FREE-SURFACE AND SEEPAGE BUBBLY FLOWS ON A GABION STEPPED SPILLWAY WEIR: EXPERIMENTAL OBSERVATIONS

E-proeedings of the 36 th IAHR World Congress FREE-SURFACE AND SEEPAGE BUBBLY FLOWS ON A GABION STEPPED SPILLWAY WEIR: EXPERIMENTAL OBSERATIONS GANGFU ZHANG (1), & HUBERT CHANSON (2) (1) The University of Queensland, Shool of Civil Engineering, Brisbane QLD 472, Australia e-mail: gangfu.zhang@uqonnet.edu.au (2) The University of Queensland, Shool of Civil Engineering, Brisbane QLD 472, Australia e-mail: h.hanson@uq.edu.au ABSTRACT Gabion stepped spillways are presented as a viable option for low to medium head designs. The material ontributes to stability, low ost, flexibility, porosity and noise redution. The steps also enhane energy dissipation, and redue the requirement of a stilling basin. This paper onstitutes a systemati study of the free-surfae and seepage bubbly flows using a ombination of phase-detetion probe and high-speed video amera. The two-phase flow properties and turbulene harateristis in the free-surfae flow were doumented. The bubbly motion through the gabion material was analysed. The results demonstrated evidene of strong air-water mixing between the free-surfae and seepage flows, and highlighted a modified avity flow pattern as a result. Keywords: Gabion stepped spillways, Seepage flow, Air-water flow, Physial modelling 1. INTRODUCTION Stepped spillways have been used as flood release failities for several enturies (Chanson 22). The steps provide enhaned energy dissipation and redue the need of a downstream stilling struture. The development of new onstrution tehniques and materials in the past several deades has led to a regained interest in stepped spillway design and researh. The flow above a stepped spillway is highly turbulent (Rajaratnam 199, Chanson and Toombes 22). At low flows, the water asades down the steps as a series of free-falling nappes (nappe flow regime). At intermediate flows, a transition flow takes plae, and the flow appears haoti with energeti droplet projetions. At large disharges, the water skims over the pseudo-bottom formed by the step edges, and signifiant momentum exhange between the main and avity flows takes plae (skimming flow regime). A distintive feature of flow down a stepped spillway is the apparition of white water. The turbulent stresses next to the air-water interfae lead to unontrolled air-entrainment in the forms of air bubbles and water droplets. This loation is known as the ineption point and annot be exatly determined. The exhange between water and the atmosphere leads to intense air-water mixing, turbulene modulation and a omplex flow pattern. For low to medium head stepped weirs, the gabions may be a suitable onstrution material, whih have the advantages of stability, low ost, flexibility, porosity and noise redution (Agostini et al. 1987, Boes and Shmid 23, Zhang and Chanson 214). The flow patterns and energy dissipation performane on suh spillways were investigated by Peyras et al. (1992) and Wuthrih and Chanson (214). The additional porosity in the steps may result in a modified avity reirulation pattern. The interations between seepage and free-surfae flow were disussed in Kells (1993). Herein physial modelling was onduted to investigate the bubbly flow above a large sale 1:2H gabion stepped spillway physial model. The two-phase flow properties in the mainstream, avity and seepage flows were doumented using a ombination of dual-tip phase-detetion probe measurements and high-speed video footage. The study aims to provide a detailed haraterization of the turbulent air-water flow and highlight the interations between seepage and avity flow motions. 215, IAHR. Used with permission / ISBN 978-9-824846--1 6624 1

