Volume 11 Issue 3
Jul.  2018
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Lin Yuan, Hong-guang Sun, Yong Zhang, Yi-ping Li, Bing-qing Lu. 2018: Statistical description of depth-dependent turbulent velocity measured in Taihu Lake, China. Water Science and Engineering, 11(3): 243-249. doi: 10.1016/j.wse.2018,09.005
Citation: Lin Yuan, Hong-guang Sun, Yong Zhang, Yi-ping Li, Bing-qing Lu. 2018: Statistical description of depth-dependent turbulent velocity measured in Taihu Lake, China. Water Science and Engineering, 11(3): 243-249. doi: 10.1016/j.wse.2018,09.005

Statistical description of depth-dependent turbulent velocity measured in Taihu Lake, China

doi: 10.1016/j.wse.2018,09.005
Funds:  This work was supported by the National Natural Science Foundation of China (Grants No. 11572112 and 41330632).
More Information
  • Corresponding author: Hong-guang Sun
  • Received Date: 2017-07-19
  • Rev Recd Date: 2018-05-10
  • Quantitative description of turbulence using simple physical/mathematical models remains a challenge in classical physics and hydrologic dynamics. This study monitored the turbulence velocity field at the surface and bottom of Taihu Lake, in China, a large shallow lake with a heterogeneous complex system, and conducted a statistical analysis of the data for the local turbulent structure. Results show that the measured turbulent flows with finite Reynolds numbers exhibit properties of non-Gaussian distribution. Compared with the normal distribution, the Lévy distribution with meaningful parameters can better characterize the tailing behavior of the measured turbulence. Exit-distance statistics and multiscaling extended self-similarity (ESS) were used to interpret turbulence dynamics with different scale structures. Results show that the probability density function of the reverse structure distance and the multiscaling ESS can effectively capture the turbulent flow dynamics varying with water depth. These results provide an approach for quantitatively analyzing multiscale turbulence in large natural lakes.

     

