Hydraulic Design and Analysis of Labyrinth Weirs. Part 2: Nappe Aeration, Instability, and Vibration

Transcription

1 posted ahead of print October 11, doi: /(asce)ir Hydraulic Design and Analysis of Labyrinth Weirs. Part 2: Nappe Aeration, Instability, and Vibration B. M. Crookston, A.M. ASCE 1 and B. P. Tullis, M. ASCE 2 Abstract: Nappe behavior should be considered in the design of labyrinth weirs to ensure hydraulic optimization and to account for potential vibrations, pressure fluctuations, noise, and flow surging. Information regarding nappe aeration conditions (clinging, aerated, partially aerated, and drowned), nappe instability, and nappe vibrations for trapezoidal labyrinth weirs on a horizontal apron with quarter- and halfround crests (6 sidewall angle 35 ) is presented. Corresponding headwater ratio ranges and hydraulic behaviors associated with nappe aeration conditions are documented and discussed to aid in labyrinth weirs design, including design options directly related to nappe behavior (e.g., crest shape, crest roughness, vents, nappe breakers, notches, staged cycles). The effects of artificial nappe aeration (a vented nappe) on nappe behavior and discharge capacity are also discussed, including recommended placements of nappe breakers. Introduction Head-discharge Estimation A labyrinth weir (Fig. 1) is a type of polygonal overflow structure that has a distinct geometric shape (triangular, trapezoidal, or rectangular cycles in plan-view) and 1 Postdoctoral Researcher, Utah Water Research Laboratory, Dept. of Civil and Environmental Engineering, Utah State University, 8200 Old Main Hill, Logan, Utah Phone: (435) ; bcrookston@gmail.com 2 Associate Professor, Utah Water Research Laboratory, Dept. of Civil and Environmental Engineering, Utah State University, 8200 Old Main Hill, Logan, Utah Phone: (435) ; Fax: (435) ; blake.tullis@usu.edu

2 advantageous hydraulic characteristics. Relative to linear weirs, labyrinth weirs have lower operating upstream heads for a given design flood, a feature that can facilitate increased reservoir storage under base-flow conditions via a higher weir crest elevation without compromising flood discharge capacity. Labyrinth weirs are used as primary or auxiliary spillways (new and rehabilitated structures) to increase discharge capacity, regulate water levels (e.g., intake ponds, residential areas, rivers with high max/min flow ratios), or as a cost-effective, passive-control alternative to gated control structures. They are hydraulically most efficient at low heads (Crookston and Tullis, 2012a); as the upstream total head (H T ) increases, hydraulic efficiency declines and energy dissipation increases. Although labyrinth weir discharge coefficient,c d( ), values may be less than that of a linear weir (C d( ) ), the increase in the crest centerline length, L c, typically more than compensates, providing an increase in discharge capacity at higher heads relative to linear weirs (Crookston and Tullis, 2012a). Discharge coefficients and discharge rating curves for labyrinth weirs have been determined from physical models for over 50 prototype structures [e.g., Avon (Darvas, 1971), Dungo (Magalhães and Lorena, 1989), Hyrum (Houston, 1983), Keddara (Magalhães and Lorena, 1989), Lake Brazos (Tullis and Young, 2005), Lake Townsend (Tullis and Crookston, 2008), Ute (Houston, 1982), and Woronora (Darvas, 1971)]. As discussed in Part 1 (Crookston and Tullis 2012a), labyrinth weir discharge is a function of crest length (L c ), cycle geometry (Fig. 2) and configuration (arced or linear), approach flow conditions (in-channel or reservoir application), and hydraulic conditions [H T, tailwater submergence (Tullis et al., 2007), local submergence (Crookston and Tullis, 2012d)].

