Jian-ping Luo(羅劍平), Yong-bo Wang (王永博),Xiang Qiu(邱翔) ,Yu-xian Xia(夏玉顯) ,Yu-lu Liu(劉宇陸)

?

Energy dissipation statistics along the Lagrangian trajectories in three-dimen-sional turbulent flows*

Jian-ping Luo1(羅劍平), Yong-bo Wang1(王永博),Xiang Qiu2(邱翔) ,Yu-xian Xia1(夏玉顯) ,Yu-lu Liu3(劉宇陸)

1.2.3.

Sweep, ejection, dispersion, quadrant analysis, turbulent channel flow

Fig. 1 Measured relative contribution from different term of the velocity gradients. The errorbar is the standard deviation from different Lagrangian trajectories

Fig. 2 Experimental cross correlation coefficients between the velocity gradientand the full energydissipation rate along the Lagrangian trajectory. The errorbar indicates the standard deviation from different Lagrangian tra- jectories

Let us recall firstly the homogeneous and isotro- pic relation in the Eulerian frame. The Eq. (2). can be rewritten as

in which stands for the standard deviation. Figure 2 shows the measured , in which the errorbar indicates a standard deviation obtained from different trajectories.Statistically speaking, term A is more correlated with the full energy dissipation rate with a value.It implies that it is more reasonable to choose to instead of the full energy dissipation rate if one has to choose one.Figure 3 shows the measured histogram of , where the Gaussian distribution with the same mean value and standard deviation is illustrated by a solid line. One can observe that the Gaussian distribution nicely fitsthe measured histogram.

We now turn to the coarse-grained energy dissi- pation rate, i.e.

Fig.4Measured cross correlation coefficients for the coarse- grained dissipation rate. The errorbar is a standard deviation from different Lagrangian trajectories

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[3] Hamlington P., Krasnov D., Boeck T. et al. Local dissipa- tion scales and energy dissipation-rate moments in channel flow [J]., 2012, 701: 419-429.

[4] Huang Y. X., Schmitt F. G., Lu Z. M. et al. Second-order structure function in fully developed turbulence [J]., 2010, 82(2): 026319.

[5] Stelzenmuller N., Polanco J. I., Vignal L. et al. Lagrangian acceleration statistics in a turbulent channel flow [J]., 2017, 2(5): 054602.

[6] Xia Y. X., Qian Y. H. Lattice Boltzmann method for Casimir invariant of two-dimensional turbulence [J]., 2016, 28(2): 319-324.

[7] Luo J. P., Lu Z. M., Qiu X. et al. Effect of sweep and ejection events on particle dispersion in wall bounded turbulent flows [J]., 2012, 24(5): 794-799.

[8] Huang Y., Biferale L., Calzavarini E. et al. Lagrangian single-particle turbulent statistics through the Hilbert- Huang transform [J]., 2013, 87(4): 041003.

[9] Huang Y., Schmitt F. G. Lagrangian cascade in three- dimensional homogeneous and isotropic turbulence [J]., 2014, 741: R2.

[10]He G. W. Anomalous scaling for Lagrangian velocity stru- cture functions in fully developed turbulence [J]., 2011, 83(2): 025301.

(October 6, 2015,Accepted November 19, 2017)

?China Ship Scientific Research Center 2018

*Project supported by the National Natural Science Foun- dation of China (Grant Nos.11572203, 11332006).

Jian-ping Luo (1964-), Female, Ph. D., Professor,

E-mail: jp_luo@163.com

Xiang Qiu,

E-mail: Emqiux@163.com