Comprehensive Exam - Professor Knack Questions
By: Cássio Rampinelli
Date: May 20, 2020
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QUESTION 1: In Stream Riparian Systems and Fluvial Morphology, we discussed, briefly, the velocity profiles that result from gravel beds. Similar changes to the velocity occurs in the presence of vegetation. There has been a lot of research into velocity profiles in the presence of vegetation for different vegetation under different conditions. Your questions relate to this body of literature and your background in ecohydraulics. Find at least one paper on field measurements and one on laboratory measurements of velocity profiles with vegetation. Using these sources, discuss the following.
a) What are some of the most significant advantages and disadvantages of laboratory measurements and field measurements?
SOLUTION
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Laboratory experiments allow experimental set up in controlled environment. Therefore, accurate experimental techniques may be arranged to provide the most suitable condition to extract reliable data, free of undesirable external interference. This advantage makes laboratory experiments an ideal alternative to verify and test theoretical formulations for phenomena descriptions, and physical understanding. However, laboratory environment may also oversimplify real world complexity, besides bringing scale issues that might misrepresenting the simulation of natural systems.
Field experiments have the advantage of allowing the identification of the complex factors and their interplay in natural systems. Being able to measure real world systems may help improving lab experimental apparatus or introducing new concepts and theoretical insights to better explain real-world systems. However, field experiments can also limit the use of specific lab equipment and/or bring external interference affecting data reliability and evaluation of some processes. Such issues are related to heterogeneity of natural environment, interplay between three-dimensional effects, seasonal variations, to name a few aspects.
b) Is there good agreement between laboratory and field measurements?
SOLUTION
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Although comparisons between field and laboratory measurements for velocity profiles in the presence of vegetation are being increasingly explored by the research community, experimental tests of real vegetation under field conditions are still scarce in the literature (Berends et al., 2020). Berends et al. (2020) have found higher vegetation parameter value for the model proposed by Järvelä (2004) in real stream scale flow experiments than expected based on a priori rigid cylinder estimator to mimic vegetation cover in lab experiments. Mohammadzade et al. (2016) have obtained greater value for drag coefficient for lab run than for field measurements. However, in experiments conducted by Cassan et al. (2015) velocity profiles based on the modified log wake law derived from laboratory flume were validated by ADV measurements in field experiments in real scale channel with natural vegetation. These findings suggest that although for some situations there might be good agreement between laboratory and field measurements, further research might be conducted to better specify the gaps in which field and lab expectations would mismatch.
c) Write a summary (maximum one page) of the significant generalizations that can be drawn from your review of the literature you found as it relates to velocity profiles.
SOLUTION
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Most of the studies related to vegetation effects on velocity profile have been performed in laboratory flumes (Cassan et al., 2015). Such condition has the advantage of allowing accurate experimental techniques to extract high quality data. Besides, in lab environment, undesirable effects may be reduced, eliminated, or conveniently controlled to provide ideal scenario to better understanding of fundamental phenomena.
However, natural systems, in which theoretical models and lab evaluations are applied for practical purposes, have great complexity associated to heterogeneity of plant species, plant distribution along channel in irregular patterns, dynamic interaction with fluid flow given plant flexibility, seasonal variations, etc.
This context requires from the scientific community initiatives to bridge field and lab experiments to improve model and theory of flow in presence of vegetation. An aspect that should be further explored is the development or improvement of models that could encompass a good fit of the velocity profile simultaneously for both layers (vegetation layer, and upper non-vegetation surface layer). Comparisons made on four commonly used two layer models of velocity have indicated acceptable agreement with flow velocity measured in lab in the vegetation layer near the bed, however, significantly discrepancies for velocity profiles in the surface layer (Tang, 2019).
Based on such findings, the propagation effect of turbulence and eddy viscosity from the vegetation layer towards the non-vegetation surface layer might be further investigated by the research community. Pu et al. (2019) have recently shown submerged flexible vegetation generates non-constant drag coefficients, unlike the constant values commonly suggested in the literature. This also highlights the importance of improving lab materials used do mimic vegetation in laboratory experiments, since they often use rigid cylinder elements.
Future research should focus on the best way to estimate the thickness of the vegetation layer from direct measurements contrasting the equivalence on lab and field scales and how they relate to each other. Such field of research is relevant since taking into account, among other factors, of plant characteristics, plant flow interaction, and heterogeneity (different macrophytes and vegetation patches) is essential to represent natural streams.
QUESTION 2: Consider a large watershed surrounding a 90-mile-long river channel. The channel has a sinuosity of 2.4 and the valley has an average slope of 0.001. A dam is added to the downstream end of the channel which impounds the entire 90-mile-long river channel. Determine:
a) What is the average slope of the channel?
SOLUTION
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Before get started, let’s assume the following sketch as reference for calculations.
Figure 1: Sketch for channel sinuosity calculations
Sinuosity \(k\) is given by:
\[ k=\frac{S_v}{S_c} \] Since \(S_v=0.001\) (given), and \(k=2.4\) (given), we can compute the average slope of the channel \(S_c\) \[ 2.4=\frac{0.001}{S_c} \] \[ S_c=\frac{0.001}{2.4} \] \[ S_c=0.000417 \]
b) How long is the valley?