3 Labyrinth weirs produce complex flow patterns that influence nappe behavior (e.g., nappe aeration conditions, nappe instability, and nappe vibration), which influences the head-discharge relationship. Knowledge of labyrinth weir nappe behavior relative to labyrinth weir geometric designs and hydraulic conditions may help avoid undesirable labyrinth weir flow conditions [e.g., nappe vibration, excessive noise, nappe instabilities (also referred to as surging flow), and fluctuating pressure forces on the weir walls]. Current labyrinth weir design information (e.g., Crookston and Tullis 2012a, Tullis et al. 1995) does not adequately address nappe instability, the connection between nappe aeration conditions and C d( ), and nappe vibration. Nappe Behavior The jet of water that passes over a weir is referred to as the nappe. Nappe aeration conditions for a variety of linear weirs have been previously investigated and documented (e.g., Kandaswamy and Rouse 1957, Chow 1959). In this study, four different labyrinth weir nappe aeration conditions were observed: clinging, aerated, partially aerated, and drowned. Clinging refers to the nappe adhering to the downstream face of the weir wall at lower values of H T /P. An aerated nappe condition refers to a condition where an air cavity exists between the nappe and weir wall, and the nappe trajectory remains relatively constant. As H T /P increases, the size of the air cavity varies both spatially and temporally; it becomes non-uniform (distributed, isolated air cavities rather than one continuous air cavity along the weir wall) and unstable (air cavity size and location changes with time). This condition is referred to as partially aerated; this condition can occur with a constant nappe trajectory. Finally, the drowned nappe

4 aeration condition, featuring a thick nappe without an air cavity, occurs at higher values of H T /P. Nappe instability refers specifically to a nappe with an unsteady or oscillating trajectory (i.e., fluctuates locally between clinging and aerated). Observations indicated that nappe instability occurs primarily with the partially aerated nappe condition and less frequently with the aerated and drowned conditions. Clinging and aerated nappe conditions are well-established weir flow pattern descriptors. Partially aerated and unstable nappe conditions have also been noted by previous researchers (e.g., Willmore, 2004; Tsang, 1987); the Lux and Hinchliff (1985) design method included aerated, transitional (partially aerated), and suppressed (drowned) nappe behavior regions on their discharge coefficient design curves. The effects of water-air interaction should be considered in many hydraulic structure designs (Falvey, 1980); labyrinth weirs display both positive and negative hydraulic behaviors related to water-air interaction. For example, labyrinth weirs are excellent aeration control structures; design methods are presented by Wormleaton and Tsang (2000), Wormleaton and Soufani (1998), and Hauser (1996). However, labyrinth weirs with a sufficient fall distance may display a flow-induced vibrating nappe (Falvey, 1980) for H T /P 0.06 that may require remedial action, as was the case with Avon spillway (Metropolitan Water, Sewerage, and Drainage Board, 1980). At high heads, nappe instability may also require remedial action, depending upon the corresponding noise levels and fluctuation frequency. Yildiz and Üzücek (1996) and Hinchliff and Houston (1984) both recommend nappe breakers to suppress nappe instability; the Flamingo spillway (Las Vegas, Nevada, USA), for example, features nappe breakers.

5 The purpose of this study is to provide new information regarding labyrinth weir nappe aeration conditions, nappe instability, and nappe vibrations for quarter-round or half-round crest shapes in relation to the labyrinth weir discharge capacity as determined by the hydraulic design method developed by Crookston and Tullis (2012a). This was accomplished by analyzing experimental data for trapezoidal labyrinth weirs of various sidewall angles ( ) ranging from 6 to 35 with quarter- and half-round crest shapes. The influence of artificial aeration (vented nappe) was quantified relative to non-vented nappe flow, and the flow conditions when nappe instabilities occur were documented. Experimental Method To explore nappe aeration conditions and nappe instability, 20 laboratory-scale labyrinth weirs were fabricated from High Density Polyethylene Plastic (HDPE) and tested in a rectangular flume (1.2 m x 14.6 m x 1.0 m) at the Utah Water Research Laboratory (UWRL). Details of the tested model geometries are summarized in Table 1. The flume used a headbox/baffle system to provide relatively uniform approach conditions. The labyrinth weirs were installed on an elevated horizontal apron with a ramp for a gradual upstream floor transition. Details regarding experimental setup and instrumentation are presented in Crookston (2010). The test program evaluated the influence of artificial aeration (i.e., venting the nappe air cavity to atmosphere pressure). Each labyrinth weir model with a quarterround crest shape was tested with and without a nappe aeration apparatus consisting of an aeration tube for each labyrinth weir sidewall (l c ) [example shown in Fig. 3(A)]. Wedge shaped nappe breakers were tested at three different locations {upstream apex, downstream apex [Fig. 3(B)], and ~l c /2 [Fig. 3(C)]} and various location combinations

