Energy spectra at low wavenumbers in homogeneous incompressible turbulence

Jonathan Gustafsson; William K. George

doi:10.1016/j.physleta.2011.05.070

Energy spectra at low wavenumbers in homogeneous incompressible turbulence

Jonathan Gustafsson
, William K. George

Department of Mechanical and Aerospace Engineering

McMaster University

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The form E(k,t) ≃ C_mk^m in the limit as k→0 and where C_m 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.

Original language	English
Pages (from-to)	2850-2853
Number of pages	4
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	375
Issue number	30-31
DOIs	https://doi.org/10.1016/j.physleta.2011.05.070
State	Published - Jul 18 2011

Keywords

Homogeneous turbulence
Incompressible turbulence
Infinite domain
Integral invariant
Turbulence theory

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10.1016/j.physleta.2011.05.070

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abstract = "The form E(k,t) ≃ 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.",

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AU - Gustafsson, Jonathan

AU - George, William K.

PY - 2011/7/18

Y1 - 2011/7/18

N2 - The form E(k,t) ≃ 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.

AB - The form E(k,t) ≃ 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.

KW - Homogeneous turbulence

KW - Incompressible turbulence

KW - Infinite domain

KW - Integral invariant

KW - Turbulence theory

UR - https://www.scopus.com/pages/publications/79959854604

U2 - 10.1016/j.physleta.2011.05.070

DO - 10.1016/j.physleta.2011.05.070

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AN - SCOPUS:79959854604

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JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 30-31

ER -

Energy spectra at low wavenumbers in homogeneous incompressible turbulence

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Keywords

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