixing (and a fortiori ergodicity) on the constant energy-helicity surface, and also isotropy of the covariance spectral tensor. This conclusion is, however, drawn not directly from the mixing definition but from the observation that one cannot evolve the trajectory numerically much beyond several characteristic corre- lation times of the smallest eddy owing to the accumulation of round-off errors. The limited evolution time is a manifestation of trajectory instability (exponential orbit separation) which underlies not only mixing, but also the stronger dynamical charac- terization of positive Kolmogorov entropy (K-system).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 120 , July 1982 , pp. 155 - 183
Copyright
© 1982 Cambridge University Press

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