6 (e.g., upstream and downstream apex locations) for a labyrinth weir cycle. Digital photography and high-definition (HD) digital video recording were used extensively to document the hydraulic behaviors of the tested labyrinth weirs. Observations noted nappe behavior, nappe stability, nappe separation points along the weir crest, areas of local submergence, wakes, and harmonic or recurring hydraulic behaviors for all tested. Finally, a dye wand was used to investigate the complex 3-dimensional flow characteristics associated with labyrinth weirs. Experimental Results Nappe Conditions The discharge efficiency of a labyrinth weir is influenced by the aeration condition of the nappe. Nappe conditions may require remedial measures to address nappe vibrations, pressure fluctuation on the weir wall, noise, and nappe instabilities. Examples of the four different labyrinth weir nappe aeration conditions observed in this study are illustrated in Fig 4. The shape of the weir crest, weir height (P), H T, the depth and nature of the flow turbulence behind the nappe, the momentum and trajectory of the flow passing over the crest, and the pressure behind the nappe (sub-atmospheric for nonvented or atmospheric for vented nappes) all influence the aeration condition. While all four of the aeration conditions may not necessarily occur for all labyrinth weir cycle geometries or crest shapes, a labyrinth weir will generally transition from clinging to aerated, to partially aerated, and finally to drowned as H T increases. A clinging nappe [Fig. 4 (A)] is generally more efficient than an aerated nappe [Fig. 4(B)] because sub-atmospheric pressures develop on the downstream face of the weir. A partially aerated nappe [Fig. 4(C)] occurs at larger values of H T /P and does not

7 have a stable air cavity behind the nappe (varies temporally and spatially). The air cavity generally oscillates between adjacent labyrinth weir apexes, and the amount of the sidewall length that is aerated fluctuates; the air cavity may disappear and then reappear as the turbulence level and unsteady flow behavior behind the nappe fluctuate. Although the air cavity behavior can be highly dynamic and can cause fluctuating pressures on the downstream face of the weir, observations noted both stable and unstable nappe trajectories (depending upon weir geometry and flow conditions) for the partially aerated nappe condition. For a stable nappe, the partially aerated condition was observed to have minimal influence on the nappe trajectory. Further increases in H T cause the nappe to shift from partially aerated to drowned [Fig. 4(D)]. The drowned nappe aeration condition features a thick nappe without an air cavity. Ranges of H T /P that correspond to observed nappe aeration condition for quarter-round and half-round labyrinth weir crests are presented in Figs. 5 and 6, respectively. For H T /P 0.05, clinging conditions were observed for a P = 0.3m laboratoryscale labyrinth weirs with a smooth quarter round crest shape. For the same H T /P range, a P = 1m, quarter-round crested labyrinth weir had an aerated (non-vibrating) nappe, suggesting that surface tension and/or other size scale effects may influence nappe behavior. Avon dam (P = 3.05 meters) produced an aerated nappe for the same H T /P range (specifically 0.01 H T /P 0.06) with notable nappe vibrations. This suggests that in addition to flow conditions at the crest (e.g., turbulence), fall height influences nappe vibrations. Successful counter measures applied to a physical model of Avon Dam to eliminate nappe vibration included rounding the downstream edge of the crest (clinging nappe), nappe breakers, and adding roughness elements to the crest (Metropolitan Water,