E-proeedings of the 36 th IAHR World Congress, Figure 1. Gabion stepped weirs Left: ourtesy of Tony Marszalek; Right: ourtesy of Offiine Maaferri 2. PHYSICAL MODELLING, EXPERIMENTAL FACILITY AND INSTRUMENTATION 2.1 Dimensional onsiderations The omplex turbulent air-water flow experiened above a stepped hute onstitutes a great hallenge in terms of physial modelling. On a stepped spillway, the dimensional analysis implies that relevant air-water flow properties must satisfy (Carosi and Chanson, 26): C,, F, u' d,... x y d q w w D H g 4 w W k s ' F 1 (,,,,,,,,,Po...) d d h w d d g h 3 w 3 where C is the void fration, is the interfaial veloity, u is a harateristi turbulene veloity, F is the bubble ount rate, d is the ritial depth, is the ritial veloity, h is the step height, qw is the disharge per unit width, DH is the hydrauli diameter, x, y are the longitudinal and normal oordinates, ρw, μw are the density and dynami visosity of water, σ is the surfae tension of water, W is the hannel width, θ is the hannel slope with respet to the horizontal, ks is the equivalent sand roughness, and Po the porosity of the gabion material. In Equation [1], the air-water flow properties at a given loation are expressed as a funtion of dimensionless terms inluding the Froude, Reynolds and Morton numbers (4 th, 5 th and 6 th terms). For eah onfiguration, the invariants were ρw, μw, g, σ, θ, ks, h, and W. In turn the Morton number was an invariant. Equation [1] may be further simplified: C,, F, u' d,... x y d F 1 (,,, d d h qw w DH,,...) g h 3 w Herein a Froude similitude was adopted based on Equation [2]. Note that a true dynami similarity mandates all dimensionless numbers to be equal in both model and prototype, whih ould not be satisfied under urrent experimental onditions. The experiments were onduted in a large-size physial model operating at high Reynolds numbers to minimize any potential sale effets. 2.2 Experimental faility and instrumentation New experiments were onduted in a large size gabion stepped weir physial model at the University of Queensland. The same faility was used by Wuthrih and Chanson (214). The test setion was.52 m wide and onsisted of a broad-rested weir followed by 1 idential steps (h =.1 m, l =.2 m) made of gabion boxes. The gabions were.3 m long,.1 m high and.52 m wide, made of 14 mm sieved gravels. The gravel material had a dry density of 1.6 tonnes/m 3, a porosity of.35.4, and a hydrauli ondutivity between 1.1 2.3 1-1 m/s. A photo of the experimental faility is provided in Figure 2. [1] [2] 26625 215, IAHR. Used with permission / ISBN 978-9-824846--1

E-proeedings of the 36 th IAHR World Congress Figure 2. Gabion stepped spillway at the University of Queensland The flow rate was dedued from total head measurement upstream of the test setion using the alibration of Felder and Chanson (212). Air-water properties in the overflow were reorded with a dual-tip phase-detetion probe (Ø =.25 mm). The probe sensors were exited by an air bubble detetor (AS2524) and sanned at 2 khz per sensor for 45 s. The probe was mounted above a trolley whih traversed along the hannel enterline. The vertial movement was ontrolled by a fine adjustment travelling mehanism attahed to a Mitutoyo digital sale with an auray of ±.1 mm. The bubbly flow motion through the gabion material was doumented using a ombination of high shutter speed digital imagery (1/1, 1/8, s) and high speed video reordings up to 1, fps (Casio EX-ZR2). Flow rates between.52 and.147 m 2 /s were investigated. Partiular emphases were plaed upon the transition and skimming flows whih inorporated a rih amount of air. The flow patterns were observed through the perspex hannel sidwalls. Air-water measurements were undertaken at the step edges and in the avities. Bubble trajetories inside the gabion material were traked at representative loations using a high speed video amera through the sidewall. 