### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 381-390 |

Number of pages | 10 |

Journal | Journal of fluid mechanics |

Volume | 440 |

Issue number | 6855 |

DOIs | |

Publication status | Published - 2001 |

### Keywords

- IR-36433
- METIS-202011

### Cite this

*Journal of fluid mechanics*,

*440*(6855), 381-390. https://doi.org/10.1017/S0022112001004852

}

*Journal of fluid mechanics*, vol. 440, no. 6855, pp. 381-390. https://doi.org/10.1017/S0022112001004852

**Scaling exponents in weakly anisotropic turbulence from the Navier-Stokes equation.** / Grossmann, Siegfried; von der Heydt, A.; Lohse, Detlef.

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

DO - 10.1017/S0022112001004852

M3 - Article

VL - 440

SP - 381

EP - 390

JO - Journal of fluid mechanics

JF - Journal of fluid mechanics

SN - 0022-1120

IS - 6855

ER -