8 Sewerage, and Drainage Board, 1980). Notched (sidewall or apex) or staged cycles (a portion of weir length set at a lower crest elevation) may also be employed to avoid H T /P 0.06 under base flow conditions (e.g., Boyd Lake emergency spillway, Lake Townsend spillway). For quarter-round crest shapes, the nappe condition shifts from aerated to partially aerated at 0.25 H T /P 0.29, depending on ( = 8 10 have the largest H T /P aeration range). The drowned condition begins at H T /P ~ 0.3 for = 6. As increases the H T /P associated with inception of the drowned condition increases. For 12, the drowned condition begins at H T /P ~ 0.5. As can be seen in Figs. 5 and 6, nappe behavior and corresponding H T /P ranges vary between the half- and quarter-round crest shape labyrinth weirs. The C d( ) values in the clinging condition range are greater than those in the aerated or partially aerated range, as exhibited by the abrupt decrease in C d( ) as the nappes transitioned from clinging to aerated or partially aerated. Labyrinth weirs with were observed to shift directly from a clinging nappe to a partially aerated nappe and the aerated nappe condition occurred only briefly for the = 35 at H T /P~0.15. Nappe Instability Figs. 5 and 6 also present the ranges of H T /P when nappe instability occurred ( 12 for quarter-round and half-round crests). Nappe instability (also termed flow surging ) refers to a nappe that has a temporally varying trajectory. Nappe instability can cause significant variation in the size of the air cavity behind the nappe, and in some instances, can cause fluctuations between aerated and drowned nappe behavior as

9 illustrated in Fig. 7. Nappe instability can also cause small local fluctuations in Q along the weir, significant noise ( flushing sound), and increased flow turbulence in the outlet cycle. Nappe instability (at the laboratory scale) is typically low frequency phenomenon; however, the frequency, magnitude, and the extent of the H T /P range over which it occurs increases with increasing ( = 35º was the maximum labyrinth weir sidewall angle tested). Nappe instability was negligible or non-existent for 12º for half- and quarterround crest shape labyrinth weirs. Nappe instability can affect complete labyrinth weir cycles (two sidewalls and the downstream apex); nappe oscillations may be synchronized or variable between adjacent labyrinth weir cycles. During testing, 3-dimenional unsteady flow conditions were observed downstream of the sidewalls using dye tracking. Turbulent mixing in that region created air bulking in the flow around the nappe. Explorations in the downstream cycle with dye noted turbulent, helical flow currents traveling relatively parallel and adjacent to the weir sidewalls. The observed fluctuations of the nappe and turbulent mixing all appeared to contribute to dynamic pressure conditions behind the nappe. Under these conditions, the nappe was drawn toward the weir wall and there appeared to be a critical point when air and/or water were drawn behind the nappe from the adjacent flow, creating an audible flushing noise. Relatively large quantities of fluid were introduced in bursts, resulting in the abrupt change of nappe trajectory. At higher flow rates, air cavity formation and nappe instability diminished (increased turbulent mixing) and artificial aeration or venting of the nappe was found to decrease nappe instability and noise. Despite artificial aeration, nappe instability was still observed to occur (to a lesser degree) for 20 in the partially aerated (quarter-round

