Structure-function scaling of bounded two-dimensional turbulence

W. Kramer, G.H. Keetels, H.J.H. Clercx, G.J.F. van Heijst

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Abstract

Statistical properties of forced two-dimensional turbulence generated in two different flow domains are investigated by numerical simulations. The considered geometries are the square domain and the periodic channel domain, both bounded by lateral no-slip sidewalls. The focus is on the direct enstrophy cascade range and how the statistical properties change in the presence of no-slip boundaries. The scaling exponents of the velocity and the vorticity structure functions are compared to the classical Kraichnan-Batchelor-Leith (KBL) theory, which assumes isotropy, homogeneity, and self-similarity for turbulence scales between the forcing and dissipation scale. Our investigation reveals that in the interior of the flow domain, turbulence can be considered statistically isotropic and locally homogeneous for the enstrophy cascade range, but it is weakly intermittent. However, the scaling of the vorticity structure function indicates a steeper slope for the energy spectrum than the KBL theory predicts. Near the walls the turbulence is strongly anisotropic at all flow scales.
Original languageEnglish
Pages (from-to)026310
Number of pages10
JournalPhysical review E: Statistical, nonlinear, and soft matter physics
Volume84
Issue number2
DOIs
Publication statusPublished - 2011

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Structure-function
vorticity
Turbulence
Cascade Range (CA-OR-WA)
turbulence
Scaling
scaling
Vorticity
Slip
Statistical property
Cascade
slip
Isotropy
Scaling Exponent
isotropy
Self-similarity
Energy Spectrum
Homogeneity
Range of data
Forcing

Cite this

Kramer, W. ; Keetels, G.H. ; Clercx, H.J.H. ; van Heijst, G.J.F. / Structure-function scaling of bounded two-dimensional turbulence. In: Physical review E: Statistical, nonlinear, and soft matter physics. 2011 ; Vol. 84, No. 2. pp. 026310.
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author = "W. Kramer and G.H. Keetels and H.J.H. Clercx and {van Heijst}, G.J.F.",
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Structure-function scaling of bounded two-dimensional turbulence. / Kramer, W.; Keetels, G.H.; Clercx, H.J.H.; van Heijst, G.J.F.

In: Physical review E: Statistical, nonlinear, and soft matter physics, Vol. 84, No. 2, 2011, p. 026310.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Structure-function scaling of bounded two-dimensional turbulence

AU - Kramer, W.

AU - Keetels, G.H.

AU - Clercx, H.J.H.

AU - van Heijst, G.J.F.

PY - 2011

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N2 - Statistical properties of forced two-dimensional turbulence generated in two different flow domains are investigated by numerical simulations. The considered geometries are the square domain and the periodic channel domain, both bounded by lateral no-slip sidewalls. The focus is on the direct enstrophy cascade range and how the statistical properties change in the presence of no-slip boundaries. The scaling exponents of the velocity and the vorticity structure functions are compared to the classical Kraichnan-Batchelor-Leith (KBL) theory, which assumes isotropy, homogeneity, and self-similarity for turbulence scales between the forcing and dissipation scale. Our investigation reveals that in the interior of the flow domain, turbulence can be considered statistically isotropic and locally homogeneous for the enstrophy cascade range, but it is weakly intermittent. However, the scaling of the vorticity structure function indicates a steeper slope for the energy spectrum than the KBL theory predicts. Near the walls the turbulence is strongly anisotropic at all flow scales.

AB - Statistical properties of forced two-dimensional turbulence generated in two different flow domains are investigated by numerical simulations. The considered geometries are the square domain and the periodic channel domain, both bounded by lateral no-slip sidewalls. The focus is on the direct enstrophy cascade range and how the statistical properties change in the presence of no-slip boundaries. The scaling exponents of the velocity and the vorticity structure functions are compared to the classical Kraichnan-Batchelor-Leith (KBL) theory, which assumes isotropy, homogeneity, and self-similarity for turbulence scales between the forcing and dissipation scale. Our investigation reveals that in the interior of the flow domain, turbulence can be considered statistically isotropic and locally homogeneous for the enstrophy cascade range, but it is weakly intermittent. However, the scaling of the vorticity structure function indicates a steeper slope for the energy spectrum than the KBL theory predicts. Near the walls the turbulence is strongly anisotropic at all flow scales.

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DO - 10.1103/PhysRevE.84.026310

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