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Bounds on energy flux for finite energy turbulence

Published online by Cambridge University Press:  29 March 2006

P. L. Sulem  and
U. Frisch
P. L. Sulem
Affiliation:
Centre National de la Recherche Scientifique, Observatoire de Nice, France
U. Frisch
Affiliation:
Centre National de la Recherche Scientifique, Observatoire de Nice, France
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Abstract

For incompressible three-dimensional (two-dimensional) turbulence of finite energy, bounds are obtained on energy (enstrophy) flux. To estimate the nonlinear terms, we use a decomposition of the Fourier space into shells of exponentially increasing radii and the property of boundedness in position space of square-integrable functions with Fourier transforms of compact support. In the limit of zero viscosity, it is shown that the three-dimensional (two-dimensional) energy (enstrophy) inertial range, if it exists, cannot have an energy spectrum steeper than $k^{-\frac{8}{3}} (k^{-4})$. Similar results are obtained for the advection of a passive scalar. The connexion with the problem of homogeneous turbulence and intermittency is briefly discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 72 , Issue 3 , 9 December 1975 , pp. 417 - 423
Copyright
© 1975 Cambridge University Press

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