Scaling exponents in weakly anisotropic turbulence from the Navier-Stokes equation

Siegfried Grossmann, A. von der Heydt, Detlef Lohse

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Scopus)

Abstract

The second-order velocity structure tensor of weakly anisotropic strong turbulence is decomposed into its SO(3) invariant amplitudes dj(r). Their scaling is derived within a scaling approximation of a variable-scale mean-field theory of the Navier–Stokes equation. In the isotropic sector j = 0 Kolmogorov scaling d0(r) [is proportional to] r2/3 is recovered. The scaling of the higher j amplitudes (j even) depends on the type of the external forcing that maintains the turbulent flow. We consider two options: (i) for an analytic forcing and for decreasing energy input into the sectors with increasing j, the scaling of the higher sectors j > 0 can become as steep as dj(r) [is proportional to] rj+2/3; (ii) for a non-analytic forcing we obtain dj(r) [is proportional to] r4/3 for all non-zero and even j.
Original languageUndefined
Pages (from-to)381-390
Number of pages10
JournalJournal of fluid mechanics
Volume440
Issue number6855
DOIs
Publication statusPublished - 2001

Keywords

  • IR-36433
  • METIS-202011

Cite this

Grossmann, Siegfried ; von der Heydt, A. ; Lohse, Detlef. / Scaling exponents in weakly anisotropic turbulence from the Navier-Stokes equation. In: Journal of fluid mechanics. 2001 ; Vol. 440, No. 6855. pp. 381-390.
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Scaling exponents in weakly anisotropic turbulence from the Navier-Stokes equation. / Grossmann, Siegfried; von der Heydt, A.; Lohse, Detlef.

In: Journal of fluid mechanics, Vol. 440, No. 6855, 2001, p. 381-390.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Scaling exponents in weakly anisotropic turbulence from the Navier-Stokes equation

AU - Grossmann, Siegfried

AU - von der Heydt, A.

AU - Lohse, Detlef

PY - 2001

Y1 - 2001

N2 - The second-order velocity structure tensor of weakly anisotropic strong turbulence is decomposed into its SO(3) invariant amplitudes dj(r). Their scaling is derived within a scaling approximation of a variable-scale mean-field theory of the Navier–Stokes equation. In the isotropic sector j = 0 Kolmogorov scaling d0(r) [is proportional to] r2/3 is recovered. The scaling of the higher j amplitudes (j even) depends on the type of the external forcing that maintains the turbulent flow. We consider two options: (i) for an analytic forcing and for decreasing energy input into the sectors with increasing j, the scaling of the higher sectors j > 0 can become as steep as dj(r) [is proportional to] rj+2/3; (ii) for a non-analytic forcing we obtain dj(r) [is proportional to] r4/3 for all non-zero and even j.

AB - The second-order velocity structure tensor of weakly anisotropic strong turbulence is decomposed into its SO(3) invariant amplitudes dj(r). Their scaling is derived within a scaling approximation of a variable-scale mean-field theory of the Navier–Stokes equation. In the isotropic sector j = 0 Kolmogorov scaling d0(r) [is proportional to] r2/3 is recovered. The scaling of the higher j amplitudes (j even) depends on the type of the external forcing that maintains the turbulent flow. We consider two options: (i) for an analytic forcing and for decreasing energy input into the sectors with increasing j, the scaling of the higher sectors j > 0 can become as steep as dj(r) [is proportional to] rj+2/3; (ii) for a non-analytic forcing we obtain dj(r) [is proportional to] r4/3 for all non-zero and even j.

KW - IR-36433

KW - METIS-202011

U2 - 10.1017/S0022112001004852

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