Power Law Exponents for Vertical Velocity Distributions in Natural Rivers

Hae-Eun Lee, Chanjoo Lee, Youg-Jeon Kim, Ji-Sung Kim, Won Kim

Department of Computational Science and Engineering, Yonsei University, Seoul, South Korea.
Water Resources Research Department, Korea Institute of Construction Technology, Goyang, South Korea.

DOI: 10.4236/eng.2013.512114                

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.

Keywords

Vertical Velocity Distribution; Power Law Exponent; Natural Rivers; Field Measurement; Flow Resistance

Conflicts of Interest

The authors declare no conflicts of interest.

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