3. EXPERIMENTAL OBSERATIONS 3.1 Presentation Four distint flow regimes were identified on the gabion stepped spillway, depending on the dimensionless disharge d /h where d = (q 2 /g) 1/3 is the ritial flow depth, and q is the flow rate per unit width. For very small disharges (d/h <.2), a porous flow regime was observed. The flow seeped from one gabion box to the next, leaving a short seepage fae above eah step tread whih terminated before reahing the step edge. A fast water jet was seen shooting out from the last step rise to fulfill ontinuity. A slight inrease in disharge above d/h =.2 resulted in water seeping through the step rise into the next gabion, and a further inrease in disharge pushed the seepage line forward until a small amount of overflow ourred past the step edge. For small disharges up to d/h <.5 to.6 a nappe flow regime was observed (Figure 3A). The gabions were saturated in the bak and overflow ourred past the step edges. From a bystander s point of view, the flow resembled a series of free-falling nappes asading down the stepped hute. Above the step tread a small water pool was present with a large ventilated avity above, and no reirulation was observed. Similar findings were disussed by Wuthrih and Chanson (214). For.6 < d/h <.9 a transition flow regime was observed. The overflow was haraterized by strong turbulene oupled with vigorous droplet ejetions and the free-surfae appeared rough and irregular. The avities were partially filled with alternating air avity sizes from small to medium. A large amount of air was entrained in the downstream portion of the flow beause of the extreme flow instability and turbulene. For large disharges d/h >.9 a skimming flow was observed (Figure 3B). The upstream flow appeared smooth and glassy with approximately parallel streamlines. The ineption point of free-surfae aeration was well defined and learly observable from the side of the hannel. Downstream, the flow was dominated by a omplex air-water mixing proess and appeared highly turbulent. The step avities were filled with a two-phase flow mixture, but ontained a lear water ore above the 1 st third of the step tread, whih was absent in onventional impervious stepped spillway strutures (Matos 21, Gonzalez and Chanson 24). 215, IAHR. Used with permission / ISBN 978-9-824846--1 6626 3

E-proeedings of the 36 th IAHR World Congress, (A) Nappe flow, d /h =.27, Re = 5.6 1 4 (B) Skimming flow, d /h = 1.2, Re = 5.2 1 5 Figure 3. Flow patterns above a gabion stepped weir For all disharges, some air bubbles were transported in the seepage through the gabion materials. A harateristi twophase flow pattern developed one the gabions beame fully saturated (Figure 4A). Streams of air bubbles entered the gabion material through the downstream half of the step tread, below the region of shear layer impat above the step tread. Slow motion videos identified these as either individual or lusters of bubbles. The bubbly movement was fastest next to the step edge, and beame subdued towards the bak of the gabion material. The majority of air bubbles aelerated through the upper half of the step rise to enter the next step avity, while a small number of bubbles reirulated down, bak and upwards before returning to the avity above. This typial pattern implied the existene of large positive pressure on the downstream end of the step tread and a subpressure zone next to the upper part of the step rise, onsistent with pressure distributions reorded on impervious stepped faes (Sanhez-Juny et al. 27). A detailed examination of the video footages revealed bubbles reirulating, breaking up and oalesing in the gabion material. A broad spetrum of bubble sizes and shapes ranging from pseudo-ellipsoidal to highly distorted and elongated existed. The ombination and onstritions of the gravels modified the shear stress distributions inside the gabion material, resulting in these proesses to take plae. The bubbly movement highlighted some interations between the overflow and seepage. Suh interation was most intense next to the step edge (Figure 4B). The majority of air bubbles were aelerated upwards and then in the streamwise diretion immediately past the step rise, surrounding a lear water ore formed above the first third of the step tread. Suh a lear water ore was previously reported for rough impervious steps (Gonzalez et al. 28, Bung and Shlenkhoff 21), but never for smooth impervious steps. The additional porosity allowed