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  • Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F., Succi, S., 1993. Extended self-similarity in turbulent flows. Physical Review E, 48(1), R29-R32. https://doi.org/10.1103/physreve.48.r29.
    Biferale, L., Cencini, M., Lanotte, A., Vergni, D., Vulpiani, A., 2001. Inverse statistics of smooth signals: The case of two dimensional turbulence. Physical Review Letters, 87(12), 124501. https://dx.doi.org/10.1103/physrevlett.87.124501.
    Biferale, L., Cencini, M., Lanotte, A.S., Vergni, D., 2003. Inverse velocity statistics in two-dimensional turbulence. Physics of Fluids, 15(4), 1012-1020. https://doi.org/10.1063/1.1557527.
    Bogachev, M.I., Eichner, J.F., Bunde, A., 2008. The effects of multifractality on the statistics of return intervals. The European Physical Journal Special Topics, 161(1), 181-193. https://doi.org/10.1140/epjst/e2008-00760-5.
    Chao, X.B., Jia, Y.F,, Shields, F.D., Wang, S.S.Y., Cooper, C.M., 2008. Three-dimensional numerical modeling of cohesive sediment transport and wind wave impact in a shallow oxbow lake. Advances in Water Resources, 31(7), 1004-1014. https://doi.org/10.1016/j.advwatres.2008.04.005.
    Chen, W., Zhou, H.B., 2005. Lévy-Kolmogorov scaling of turbulence. Mathematical Physics, arXiv: math-ph/0506039.
    Chen, Y.M., Hu, G.X., Yang, S.Y., Li, Y.P., 2012. Study on wind-driven flow under the influence of water freezing in winter in a northern shallow lake. Advances in Water Science, 23(6), 837–843 (in Chinese).
    Csanady, G., 1973. Wind-induced barotropic motions in long lakes. Journal of Physical Oceanography, 3(4), 429–438. https://doi.org/10.1175/1520-0485(1973)003<0429:wibmil>2.0.co;2.
    Davidson, P.A., 2015. Turbulence: An Introduction for Scientists and Engineers. Oxford University Press, New York.
    Douady, S., Couder, Y., Brachet, M.E., 1991. Direct observation of the intermittency of intense vorticity filaments in turbulence. Physical Review Letters, 67(8), 983-986. https://doi.org/10.1103/physrevlett.67.983.
    Feller, W., 2008. An Introduction to Probability Theory and Its Applications (Vol. 2). John Wiley & Sons, New York.
    Feynman, R.P., Leighton, R.B., Sands, M., Lindsay, R.B., 1966. The feynman lectures on physics, vol. 3: Quantum mechanics. Physics Today, 19(11), 80-83. https://doi.org/10.1063/1.3047826.
    Frisch, U., 1991. From global scaling, a la Kolmogorov, to local multifractal scaling in fully developed turbulence. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 434(1890), 89-99. https://doi.org/10.1098/rspa.1991.0082.
    Frisch, U., 1995. Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press, Cambridge.
    Han, H.J., Hu, W.P., Jin, Y.Q., 2008. Numerical experiments on influence of wind speed on current in lake. Oceanologia Et Limnologia Sinica, 39, 567–576 (in Chinese).
    Hawley, N., Lesht, B.M., 1992. Sediment resuspension in lake St. Clair. Limnology and Oceanography, 37(8), 1720-1737. https://doi.org/10.4319/lo.1992.37.8.1720.
    Holmes, P., Lumley, J.L., Berkooz, G., 1998. Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press, Cambridge.
    Hu, L.M., Hu, W.P., Zhai, S.H., Wu, H.Y., 2010. Effects on water quality following water transfer in Lake Taihu, China. Ecological Engineering, 36(4), 471–481 (in Chinese).
    Jensen, M.H., 1999. Multiscaling and structure functions in turbulence: An alternative approach. Physical Review Letters, 83(1), 76-79. https://doi.org/10.1103/physrevlett.83.76.
    Jin, K.R., Sun, D.T., 2007. Sediment resuspension and hydrodynamics in Lake Okeechobee during the late summer. Journal of Engineering Mechanics, 133(8), 899–910. https://doi.org/10.1061/(asce)0733-9399(2007)133:8(899).
    Kolmogorov, A.N., 1941. Dissipation of energy in locally isotropic turbulence. Akademiia Nauk Sssr Doklady, 32(1890), 15-17 (in Russian).
    Kolmogorov, A.N., 1968. Local structure of turbulence in an incompressible viscous fluid at very high Reynolds numbers. Soviet Physics Uspekhi, 10(6), 734-746. https://doi.org/10.1070/pu1968v010n06abeh003710.
    Laherrere, J., Sornette, D., 1998. Stretched exponential distributions in nature and economy:“fat tails” with characteristic scales. Physics of Condensed Matter, 2(4), 525-539. https://doi.org/10.1007/s100510050276.
    Li, Y.P., Jalil, A., Du, W., Gao, X.M., Wang, J.W., Luo, L.C., Li, H.Y., Dai, S.J., Hashim, S., Yu, Z.B., et al., 2017. Wind induced reverse flow and vertical profile characteristics in a semi-enclosed bay of large shallow Lake Taihu, China. Ecological Engineering, 102, 224-233. https://doi.org/10.1016/j.ecoleng.2017.02.022.
    Liang, R.J., Zhong, J.H.,1994. A three-dimensional numerical simulation of wind-driven water current in Taihu Lake. Journal of Lake Science, 6(4), 289-297 (in Chinese).
    Liang, Y.J., Chen, W., 2013. A survey on computing Lévy stable distributions and a new Matlab toolbox. Signal Processing, 93(1), 242-251. https://doi.org/10.1016/j.sigpro.2012.07.035.
    Liu, W., Jiang, N., 2004. Three structure functions in turbulence. In: Proceedings of the 10th National Conference on Modern Mathematics and Mechanics. Shanghai University Press, Shanghai, pp 499-503 (in Chinese).
    Luettich, R.A., Harleman, D.R.F., Somlyody, L., 1990. Dynamic behavior of suspended sediment concentrations in a shallow lake perturbed by episodic wind events. Limnology and Oceanography, 35(5), 1050-1067. https://doi.org/10.4319/lo.1990.35.5.1050.
    Ma, X.G., Hu, F., 2004. Refined structure of energy spectrum and energy cascade in atmosph eric turbulence. Chinese Journal of Geophysics, 47(2), 195-199 (in Chinese).
    Mehta, A.J., Partheniades, E., 1975. An investigation of the depositional properties of flocculated fine sediment. Journal of Hydraulic Research, 13(4), 361–381. https://doi.org/10.1080/00221687509499694.
    Nelkin, M., 1992. In what sense is turbulence an unsolved problem? Science, 255(5044), 566-570. https://doi.org/10.1126/science.255.5044.566.
    Nolan, J.P., 2003. Stable Distributions: Models for Heavy-tailed Data. Birkhauser, New York.
    Qian, J., 2001. On the normal and anomalous scaling in turbulence. Advances in Mechanics, 31(3), 405-416 (in Chinese).
    Qu, W.C., Dickman, M., Wang, S.M., 2001. Multivariate analysis of heavy metal and nutrient concentrations in sediments of Taihu Lake, China. Hydrobiologia, 450(1-3), 83–89. https://doi.org/10.1023/A:1017551701587.
    Shlesinger, M.F., West, B.J., Klafter, J., 1987. Lévy dynamics of enhanced diffusion: Application to turbulence. Physical Review Letters, 58(11), 1100-1103. https://doi.org/10.1103/physrevlett.58.1100.
    Stull, R.B., 2012. An Introduction to Boundary Layer Meteorology. Springer, Netherlands.
    Švihlová, H., Hron, J., Málek, J., Rajagopal, K.R., Rajagopal, K., 2017. Determination of pressure data from velocity data with a view towards its application in cardiovascular mechanics. Part 2. A study of aortic valve stenosis. International Journal of Engineering Science, 114, 1-15. https://doi.org/10.1016/j.ijengsci.2017.01.002.
    Tabeling, P., 2002. Two-dimensional turbulence: A physicist approach. Physiological Reports, 362(1), 1-62. https://doi.org/10.1016/s0370-1573(01)00064-3.
    Uchaikin, V.V., Zolotarev, V.M., 1999. Chance and Stability: Stable Distributions and Their Applications. Walter de Gruyter, Utrecht.
    Viggiano, B., Gion, M.S., Ali, N., Tutkun, M., Cal, R.B., 2016. Inverse structure functions in the canonical wind turbine array boundary layer. Journal of Renewable and Sustainable Energy, 8(5), 053310. https://doi.org/10.1063/1.4966228.
    Vincent, A., Meneguzzi, M., 1991. The satial structure and statistical properties of homogeneous turbulence. Journal of Fluid Mechanics, 225, 1-20. https://doi.org/10.1017/s0022112091001957.
    Weron, R., 2004. Computationally intensive value at risk calculations. In: Gentle, J.E., Härdle, W., Mori, Y. eds., Handbook of Computational Statistics, Springer, Berlin, pp.911–950.
    Wetzel, R.G., 2001. Limnology: Lake and River Ecosystems. Academic Press, San Diego.
    Zhou, W.X., Sornette, D., Yuan, W.K., 2006. Inverse statistics and multifractality of exit distances in 3D fully developed turbulence. Physica. Section D: Nonlinear Phenomena, 214(1), 55-62. https://doi.org/10.1016/j.physd.2005.12.004.
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