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A consequence of the zero fourth cumulant approximation

Published online by Cambridge University Press:  28 March 2006

Edward E. O'Brien  and
George C. Francis
Edward E. O'Brien
Affiliation:
State University of New York, Long Island Center, Oyster Bay, New York
George C. Francis
Affiliation:
Computing Laboratory, Ballistics Research Laboratory, Aberdeen Proving Ground, Maryland
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Abstract

Recent investigations by Kraichnan (1961) and Ogura (1961) have raised doubts concerning the usefulness of the zero fourth cumulant approximation in turbulence dynamics. It appears extremely tedious to examine, by numerical computation, the consequences of this approximation on the turbulent energy spectrum although the appropriate equations have been established by Proudman & Reid (1954) and Tatsumi (1957). It has proved possible, however, to compute numerically the sequences of an analogous assumption when applied to an isotropic passive scalar in isotropic turbulence.

The result of such computation, for specific initial conditions described herein, and for stationary turbulence, is that the scalar spectrum does develop negative values after a time approximately $2 \Lambda | {\overline {(u^2)}} ^{\frac {1}{2}}$, Where Λ is a length scale typical of the energy-containing components of both the turbulent and scalar spectra and $\overline {(u^2)}^{\frac {1}{2}}$ is the root mean square turbulent velocity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 13 , Issue 3 , July 1962 , pp. 369 - 382
Copyright
© 1962 Cambridge University Press

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References

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