SOLUTION
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Sinuosity \(k\) can also be expressed as:
\[ k=\frac{L_c}{L_v} \]
Since the channel length \(L_c=90 \ miles\) (given), and \(k=2.4\) (given), one can compute the valley length \(L_v\) by:
\[ 2.4=\frac{90}{L_v} \] \[ L_v=\frac{90}{2.4} \] \[ L_v=37.5 \ miles \]
c) Does the pre-dam or post-dam condition have the longest time of concentration?; d) What are the major factors that cause the differences in time of concentration?
SOLUTION
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Let’s assume the pre and post dam scenarios as presented in the sketch below:
Figure 2: Sketch for pre and post dam conditions
Time of concentration \(T_c\) consists of the time required for runoff to travel from the hydraulically most distant point in the watershed to the outlet. Several factors may affect the time of concentration such as slope and character of the watershed and the flow path (USDA,2010), surface roughness, channel shape. Many methods are available to estimate the time of concentration including the Kirpich formula, Kerkby formula, NRCS Velocity Method, and NRCS Lag Method. The NRCS Velocity and Lag methods are two of the most used methods for determining time of concentration (IOWA-SUDAS,2013).
The selection of a method depends on various factors including watershed characteristics (especially drainage area), climatic conditions, available data, and available time, and should be performed wisely since the results might significantly differ among the methods (Salimini, et al. 2017).
In the study case, the scenario post-dam certainly has the longest time of concentration. The impoundment created by the dam generates a reduction in the flow velocity (by reducing the slope of the energy grade line ) in relation to the natural stream flow. Flow velocity tend to reduce for cross-sections closer to the dam axis. This entails in longer time needed for a water particle to move downstream toward the dam wall. Depending on the size of the reservoir, in the limit, the velocity tends to be deemed null for practical purposes, close to the dam axis.
e) What impact does the addition of the dam have on peak flows in the watershed? Assume there is no flood storage for the dam.
SOLUTION
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In terms of impact, if we assume there is no flood storage for the dam reservoir, based on the sketch presented in Figure 2, after the water level reaches the dam capacity level, despite of the backwater effect, all the inflow will become outflow. Therefore, for a reference section at downstream, far enough to reduce local flow effects, the hydrograph post-dam will be basically the same of pre-dam scenario. For extreme flow events, minor attenuation of peak flow might be observed at a downstream reference section (Figure 3) since some hydraulic head will be required over the spillway (in case of free spillway) to release the excess of water that will not pass through the dam outlet.
In terms of impact on water profile, for a regular flow condition (low flow or average flow), stream reach upstream at dam site will result in higher water levels for the same flow at pre-dam condition (Figure 3). For higher flow events the backwater effect should be imperceptible , and the water level profile post and pre dam conditions should almost match, except for slight differences along the spillway crest (Figure 3).
Figure 3: Sketch for pre and post dam conditions considering water profiles for low and extreme flow
REFERENCES
Berends, K. D., Ji, U., Penning, W. E. Ellis., Warmink, J. J., Kang, J., & Hulscher, S. J. M. H. (2020). Stream-scale flow experiment reveals large influence of understory growth on vegetation roughness. Advances in Water Resources, 143(February). https://doi.org/10.1016/j.advwatres.2020.103675.
Beven, K.J. (2020). A history of the concept of time of concentration. Hydrology and Earth System Sciences, 24(5),2655-2670.doi: 10.5194/hess-24-2655-2020.
Cassan, L., Belaud, G., Baume, J. P., Dejean, C., & Moulin, F. (2015). Velocity profiles in a real vegetated channel. Environmental Fluid Mechanics, 15(6), 1263–1279.https://doi.org/10.1080/15715124.2004.9635222
IOWA – SUDAS. (2013). Design Manual – Chapter 2 – Stormwater 2B – Urban Hydrology and Runoff-Time of concentration. Paddy Water Environ. 15:123-132. Doi: 10.1007/s10333-016-0534-2.
Järvelä, J. (2004). Determination of flow resistance caused by non-submerged woody vegetation. International Journal of River Basin Management, 2(1), 61–70.
Mohammadzade, N., Afzalimehr, H., Singh, V. P., & Miyab, N. M. (2016). Experimental Investigation of Influence of Vegetation on Flow Turbulence. International Journal of Hydraulic Engineering, 2015(3). 54–69.https://doi.org/10.13140/RG.2.1.5017.5441.
Pu, J. H., Hussain, A., Guo, Y. kun, Vardakastanis, N., Hanmaiahgari, P. R., & Lam, D. (2019). Submerged flexible vegetation impact on open channel flow velocity distribution: An analytical modelling study on drag and friction. Water Science and Engineering, 12(2), 121–128. https://doi.org/10.1016/j.wse.2019.06.003
Salimi, E.T., Nohegar, A., Malekian, A. Hoseini, M., Holisaz, A. (2017). Estimating time of concentration in large watersheds.
Tang, X. (2019). Evaluating Two-Layer Models for Velocity Profiles in Open-Channels with Submerged Vegetation. Journal of Geoscience and Environment Protection, 07(01), 68–80. https://doi.org/10.4236/gep.2019.71006
USDA Natural Resource Conservation Service. (2010). National Engineering Handbook - Part 630. Chapter 15: Time of Concentration.