a redution of form drag in the downstream avity and aused the reirulating fluid to be modified ompared to traditional impervious steps. This effet was known as ventilation and was doumented in monophase flows (Naudasher and Rokwell 1994). Additionally, the step roughness may indue some turbulene manipulation in the developing boundary layer, similar to riblets and d-type roughness (Djenidi and Antonia 1995). (A) Charateristi two-phase flow pattern (B) Bubbly motion inside gabions flow from left to right, 1/5,435 s Figure 4. Two-phase skimming flow above a gabion stepped spillway 46627 215, IAHR. Used with permission / ISBN 978-9-824846--1

E-proeedings of the 36 th IAHR World Congress 4. TWO-PHASE FLOW PROPERTIES 4.1 Free surfae flow On a stepped hute, the turbulene interations next to the free-surfae ause a large amount of air to be entrained. Downstream of the ineption point, the void fration profile above eah step edge exhibited an inverted S-urve, typial of skimming flows (Chanson and Toombes 22, Gonzalez and hanson 28). Typial results are presented in Figure 5A, where C is the void fration, y is the distane normal to the pseudo-bottom, and y9 is the height for C =.9. Comparison between the data and an analytial diffusion equation developed by Chanson and Toombes (22) for skimming flows showed an exellent agreement. A subtle observation in Figure 5A is the non-zero void fration at y =, resulting from the bubbly flux through the gabion materials. y/y9 1.6 1.4 1.2 1.8.6.4.2 Step edge 5 Step edge 6 Step edge 7 Step edge 8 Step edge 9 Step edge 1 Step edge 7 Theory.1.2.3.4.5.6.7.8.9 1 C y/y9.8 Step edge 5.75 Step edge 6 Step edge 7.7 Step edge 8.65 Step edge 9.6 Step edge 1.55.5.45.4.35.3.25.2.15.1.5 2.5 5 7.5 1 12.5 15 17.5 2 22.5 F d / (A) oid fration distributions - d /h = 1., Re = 4. 1 5 (B) Bubble ount rate distributions d /h = 1., Re = 4. 1 5 (C) oid fration distribution inside step avity d /h = 1.3, Re = 5.9 1 5, step edges 7-9 Figure 5. Two-phase flow properties above a gabion stepped spillway The bubble ount rate F is defined as half the number of air-water interfaes deteted by the probe sensor per seond. For a given interfaial veloity, F is proportional to the speifi interfae area (Chanson 22). Typial bubble ount rate 215, IAHR. Used with permission / ISBN 978-9-824846--1 6628 5

E-proeedings of the 36 th IAHR World Congress, distributions above the step edge are presented in dimensionless terms in Figure 5B, where = (g d).5 is the ritial veloity. The data exhibited a distint bell shape in the free-surfae flow (y > ), with a maximum value found in the midwater olumn (.3 < y/y9 <.4) orresponding to a void fration about.4.5 as previously reported (Chanson and Toombes 22, Felder and Chanson 211). Below the pseudo-bottom, both visual observations and phase-detetion probe measurements indiated a drastially lesser extent of aeration. Typial void fration distribution inside step avities are presented in Figure 5C, where x and y are the distanes along and normal to the step tread respetively. The data showed typial void frations less than 1% below the pseudo-bottom and highlighted a lear water region above the first half of the step avity, as disussed in Setion 3. The interfaial veloity () and turbulene intensity (Tu) distributions above step edges are presented in Figure 6 in dimensionless terms, where 9 is the veloity at y = y9. Both data presented some self-similar shapes. The veloity profiles were modelled losely using a 1/1 power law, similar to some previous studies (e.g. Wuthrih and Chanson 214). The shape of the veloity data highlighted a developing shear layer in the wake of the step edge (Figure 4A). The turbulene intensity is defined as the ratio between the standard deviation to the mean interfaial veloity, and was alulated based upon a ross-orrelation tehnique between the probe signals (Chanson and Toombes 22). The turbulent intensity value is refletive of the extent of turbulent flutuations at different loations aross the flow olumn. The maximum Tu value