Power Law Exponents for Vertical Velocity Distributions in Natural Rivers

Abstract

While log law is an equation theoretically derived for near-bed region, in most cases, power law has been researched by experimental methods. Thus, many consider it as an empirical equation and fixed power law exponents such as 1/6 and 1/7 are generally applied. However, exponent of power law is an index representing bed resistance related with relative roughness and furthermore influences the shapes of vertical velocity distribution. The purpose of this study is to investigate characteristics of vertical velocity distribution of the natural rivers by testing and optimizing previous methods used for determination of power law exponent with vertical velocity distribution data collected with ADCPs during the years of 2005 to 2009 from rivers in South Korea. Roughness coefficient has been calculated from the equation of Limerinos. And using theoretical and empirical formulae, and representing relationships between bed resistance and power law exponent, it has been evaluated whether the exponents suggested by these equations appropriately reproduce vertical velocity distribution of actual rivers. As a result, it has been confirmed that there is an increasing trend of power law exponent as bed resistance increases. Therefore, in order to correctly predict vertical velocity distribution in the natural rivers, it is necessary to use an exponent that reflects flow conditions at the field.

Share and Cite:

Lee, H. , Lee, C. , Kim, Y. , Kim, J. and Kim, W. (2013) Power Law Exponents for Vertical Velocity Distributions in Natural Rivers. Engineering, 5, 933-942. doi: 10.4236/eng.2013.512114.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] ISO, “Hydrometry-Measuring River Velocity and Discharge with Acoustic Doppler Profilers,” International Organization for Standardization, Geneva, Switzerland, ISO/TS 24154, 2005.
[2] J. A. Gonzalez-Castro and M. Muste, “Framework for Estimating Uncertainty of ADCP Measurements from a Moving Boat Using Standardized Uncertainty Analysis,” Journal of Hydraulic Engineering, Vol. 133, No. 12, 2007, pp. 1390-1411.
http://dx.doi.org/10.1061/(ASCE)0733-9429(2007)133:12(1390)
[3] D. S. Mueller, “extrap: Software to Assist the Selection of Extrapolation Methods for Moving-Boat ADCP Streamflow Measurements,” Computers and Geosciences, Vol. 54, 2013, pp. 211-218.
http://dx.doi.org/10.1016/j.cageo.2013.02.001
[4] C.-L. Chen, “Unified Theory on Power Laws for Flow Resistance,” Journal of Hydraulic Engineering, Vol. 117, No. 3, 1991, pp. 371-389.
http://dx.doi.org/10.1061/(ASCE)0733-9429(1991)117:3(371)
[5] B. C. Yen, “Open Channel Flow Resistance,” Journal of Hydraulic Engineering, Vol. 128, No. 1, 2002, pp. 20-39.
http://dx.doi.org/10.1061/(ASCE)0733-9429(2002)128:1(20)
[6] J. O. Hinze, “Turbulence,” McGraw-Hill Book Co., New York, 1975.
[7] ISO, “Measurement of Liquid Flow in Open Channels: Velocity-Area Methods,” International Organization for Standardization, Geneva, Switzerland, ISO 748, 1997.
[8] N.-S. Cheng, “Power-Law Index for Velocity Profiles in Open Channel flows,” Advances in Water Resources, Vol. 30, No. 8, 2007, pp. 1775-1784.
http://dx.doi.org/10.1016/j.advwatres.2007.02.001
[9] J. A. González-Castro, C. S. Melching and K. A. Oberg, “Analysis of Open-Channel Velocity Measurements Collected with an Acoustic Doppler Current Profiler,” 1st International Conference on New/Emerging Concepts for Rivers, RIVERTECH 96, IWRA, Chicago, 22-26 September 1996, pp. 838-845.
[10] M. Muste, K. Yu and M. Spasojevic, “Practical Aspects of ADCP Data Use for Quantification of Mean River Flow Characteristics; Part I: Moving-Vessel Measurements,” Flow Measurement and Instrumentation, Vol. 15, 2004, pp. 1-16.
[11] M. Muste, K. Yu and M. Spasojevic, “Practical Aspects of ADCP Data Use for Quantification of Mean River Flow Characteristics; Part II: Fixed-Vessel Measurements,” Flow Measurement and Instrumentation, Vol. 15, 2004, pp. 17-28.
[12] D. Kim, M. Muste, J. A. González-Castro and M. Ansar, “Graphical User Interface for ADCP Uncertainty Analysis,” Proceedings of the ASCE World Water and Environmental Resources Congress, Anchorage, 15-19 May 2005, pp. 1-12.
[13] J. Le Coz, G. Pierrefeu and A. Paquier, “Evaluation of River Discharges Monitored by a Fixed Side-Looking Doppler Profiler,” Water Resources Research, Vol. 44, 2008, Article ID: W00D09.
http://dx.doi.org/10.1029/2008WR006967
[14] P. M. Pelletier, “Uncertainties in the Single Determination of River Discharge: A Literature Review,” Canadian Journal of Civil Engineering, Vol. 15, No. 5, 1988, pp. 834-850.
http://dx.doi.org/10.1139/l88-109
[15] J. T. Limerinos, “Determination of the Manning Coefficient from Measured Bed Roughness in Natural Channels,” U.S. Geological Survey Water-Supply Paper 1898B, 1970.
[16] G. M. Smart, M. J. Duncan and J. M. Walsh, “Relatively Rough Flow Resistance Equations,” Journal of Hydraulic Engineering, Vol. 128, No. 6, 2002, pp. 568-578.
http://dx.doi.org/10.1061/(ASCE)0733-9429(2002)128:6(568)

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.