Analytical solutions of velocity profile in flow through submerged vegetation with variable frontal width

TLDR: In this article, a new shape function is proposed for vegetation with variable frontal width in the vertical direction, where the frontal width exhibits a gradual increase in vertical direction from bottom up in the vegetation.

About: This article is published in Journal of Hydrology.The article was published on 2019-11-01 and is currently open access. It has received 24 citations till now. The article focuses on the topics: Flow velocity & Vegetation (pathology).

Figures

Figure 1: Sketch of flow through vegetation with non-uniform frontal width in the vertical direction

Figure 5: Comparison between measured and predicted turbulence index kn in surface layer.

Figure 2: Comparison of analytical solutions with measured data for different cases

Figure 4: Comparison between measured and predicted formula for turbulence length scale cpl in the vegetation layer. The predicted Cpl for the left, middle, and right panels are obtained from equations (21) and (22), and proposed equation (60), respectively.

Figure 3: Comparison between measured and predicted drag coefficients. The predicted Cds given in the left, middle, and right panels are Cd,iso from equation (53), Cd,wang from equation (56), and Cd,new from equation (59), respectively.

Table 1: Summary of present research on flow in vegetation

Frequently asked questions

Q1. What are the contributions in this paper?

Different from an19 alytical models of velocity distribution in literature, which is mainly suitable 20 for vegetation with uniform frontal width, this paper establishes new analyti21 cal solutions of the velocity profile for vegetation such as shrub and sedge that 22 have a variable frontal width in the vertical direction. 

Q2. how many experiments were needed to determine vegetation resis?

Although empirical expressions for determining parameters such as drag456 coefficient Cd, turbulence length scale for vegetation layer cpl, and surface layer457 kn were proposed for a number of limited scenarios, further investigation and458more experiments are needed in considering different vegetation types and flow459 conditions. 

Q3. What is the drag coefficient for a cylinder?

Cd is a key factor for quantifying the resistance to flow (Nepf363 and Ghisalberti, 2008; Wang et al., 2018a; Baptist et al., 2007). 

Q4. What is the way to describe vegetation shape?

449 (3) Because the shape of vegetation is different from the simplified vegetation450 models using cylinders or single strips, the former empirical formulas of the451 drag coefficient and the turbulence length scale were not suitable for the width-452 varying vegetation here. 

Q5. What is the traditional logarithmic formula for vegetation flow?

The traditional logarithmic formula (equation 45) describes the flow profile413 of the surface layer with two parameters: zero-plane displacement d and hy-414 drodynamic roughness height z0. 

Q6. What is the drag coefficient of a cylinder?

Many377 experiments show a monotonic decline in Cd with increasing vegetation-related378 Reynolds number (Rev) for canopies composed of cylinders (Ishikawa et al.,379 2000; James et al., 2004; Tanino and Nepf, 2008; Liu et al., 2008; Ferreira et al.,380 2009; Kothyari et al., 2009; Stoesser et al., 2010), which can be expressed as381 (Wang et al., 2019)382Cd,wang = 0.819 + 58.5√π(1−φ) 4φ Red. (56)Due to the variation of Dz in the vertical direction, there is a need to calcu-383 late the averaged width Dave when adopting these formulas (equations 53 and38456).