10 and half-round crest shapes) and drowned (quarter-round crest shape only) nappe conditions, indicating that aeration vents are a less effective remedy. Nappe instability was not observed to occur for < 12 and < 10 for quarter- and half-round crest shapes, respectively. The net effect of nappe instability on prototype structural loading is unclear; however, avoiding these ranges in labyrinth weir design is suggested as undesirable levels of vibration, pressure fluctuation, and noise may result in structural damage to spillway components, especially if nappe instability frequencies correspond to the natural frequencies of the structure. Artificial Nappe Aeration Artificial aeration (venting the nappe to atmosphere) had a negligible effect on the discharge capacity of quarter-round labyrinth weirs (~0.5% to 1.7%). With respect to discharge efficiency, venting a half-round labyrinth weir crest (using aeration vents or nappe breakers) reduces the range of H T /P for the clinging nappe aeration condition, thereby reducing flow efficiency at low heads and partially diminishing the benefit of a half-round crest shape. It is suggested that nappe breakers (also termed flow splitters) be designed with a triangular-type cross-section (plan view) and be placed on the downstream apexes with the point oriented into the flow (similar non-obstructive shapes may also be used to split the flow for aeration). The leading edge should be protected to minimize the potential damage from debris impact and debris collection. This orientation produced no measurable reduction in the labyrinth weir discharge capacity, which is not the case for nappe breakers located on the sidewall (sidewall nappe breaker locations near the downstream apex or sidewall midpoint were evaluated). Downstream apex placement

11 minimizes the number of required nappe breakers and also reduces the number of potential debris-collection locations. Nappe breakers have previously been recommended at 0.08 to 0.1 l c from the downstream apex (Hinchliff and Houston, 1984). However, as the streamlines passing over the labyrinth weir crest change with Q, nappe breakers placed on the weir sidewall will only be aligned with the approach flow for a small range of discharges. Although they will likely aerate the nappe effectively, nappe breakers that are not aligned with the approach flow will act as head loss devices at other discharge conditions and will decrease the efficiency of the weir. Summary and Conclusions Nappe behavior should be considered in the design of labyrinth weirs, particularly to optimize the hydraulic performance of the weir (e.g., crest shape selection) and to determine if any remedial actions (e.g., notched or staged cycles, crest roughness, nappe breakers, etc.) are required to address nappe vibrations and/or nappe instability. This study provides new hydraulic information and insights regarding nappe behavior, nappe vibrations, nappe instability, and nappe ventilation (e.g., nappe breakers, aeration vents) to be used in combination with the labyrinth weir design method presented in Crookston and Tullis (2012a). Twenty physical models (Table 1) were used to determine the influence of these phenomena on labyrinth weir discharge capacity. The H T /P ranges for clinging, aerated, partially aerated, and drowned nappe behavior conditions were identified in Figs. 5 and 6. These regions are crest-shape specific and vary nonlinearly with ; they were discussed in detail to clearly characterize nappe behavior. Nappe behavior conditions also account for changes in C d( ) ; a clinging nappe is more efficient than an aerated, partially aerated, or drowned nappe. The

12 influence of artificial aeration (vented nappe via nappe breakers or aeration vents) on discharge capacity was found to be negligible (~0.5% to 1.7%), relative to the non-vented nappe conditions, for quarter-round crest shapes. For half-round labyrinth weirs, aeration vents or nappe breakers limit the operating range of the clinging nappe and therefore diminish the increased hydraulic efficiency provided by the half-round crest shape at lower heads. The artificially aerated (vented) half-round crest labyrinth weirs performed hydraulically similar to the quarter-round crest labyrinth weirs. If nappe breakers are used, it is recommended that nappe breakers be placed on the downstream apexes to minimize head loss. Physical modeling also identified regions of nappe instability (flow surging) for 12 for quarter and half-round crest shapes. During nappe instability, observations noted the presence of sweeping turbulent flow exiting the downstream cycle, a fluctuating water volume behind the nappe, dynamic pressures behind the nappe, and turbulent mixing. For half-round crest shapes, nappe instability was limited to the partially aerated nappe condition. Nappe instability occurred to a lesser degree for 20 in the partially aerated (quarter-round and half-round crest shapes) and drowned (only quarter-round crest shape) nappe conditions when the nappe was vented. The net effect of nappe instability on prototype structures is unclear, but it is recommended that these ranges be avoided in labyrinth weir design, as high levels of vibration, pressure fluctuation, and noise may produce negative structural and/or environmental conditions. Acknowledgements Funding for this study was provided by the State of Utah and the Utah Water Research Laboratory (Utah State University).

