Anisotropic scaling contributions to high-order structure functions in high-Reynolds-number turbulence

Research output: Contribution to journalArticle

Abstract

We make an attempt at obtaining the scaling exponents for the anisotropic components of structure functions of order 2 through 6. We avoid mixing these components with their isotropic counterparts for each order by using tensor components that are entirely anisotropic. We do this by considering terms of the isotropic sector corresponding to j = 0 in the SO(3) decomposition of each tensor, and then constructing components that are explicitly zero in the isotropic sector. We use an interpolation formula to compensate for the large-scale encroachment of inertial-range scales. This allows us to examine the lowest order anisotropic scaling behavior. The resulting anisotropic exponents for a given tensorial order are larger than those known for the corresponding isotropic part. One conclusion that emerges is that the anisotropy effects diminish with decreasing scale, although much more slowly than previously thought.

Original languageEnglish (US)
Pages (from-to)2206-2212
Number of pages7
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume62
Issue number2 B
StatePublished - Aug 2000

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high Reynolds number
Structure-function
Reynolds number
Turbulence
turbulence
Scaling
Higher Order
scaling
Sector
sectors
Tensor
exponents
tensors
Scaling Exponent
Scaling Behavior
interpolation
Anisotropy
Lowest
Interpolate
Exponent

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

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abstract = "We make an attempt at obtaining the scaling exponents for the anisotropic components of structure functions of order 2 through 6. We avoid mixing these components with their isotropic counterparts for each order by using tensor components that are entirely anisotropic. We do this by considering terms of the isotropic sector corresponding to j = 0 in the SO(3) decomposition of each tensor, and then constructing components that are explicitly zero in the isotropic sector. We use an interpolation formula to compensate for the large-scale encroachment of inertial-range scales. This allows us to examine the lowest order anisotropic scaling behavior. The resulting anisotropic exponents for a given tensorial order are larger than those known for the corresponding isotropic part. One conclusion that emerges is that the anisotropy effects diminish with decreasing scale, although much more slowly than previously thought.",
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AB - We make an attempt at obtaining the scaling exponents for the anisotropic components of structure functions of order 2 through 6. We avoid mixing these components with their isotropic counterparts for each order by using tensor components that are entirely anisotropic. We do this by considering terms of the isotropic sector corresponding to j = 0 in the SO(3) decomposition of each tensor, and then constructing components that are explicitly zero in the isotropic sector. We use an interpolation formula to compensate for the large-scale encroachment of inertial-range scales. This allows us to examine the lowest order anisotropic scaling behavior. The resulting anisotropic exponents for a given tensorial order are larger than those known for the corresponding isotropic part. One conclusion that emerges is that the anisotropy effects diminish with decreasing scale, although much more slowly than previously thought.

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