Correction factor for determining mean velocity of shallow flow on rough surfaces under varying inundation conditions using dye tracer method

Abstract

Accurate estimation of mean flow velocity is crucial for hydraulics and soil erosion studies. A correction factor (α) is required to convert flow surface velocity to mean velocity when using the dye tracer method. However, the determination of an appropriate α value is challenging and little information is available about how α varies with progressive inundation conditions, especially for rough surfaces with protruding roughness elements (e.g., stones). Therefore, laboratory experiments were conducted in a flume with sandpaper (SD) and stones (ST) surfaces to investigate the impact of roughness elements on the correction factor with varying inundation conditions. The results showed that using a single α value is inappropriate for rough surfaces. The correction factor was positively correlated with the Reynolds number and is controlled by flow regimes as well. Moreover, the impacts of inundation conditions as well as protruding roughness elements should be taken into account for determining α. Correction factor varied non‐monotonically with inundation ratio, depending on the progressive inundation status of protruding roughness elements. The developed equations introducing the inundation ratio performed well in predicting α, with R2 = 0.86 and NSE = 0.91. The results contribute to our understanding of measuring mean flow velocity using the dye tracer method.

On the variation of the correction factor of surface velocity with the measurement vertical for shallow flows over rough beds

“…Figure 5 shows that α vv decreases for increasing values of the hemisphere concentration C h , similarly to what was highlighted by Di Stefano et al (2020), and Fan et al (2023) for transitional and turbulent flows.…”

“…The circumstance that the relationships between α vv and the Froude number (Figure 4a) and the Reynolds number (Figure 4b) are independent of the hemisphere arrangement can be justified considering that, for low concentration values (9%–25%), the velocity distributions are similar while, for the highest values (49%–64%), the occurrence of the quasi‐skimming flow regime limits the influence of the element arrangement (Carollo & Ferro, 2021; Morris, 1959). A slight effect of the Reynolds number on the correction factor was found by Fan et al (2023) for transitional and turbulent shallow flows over a bed roughness due to hemisphere arrangement. This was the overall result obtained for two hydraulic conditions of submerged and non‐submerged hemispheres.…”

“…Di Stefano et al, 2020; Fan et al, 2023). Fan et al (2023) investigated element concentrations, ranging from 10% to 30%, by using hemispheres in a hexagonal pattern with a staggered structure glued on a sand bed. Two hydraulic conditions of submerged and non‐submerged hemispheres were tested.…”

“…Most available investigations refer to the grain roughness case while scarce information concerns the study of the correction factor for shallow flows on rougher surfaces (e.g. Di Stefano et al, 2020; Fan et al, 2023). Fan et al (2023) investigated element concentrations, ranging from 10% to 30%, by using hemispheres in a hexagonal pattern with a staggered structure glued on a sand bed.…”

“…sediment/depth ratio h/k s varies from 1.57 to 6.13 (submerged flow), while the complete dataset byFan et al (2023) features h/k s ranging approximately from 0.3 to 1.7 (non-submerged and submerged flows). The channel slope is also very different, as it is equal to 0.5% here, while it ranges from 7% to 17.6% for the literature dataset.…”