was typially reorded at.3 < y/d <.4, lose to the loation of the maximum bubble ount rate where C.5. The loation orresponded to approximately the middle of the shear layer. Overall larger turbulene levels were reorded above the last step edge (step edge 1), whih may be linked with the interation between the overflow and the inreased seepage oming out of the last step rise. 1.8 1.5 1.2 Step edge 7 Step edge 8 Step edge 9 Step edge 1 1/1 power law / 9 = 1.9.8.7.6 Step edge 5 Step edge 6 Step edge 7 Step edge 8 Step edge 9 Step edge 1 y/y9.9 y/d.5.4.6.3.3.2.4.6.8 1 1.2 / 9.2.1.2.4.6.8 1 1.2 1.4 1.6 1.8 Tu (A) Dimensionless veloity profiles d /h = 1.3, Re = 5.9 1 5 (B) Turbulene intensity profiles d /h = 1., Re = 4. 1 5 Figure 6. eloity and turbulene intensity profiles on a gabion stepped spillway 4.2 Seepage flow High-speed movies were analysed to obtain the bubble trajetories, veloities and sizes in the gabion material. Figure 7 desribes typial bubbly veloity distributions inside the gabion material, where X and Y are the horizontal and vertial oordinates respetively. The veloity analysis was repeated twie. In the first stage, eah veloity vetor was averaged over 2 (±1) bubbles. The results highlighted a region of signifiant bubbly motion next to the step orner (Figure 7). Maximum veloities up to 1 m/s were observed, with instantaneous veloities reahing 2 m/s. The average bubble veloities were smaller elsewhere inside the gabion, and were smallest below the step orner. The bubbles trajetories were typial for both transition and skimming flows, exept below the step orner. In a skimming flow, the positive pressure on the first third of the step tread (i.e. lear water ore) was large enough to drive some bubbles bak into the previous gabion box, while in a transition flow they travelled forward in the flow diretion. Some reirulation was also observed below the middle of the step, driven by an impating shear layer above. Figure 7C illustrates the veloity distributions obtained in the seond pass, where 1 (±5) bubbles were averaged to obtain eah veloity vetor. The seepage veloities aelerated in average through gabion boxes 6 8, and reahed a maximum mean veloity of.8 m/s at step edge 8. The seepage next to the step edge appeared to aelerate more than elsewhere inside the gabion beause of diret interation with the spillway overflow. A lose examination revealed subtly distintive flow paths in different steps (step 7 vs 8). While this may be a result of physial onstritions (i.e. gravel layout et), it may also be an indiation of varying pressure distributions on the step faes, and that uniform equilibrium onditions were not ahieved. 66629 215, IAHR. Used with permission / ISBN 978-9-824846--1

E-proeedings of the 36 th IAHR World Congress -1-1 1 step edge 8 1 step edge 8 2 2 3 3 Y (m) 4 5 6 7 8 9 avg (m/s).5.2.35.5.65.8.95 1.1 Y (m) 4 5 6 7 8 9 avg (m/s).5.2.35.5.65.8.95 1.1 1-2.5 2.5 5 7.5 1 12.5 15 17.5 2 22.5 X (m) 1-2.5 2.5 5 7.5 1 12.5 15 17.5 2 22.5 X (m) (A) Step 8, d /h =.7, Re = 2.3 1 5, average of 2±1 samples (B) Step 8, d /h = 1.3, Re = 5.9 1 5, average of 2±1 samples 5 1 Step edge 6 Step edge 7 avg (m/s).5.2.35.5.65.8.95 1.1 Y (m) 15 2 Step edge 8 25 3 1 2 3 4 5 6 7 X (m) (C) Step 6-8, d/h = 1.3, Re = 5.9 1 5, average of 1±5 samples Figure 7. Average bubbly seepage veloity inside gabion material The veloity flutuations inside the gabion material are presented in Figure 8, in terms of the veloity differenes (75 25) and (9 1), where the subsript denotes the veloity perentile. (9 1) and (75 25) are respetively the differenes between the ninth and first deiles and between the third and first quartiles of the data ensemble. Assuming a Gaussian distribution, (9 1) and (75 25) would be equal to 2.66 and 1.3 times the standard deviation respetively. In Figure 8, the marker sizes are proportional to veloity flutuations. The distribution of veloity flutuations showed relatively large veloity flutuations throughout the entire gabion materials, with the largest veloity flutuations