13 Nomenclature A Inside apex width A c B C d( ) C d(90 ) g h H T H T /P L c l c L c-cycle Apex center-line width Sidewall angle Length of labyrinth weir (Apron) in flow direction Discharge coefficient, data from current study Discharge coefficient for linear weir Acceleration constant of gravity Depth of flow over the weir crest Total upstream head measured relative to the weir crest Headwater ratio Total centerline length of labyrinth weir Centerline length of weir sidewall Centerline length for a single labyrinth weir cycle M Magnification ratio, L c-cycle /w N P Q V w W Number of labyrinth weir cycles Weir height Discharge over weir Average cross-sectional flow velocity upstream of weir Width of a single labyrinth weir cycle Total width of a labyrinth weir w/p Cycle width ratio

14 References Chow, V.T. (1959). Open-channel Hydraulics. McGraw-Hill, New York, NY. Crookston, B. M. (2010). Labyrinth weirs. Ph.D. dissertation, Utah State Univ., Logan, UT. Crookston, B.M. and Tullis, B.P. (2012a). Hydraulic design and analysis of labyrinth weirs. Part 1: Discharge relationships. J. Irrig. Drain. Engr., ASCE, #(#). Posted ahead of print (date). Crookston, B.M. and Tullis, B.P. (2012b). Discharge efficiency of reservoirapplication-specific labyrinth weirs. J. Irrig. Drain. Engr., ASCE, 138(6), Crookston, B.M. and Tullis, B.P. (2012c). Arced labyrinth weirs. J. of Hydr. Engrg., ASCE, 138(6), Crookston, B.M. and Tullis, B.P. (2012d). Labyrinth weirs: Nappe interference and local submergence. J. Irrig. Drain. Engr., ASCE, 138(8), Darvas, L. (1971). Discussion of performance and design of labyrinth weirs, by Hay and Taylor. J. of Hydr. Engrg., ASCE, 97(80), Falvey, H. (1980). Practical experiences with flow-induced vibrations, edited by Naudascher, E., and Rockwell, D., Springer-Verlag, Berlin/Heidelberg/New York. Hauser, G. (1996). Design of aerating weirs. EPRI Report TR , Dec. Prepared by TVA for the Electrical Power Research Institute, Palo Alto, Calif. Hay, N., & Taylor, G. (1970). Performance and design of labyrinth weirs. J. of Hydr. Engrg., ASCE, 96(11),

15 Hinchliff, D., and Houston, K. (1984). Hydraulic design and application of labyrinth spillways. Proc. 4 th Annual USCOLD Lecture. Houston, K. (1982). Hydraulic model study of Ute dam labyrinth spillway. Report No. GR-82-7, U.S. Bureau of Reclamation, Denver, CO. Houston, K. (1983). Hydraulic model study of Hyrum dam auxiliary labyrinth spillway. Report No. GR-82-13, U.S. Bureau of Reclamation, Denver, CO. Kandaswamy, P. and Rouse, H. (1957). Characteristics of flow over terminal weirs and sills. J. Hydr. Div., ASCE, no HY4, 1345 (83). Lux III, F. and Hinchliff, D. (1985). Design and construction of labyrinth spillways. 15 th Congress ICOLD, Vol. IV, Q59-R15, Magalhães, A., & Lorena, M. (1989). Hydraulic design of labyrinth weirs. Report No. 736, National Laboratory of Civil Engineering, Lisbon, Portugal. Metropolitan Water, Sewerage and Drainage Board, (1980). Investigation into spillway discharge noise at Avon Dam. ANCOLD Bulletin No. 57, Paxson, G., D. Campbell, and J. Monroe (2011). Evolving design approaches and considerations for labyrinth spillways, Proc. of USSD conference, Denver, CO. Tsang, C. (1987). Hydraulic and aeration performance of labyrinth weirs. Ph.D. dissertation, University of London, U.K. Tullis, B. and Crookston, B. (2008). Lake Townsend dam spillway hydraulic model study report. Utah Water Research Laboratory, Logan, UT. Tullis, B. and Young, J. (2005). Lake Brazos dam model study of the existing spillway structure and a new labyrinth weir spillway structure. Utah Water Research Laboratory, Logan, UT.

