![Sample our Geography journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5937/TOC-Subject-Sample-2021-Geography.jpg"})
Abstract
On a stepped channel, three distinct flow regimes, nappe, transition, and skimming, occur successively with increasing discharge. This work proposes a criterion of the transition flow occurrence: a critical slope of the channel exists between mild and steep slopes, and for mild slopes, air pocket disappearance and nappe parallel to channel slope are defined as the lower and upper limits of transition flow, whereas for steep slopes, the two phenomena oppositely represent the upper and lower limits. The analytical approaches based on the criterion demonstrate the critical slope of 30° and predict the lower and upper limits of transition flow. The experimental data verify the existence of the critical slope and its prediction accuracy, and indicate that the prediction of the lower and upper limits of transition flow works well for both mild (<30°) and steep (>30°) slopes. During stepped channel design, employing the critical slope can control the transition flow occurrence, therefore reducing the risks caused by structure vibration and excessive splashing.
Disclosure statement
No potential conflict of interest was reported by the authors.
Supplemental data
Supplemental data for this article can be accessed https://doi.org/10.1080/00221686.2021.1978569. Fig. S1, showing comparison between experimental data and our predictions of lower and upper limits of transition flow, can be accessed from the online version of the paper.
Notation
| b | = | step height (m) |
| D | = | drop number (–) |
| Fb | = | Froude number at step edge (–) |
| g | = | gravity acceleration constant (m s−2) |
| hb | = | flow depth at section AB (m) |
| hc | = | critical flow depth (m) |
| hd | = | flow depth at section HG (m) |
| hp | = | depth of recirculating pool at section EF (m) |
| K | = | brink pressure coefficient (–) |
| N | = | brink depth ratio (–) |
| q | = | unit discharge (m2 s−1) |
| qm | = | unit discharge in the mixing zone (m2 s−1) |
| qp | = | recirculating unit discharge in pool (m2 s−1) |
| vb | = | mean velocity at section AB (m s−1) |
| vd | = | mean velocity at section HG (m s−1) |
| vj | = | velocity of nappe before entering recirculating pool (m s−1) |
| vj′ | = | local jet velocity immediately after impacting pool (m s−1) |
| w | = | channel width (m) |
| α | = | inclination of jet at pool surface and horizontal step face (°) |
| η | = | relative energy loss in control volume EFGHD (–) |
| θ | = | channel slope (°) |
| θ* | = | critical slope of channel between mild and steep slopes (°) |
| ρ | = | density of water (kg m−3) |