Asymptotic model for velocity dip position in open channelsReport as inadecuate

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Applied Water Science

pp 1–12

First Online: 11 July 2017Received: 27 March 2017Accepted: 04 July 2017


An empirical model is proposed to predict the velocity dip position at the central section of open channels. The model is fitted based on asymptotic matching technique and validated by using a wide range of aspect ratios channel width-flow depth from 0.155 to 15. The matching approach, which relies on dividing the trend into smaller segments that can be combined into an overall relation, employs regression technique and thus warrants the best-fit accuracy results. The obtained model satisfies the upper and lower bounds of dip positions equal to 0.5 and 1, respectively. A comparison with other formulas widely reported in the literature is provided. The model is also applied to predict Reynolds shear stress and velocity distribution in open channels. This model will help extending our ability for analyzing velocity field in open channels under different flow and boundary conditions.

KeywordsVelocity distribution Secondary current Asymptotic matching Aspect ratio Sidewall effect AbbreviationsArAspect ratio −

bChannel width m

b0, b1Parameters −

hFlow depth m

mMatching constant −

MASEMean absolute standard error −

NTotal number of data points −

rAverage percentage relative error −

RMSERoot mean square error −

s1Sum of squared relative error −

s2Sum of logarithmic deviation error −

uMean longitudinal velocity m-s

\u^{\prime}\Longitudinal velocity fluctuation m-s

u*Shear velocity m-s

\v^{\prime}\Vertical velocity fluctuation m-s

xLongitudinal direction m

yVertical direction m

ydLocation of dip position m

zLateral direction m

YiAsymptotes −

\\lambda\, \\beta\Parameters −

\\kappa\Von Karman coefficient −

ΠColes’ wake parameter −

\\xi {d}\Dimensionless dip position −

\\xi {0}\Zero velocity bed level m

\\xi {d,c}\Computed value of \\xi {d}\ −

\\xi {d,o}\Observed value of \\xi {d}\ −

\\varphi {i}\Matching functions −

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Author: Snehasis Kundu


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