observed next to the step edges (up to.4 m/s). Lower quantitative values were observed below the step orner and deep inside the gabion box. In general, relatively higher levels of veloity flutuations were reorded next to the gabion-avity interfaes. The findings were onsistent for both transition and skimming flows and agreed with visual observations. An inrease in overflow disharge did only result in small hange in veloity flutuations. Inside the gabions, the bubbles showed a variety of shapes and sizes aused by an unstable seepage motion oupled with interations with the avity fluid above. For a transition and a skimming flow rate, bubble sizes were dedued from detailed frame-by-frame video analyses with their distributions drawn in Figure 8. The bubbles were sampled aross the entire gabion and their sizes were measured perpendiular to the seepage diretion. For both flow regimes, Figure 9 reorded a skewed distribution with a preponderane of smaller bubble sizes. The dominant bubble size was between.6 and.9 mm in diameter. isual observations also identified oasional ourrenes of large bubbles (> 5mm) that were 215, IAHR. Used with permission / ISBN 978-9-824846--1 663 7

E-proeedings of the 36 th IAHR World Congress, mostly trapped in the interstitial gaps between gravels. The study ignored bubbles whih oalesed or travelled in lusters. A dispersion analysis was performed on the bubble trajetories next to step edge 8. Figure 1 plots the spatial deviations in the streamwise and normal diretions as a funtion of elapsed time. A turbulent diffusion pattern was observed for t-tstart <.1 s, whih may be simulated using a random walk model (Chanson 24). Another ombination of disharge, loation, and layout of the gravels may result in a different dispersion pattern. 9 1 (m/s) 75 25 (m/s) (A) 75 25 (B) 9 1 Figure 8. eloity flutuations in gabion box 8 d /h = 1.3, Re = 5.9 1 5.45.45.4 number of bubbles: 969.4 number of bubbles: 337.35.35.3.3 PDF.25.2 PDF.25.2.15.15.1.1.5.5..3.6.9 1.2 1.5 1.8 2.1 2.4 2.7 3 3.3 Size (mm)..3.6.9 1.2 1.5 1.8 2.1 2.4 2.7 3 3.3 Size (mm) (A) d /h =.7, Re = 2.3 1 5 (B) d /h = 1.3, Re = 5.9 1 5 Figure 9. Bubbly size distributions in gabion materials 86631 215, IAHR. Used with permission / ISBN 978-9-824846--1

E-proeedings of the 36 th IAHR World Congress 1.25.2 1..1. x - xstart (m).75.5 y - ystart (m) -.1 -.2 -.3.25 -.4...4.8.12.16.2 t - t start (s) -.5..5.1.15.2 t - t start (s) Figure 1. Spatial dispersion of air bubbles next to step edge 8 d /h = 1.3, Re = 5.9 1 5 5. CONCLUSION The free-surfae and seepage bubbly flow on a gabion stepped weir was investigated. The two-phase flow properties were doumented with a phase-detetion probe in the overflow and high speed video movies in the gabion material. The results highlighted omplex interations between the free-surfae and the atmosphere, and a modified avity flow pattern resulting from the presene of seepage. Quantitative measurements revealed strong air-water mixing in the overflow, in ontrast to the drastially less aerated step avities. The void fration profiles mathed an inverted S-shape preditable by theory, and the bubble ount rates resembled a bell urve. The veloity profiles were losely modelled by a 1/1 power law and highlighted a developing shear layer in the wake of eah step edge. The turbulene intensity profiles had maximum values in the mid-flow olumn, orresponding to loations of maximum bubble ount rates. High speed video analyses doumented bubble trajetories as a funtion of the overflow disharge, flow regime, interstitial shape and loation. Intense avity-seepage interation ourred on either side of the step edge, whih was haraterized by fast bubble veloities and large veloity flutuations. Negative seepage was observed below the step orner in skimming flows, whih may be a result of large positive pressures in the lear water ore. Large positive and sub- pressures were identified above the downstream half of the step tread and in the wake of the step edge, orresponding to pressure distributions measured above impervious steps. The ventilation effet enhaned mixing between the free-surfae and seepage flow, resulting in a omplex avity reirulation flow pattern. The air bubbles transported in the seepage were predominantly between.6 and.9 mm in diameter, and the diffusion proess may be simulated with a random walk model. 