@article{Gustafsson20112850,
title = "Energy spectra at low wavenumbers in homogeneous incompressible turbulence",
journal = "Physics Letters A",
volume = "375",
number = "30-31",
pages = "2850 - 2853",
year = "2011",
note = "",
issn = "0375-9601",
doi = "DOI: 10.1016/j.physleta.2011.05.070",
url = "http://www.sciencedirect.com/science/article/pii/S0375960111006980",
author = "Jonathan Gustafsson and William K. George",
keywords = "Homogeneous turbulence",
keywords = "Incompressible turbulence",
keywords = "Turbulence theory",
keywords = "Integral invariant",
keywords = "Infinite domain",
abstract = "
The form E(k,t)[similar, equals]Cmkm in the limit as k-->0 and where Cm is independent of k is examined under the assumption that the turbulence is homogeneous and the three-dimensional energy spectrum function is continuous. By using fractional derivatives together with the integrals that relate E(k,t) to moments of the two-point correlation functions, it is possible to show that m has to be an even integer. Thus fractional and odd powers are not possible in an infinite domain."
}