Abstract
This paper investigated the spacing threshold of nonsubmerged spur dikes with alternate layout to classify the impact scale of spur dikes. A mathematical model was built based on standardk-εmodel, finite volume method (FVM), and rigid lid assumption and was verified by experimental data. According to dimensional analysis, three indices, that is,Fr(Froude number),B/b(channel width to dike length), andB/h(channel width to water depth), were identified as the influencing factors on the spacing threshold, based on which fifteen sets of conditions were simulated. The calculation results indicate thatB/his the most influencing parameter onSc/b(spacing threshold to dike length), followed byB/bandFr. A dimensionless empirical formula of spacing threshold is fitted by multivariate regression. The results of four sets of additional conditions illustrate that the generalization of empirical formula is satisfactory and the precision of interpolation is higher than that of extrapolation. Furthermore, the spacing threshold of alternate spur dikes is generally smaller than ipsilateral spur dikes.
Highlights
Spur dikes are one of the most widely used structures in hydraulic engineering
In our past research [8], we have proposed the definition of spacing threshold of nonsubmerged double spur dikes with ipsilateral layout and same length in straight rectangular channel, that is, the spacing when lateral distributions of velocities at adjacent two spur dike sections become coincided
The threshold value should be redefined as the spacing when the lateral distribution of velocities at adjacent two spur dike sections becomes just coincided in reverse direction, while the criterion for the ipsilateral spur dikes s5-u (m/s) z1-u (m/s) z6-u (m/s) z11-u (m/s) x1-u (m/s)
Summary
Spur dikes are one of the most widely used structures in hydraulic engineering. They are introduced in rivers for channel regulation, flood prevention, and river diversion [1,2,3]. Spur dike exerts influence on river system usually in the form of groups [4, 5] These spur dikes (or groups) interact with each other in a certain range, beyond which they are independent [6]. The past research of spur dikes has mainly been focused on the effects of small-scale spur dike groups on local river ways, but rarely on the overall impact of large-scale spur dike groups on river systems [9,10,11,12]. It is necessary to firstly find the cut-off point between small-scale and largescale groups On this matter, several scholars have proposed the concepts of spur dike’s recovery length or uninfluenced distance [6, 9, 16], but so far, they did not obtain a clear conclusion. It is necessary to conduct further investigations on the spacing threshold of alternate spur dikes
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