6. ACKNOWLEDGEMENTS The authors aknowledge the tehnial assistane of Jason an de Gevel and Stewart Matthews. The finanial support of Australian Researh Counil (Grant DP121481) is aknowledged. 7. REFERENCES Agostini, R., Bizzarri, A., Masetti, M., and Papetti, A. (1987). Flexible Gabion and Reno Mattress Strutures in River and Stream Training Works. Setion One: Weirs. Offiine Maaferri, Bologna, Italy, 2nd edition. Bung, D.B., and Shlenkoff, A. (21). Self-aerated Flow on Embankment Stepped Spillways - The Effet of Additional Miro-roughness on Energy Dissipation and Oxygen Transfer." Pro. 1st IAHR European Congress, 4-6 May, Edinburgh, Sotland, 6 pages (CD-ROM). Carosi, G., and Chanson, H. (26). Air-water time and length sales in skimming flow on a stepped spillway. Appliation to the spray haraterisation. Report No. CH59/6, Division of Civil Engineering, The University of Queensland, Brisbane, Australia, July, 142 pages. Chanson, H. (21). The Hydraulis of Stepped Chutes and Spillways. Balkema, Lisse, The Netherlands, 418 pages. Chanson, H. (24). The Hydraulis of Open Channel Flow. An Introdution. Butterworth-Heinemann, 2nd edition, Oxford, UK, 63 pages. Chanson, H., and Toombes, L. (22). Air-Water Flows down Stepped hutes. Turbulene and Flow Struture Observations. International Journal of Multiphase Flow, ol. 28, No. 11, pp. 1737-1761. Djenidi, L., and Antonia, R. A. (1995). Riblet modelling using a seond moment losure. Applied Siene Researh, ol. 54, No. 4, pp. 249-266. 215, IAHR. Used with permission / ISBN 978-9-824846--1 6632 9

E-proeedings of the 36 th IAHR World Congress, Felder, S., and Chanson, H. (211). Air-Water Flow Properties in Step Cavity down a Stepped Chute. International Journal of Multiphase Flow, ol. 37, No. 7, pp. 732 745. Felder, S., and Chanson, H. (212). Air-Water Flow Measurements in Instationary Free-Surfae Flows. a Triple Deomposition Tehnique. Hydrauli Model Report No. CH85/12, Shool of Civil Engineering, The University of Queensland, Brisbane, Australia, 151 pages. Gonzalez, C.A., and Chanson, H. (24). Interations between Cavity Flow and Main Stream Skimming Flows. an Experimental Study. Canadian Journal of Civil Engineering, ol. 31, No. 1, pp. 33-44. Gonzalez, C.A., Takahashi, M., and Chanson, H. (28). An Experimental Study of Effets of Step Roughness in Skimming Flows on Stepped Chutes. Journal of Hydrauli Researh, IAHR, ol. 46, No. Extra Issue 1, pp. 24-35. Kells, J.A. (1993). Spatially varied flow over rokfill embankments. Canadian Journal of Civil Engineering, ol. 2, pp. 82-827. Matos, J. (21). Onset of skimming flow on stepped spillways - Disussion. Journal of Hydrauli Engineering-Ase, 127(6), 519-521. Naudasher, E., and Rokwell, D. (1994). Flow-indued vibrations. An engineering guide. IAHR Hydrauli Strutures Design Manual No. 7, Balkema, The Netherlands. Peyras, L., Royet, P. and Degoutte, G. (1992), Flow and energy dissipation over stepped gabion weirs, Journal of Hydrauli Engineering-ASCE, 118 (5), 77-717. Rajaratnam, N. (199). Skimming Flow in Stepped Spillways. Journal of Hydrauli Engineering, ASCE, ol. 116, No. 4, pp. 587-591. Sanhez-Juny, M.; Blade, E.; Dolz, J. (27). Pressures on a stepped spillway. Journal of Hydrauli Researh, ol. 45, No. 4, pp. 55-511. Wuthrih, D, and Chanson, H. (214). Hydraulis, Air Entrainment and Energy Dissipation on Gabion Stepped Weir. Journal of Hydrauli Engineering, ASCE, ol. 14, No. 9, Paper 41446, 1 pages. Zhang, G., and Chanson, H. (214). Step Cavity and Gabion Aeration on a Gabion Stepped Spillway. Proeedings of the 5th IAHR International Symposium on Hydrauli Strutures (ISHS214), 25-27 June 214, Brisbane, Australia, 8 pages. 1 6633 215, IAHR. Used with permission / ISBN 978-9-824846--1