16 Tullis, B., Young, J., & Chandler, M. (2007). Head-discharge relationships for submerged labyrinth weirs. J. of Hydr. Engrg., ASCE, 133(3), Tullis, P., Amanian, N., & Waldron, D. (1995). Design of labyrinth weir spillways. J. of Hydr. Engrg., ASCE, 121(3), Willmore, C. (2004). Hydraulic characteristics of labyrinth weirs. M.S. Report, Utah State Univ., Logan, UT. Wormleaton, P. and Soufiani, E. (1998). Aeration performance of triangular planform labyrinth weirs. J. Env. Engr., ASCE, 124(8), Wormleaton, P. and Tsang, C. (2000). Aeration performance of rectangular planform labyrinth weirs. J. Env. Engr., ASCE, 127(5), Yildiz, D. and Üzücek, E. (1996). Modeling the performance of labyrinth spillways. Hydropower, 3(71-76).

17 Table 1. Physical model test program Model P L c-cycle L c-cycle /w w/p N Crest Type Orientation ( ) ( ) (mm) (cm) ( ) ( ) ( ) ( ) ( ) ( ) HR Trap Inverse QR, HR Trap Normal QR, HR Trap Normal QR, HR Trap Normal QR, HR Trap Normal QR, HR Trap Normal QR, HR Trap Normal QR Trap Normal QR Trap Normal QR Trap Normal QR, HR Trap Normal QR, HR - - Linear configuration was used for all model orientations

18 Journal of Irrigation and Drainage Engineering. Submitted July 6, 2011; accepted October 9, 2012; posted ahead of print October 11, doi: /(asce)ir List of Figures Fig. 1. Example of a labyrinth weir (courtesy of Greg Paxson and Schnabel Engineering) Fig. 2. Labyrinth weir schematic, including apex notch, sidewall notch, and nappe breaker examples Fig. 3. Aeration tube apparatus for N = 2 (A) and nappe breakers located on the downstream apex (B) and on the sidewall (C) Fig. 4. Examples of Clinging, Aerated (B), Partially Aerated (C), and Drowned (D) nappe aeration conditions observed for trapezoidal labyrinth weirs Fig. 5. Nappe aeration and instability conditions for labyrinth weirs with a quarter-round crest Fig. 6. Nappe aeration and instability conditions for labyrinth weirs with a half-round crest Fig. 7. Illustration half-round crest labyrinth weir nappe instabilities [nappe fluctuating between aerated (a) and drowned (b), H T /P=0.4, = 20º]

19 Journal of Irrigation and Drainage Engineering. Submitted July 6, 2011; accepted October 9, 2012; posted ahead of print October 11, doi: /(asce)ir

20 Journal of Irrigation and Drainage Engineering. Submitted July 6, 2011; accepted October 9, 2012; posted ahead of print October 11, doi: /(asce)ir

21 Journal of Irrigation and Drainage Engineering. Submitted July 6, 2011; accepted October 9, 2012; posted ahead of print October 11, doi: /(asce)ir

22 Journal of Irrigation and Drainage Engineering. Submitted July 6, 2011; accepted October 9, 2012; posted ahead of print October 11, doi: /(asce)ir

23 Journal of Irrigation and Drainage Engineering. Submitted July 6, 2011; accepted October 9, 2012; posted ahead of print October 11, doi: /(asce)ir

24 Journal of Irrigation and Drainage Engineering. Submitted July 6, 2011; accepted October 9, 2012; posted ahead of print October 11, doi: /(asce)ir

25 Journal of Irrigation and Drainage Engineering. Submitted July 6, 2011; accepted October 9, 2012; posted ahead of print October 11, doi: /(asce)ir