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**Gampert, Markus and Goebbert, Jens Henrik and Schaefer, Philip and Gauding, Michael and Peters, Norbert and Aldudak, Fettah and Oberlack, Martin** (2011):

*Extensive strain along gradient trajectories in the turbulent kinetic energy field.*

In: New Journal of Physics, 13 (4), Institute of Physics, pp. 043012, ISSN 1367-2630,

[Online-Edition: http://stacks.iop.org/1367-2630/13/i=4/a=043012],

[Article]

## Abstract

Based on direct numerical simulations of forced turbulence, shear turbulence, decaying turbulence, a turbulent channel flow as well as a Kolmogorov flow with Taylor-based Reynolds numbers Reλ between 69 and 295, the normalized probability density function of the length distribution P(l) of dissipation elements, the conditional mean scalar difference Δkl at the extreme points as well as the scaling of the two-point velocity difference along gradient trajectories Δun are studied. Using the field of the instantaneous turbulent kinetic energy k as a scalar, we find good agreement between the model equation for P(l) as proposed by Wang and Peters (2008 J. Fluid Mech. 608 113–38) and the results obtained in the different direct numerical simulation cases. This confirms the independence of the model solution from both the Reynolds number and the type of turbulent flow, so that it can be considered universally valid. In addition, we show a 2/3 scaling for the mean conditional scalar difference. In the second part of the paper, we examine the scaling of the conditional two-point velocity difference along gradient trajectories. In particular, we compare the linear s/τ scaling, where τ denotes an integral time scale and s the separation arclength along a gradient trajectory in the inertial range as derived by Wang (2009 Phys. Rev. E 79 046325) with the sa∞ scaling, where a∞ denotes the asymptotic value of the conditional mean strain rate of large dissipation elements.

Item Type: | Article |
---|---|

Erschienen: | 2011 |

Creators: | Gampert, Markus and Goebbert, Jens Henrik and Schaefer, Philip and Gauding, Michael and Peters, Norbert and Aldudak, Fettah and Oberlack, Martin |

Title: | Extensive strain along gradient trajectories in the turbulent kinetic energy field |

Language: | English |

Abstract: | Based on direct numerical simulations of forced turbulence, shear turbulence, decaying turbulence, a turbulent channel flow as well as a Kolmogorov flow with Taylor-based Reynolds numbers Reλ between 69 and 295, the normalized probability density function of the length distribution P(l) of dissipation elements, the conditional mean scalar difference Δkl at the extreme points as well as the scaling of the two-point velocity difference along gradient trajectories Δun are studied. Using the field of the instantaneous turbulent kinetic energy k as a scalar, we find good agreement between the model equation for P(l) as proposed by Wang and Peters (2008 J. Fluid Mech. 608 113–38) and the results obtained in the different direct numerical simulation cases. This confirms the independence of the model solution from both the Reynolds number and the type of turbulent flow, so that it can be considered universally valid. In addition, we show a 2/3 scaling for the mean conditional scalar difference. In the second part of the paper, we examine the scaling of the conditional two-point velocity difference along gradient trajectories. In particular, we compare the linear s/τ scaling, where τ denotes an integral time scale and s the separation arclength along a gradient trajectory in the inertial range as derived by Wang (2009 Phys. Rev. E 79 046325) with the sa∞ scaling, where a∞ denotes the asymptotic value of the conditional mean strain rate of large dissipation elements. |

Journal or Publication Title: | New Journal of Physics |

Volume: | 13 |

Number: | 4 |

Publisher: | Institute of Physics |

Divisions: | 16 Department of Mechanical Engineering 16 Department of Mechanical Engineering > Fluid Dynamics (fdy) Exzellenzinitiative Exzellenzinitiative > Clusters of Excellence Zentrale Einrichtungen Exzellenzinitiative > Clusters of Excellence > Center of Smart Interfaces (CSI) |

Date Deposited: | 24 Aug 2011 18:16 |

Official URL: | http://stacks.iop.org/1367-2630/13/i=4/a=043012 |

Additional Information: | doi: 10.1088/1367-2630/13/4/043012 |

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