Submerged and unsubmerged natural hydraulic jumps in a bedrock step-pool mountain channel
Brett L. Vallé ⁎, Gregory B. Pasternack
Department of Land, Air, and Water Resources, University of California, Davis, 95616, USA Accepted 2 September 2005 Available online 19 June 2006
Abstract High-resolution digital elevation models (DEMs) for natural submerged and unsubmerged jump regions were tested against the classical hydraulic jump (CHJ) and engineering analogues that have dominated previous geomorphic and engineering research. DEMs were compared for two discharge conditions. The data showed bed and water surface features of the natural jump regions differ significantly from CHJ conditions and engineering analogues with respect to boundary conditions. Roughness elements were highly irregular in frequency, spacing, size, and orientation, and were comprised of form obliquity and bed scour in boulder-bed and pure-bedrock conditions. The data also showed bed and water surface features of natural jump regions have similarities and deviations from CHJ conditions and engineering analogues with respect to hydraulic characteristics. Several variations were observed in the hydraulic characteristics between the ballistic and sloping jets. Revised conceptual models based on idealized corollaries were developed for the natural jump regions based on upstream energy head relative to the downstream tailwater depth and step geometry. The DEMs highlight the importance of recognizing the interrelationship between spatial transcritical flow structures and localized topographic heterogeneities in bedrock channels. © 2006 Elsevier B.V. All rights reserved.
Keywords: Hydraulic jump; Mountain channel; Supercritical flow; High-resolution data; Rapidly varied flow
1. Introduction Tumbling flow features such as supercritical jets and hydraulic jumps have increasingly been recognized as important morphologic
References: Abt, S.R., Wittler, R.J., Taylor, A., Love, D.J., 1989. Human stability in a high flood hazard zone. Water Resources Bulletin 25 (4), 881–890. Alexandrowicz, Z., 1994. Geologically controlled waterfall types in the Outer Carpathians. Geomorphology 9, 155–165. Alonso, C.V., Bennett, S.J., Stein, O.R., 2002. Predicting head cut erosion and migration in concentrated flows typical of upland areas. Water Resources Research 38 (12), 39-1–39-15. American Society of Civil Engineers, 1986. Lessons Learned from Design, Construction, and Performance of Hydraulic Structures. American Society of Civil Engineers, New York. Bakhmeteff, B.A., Matzke, A.E., 1936. The hydraulic jump in terms of dynamic similarity. Transactions, ASCE 101, 630–647. Balachandar, R., Kells, J.A., Thiessen, R.J., 2000. The effect of tailwater depth on the dynamics of local scour. Canadian Journal of Civil Engineering 27 (1), 138–150. Bellin, A., Fiorotto, V., 1995. Direct dynamic force measurement on slabs in spillway stilling basins. Journal of Hydraulic Engineering, ASCE 121 (10), 686–693. Bennett, S.J., Casali, J., 2001. Effect of initial step height on headcut development in upland concentrated flows. Water Resources Research 37 (5), 1475–1484. Bennett, S.J., Alonso, C.V., Prasad, S.N., Römkens, M.J.M., 2000. An experimental study of headcut growth and migration in upland concentrated flows. Water Resources Research 36 (7), 1911–1922. Bollaert, E., Schleiss, A., 2003. Scour of rock due to the impact of plunging high velocity jets: Part I. A state-of-the-art review. Journal of Hydraulic Research 41 (5), 451–464. Bombardelli, F.A., Guala, M., García, C.M., Briskin, B., García, M.H., 2002. Mean flow, turbulence, and free-surface location in a canoe chute model. In: Wahl, T.L., Pugh, C.A., Oberg, K.A., Vermeyen, T.B. (Eds.), Hydraulic Measurement and Experimental Methods Conf. American Society of Civil Engineers. Estes Park, CO, USA. Canepa, S., Hager, W.H., 2003. Effect of jet air content on plunge pool scour. Journal of Hydraulic Engineering, ASCE 129 (5), 358–365. Carling, P.A., 1995. Flow-separation berms downstream of a hydraulic jump in a bedrock channel. Geomorphology 11 (3), 245–253. Carling, P., Tinkler, K., 1998. Conditions for the entrainment of cuboid boulders in bedrock streams: an historical review of literature with respect to recent investigations. In: Tinkler, K.J., Wohl, E.E. (Eds.), Rivers Over Rock: Fluvial Processes in Bedrock Channels. Geophysical Monograph, vol. 107. American Geophysical Union, Washington, DC, pp. 19–34. Chanson, H., 1994. Hydraulic Design of Stepped Cascades, Channels, Weirs, and Spillways. Pergamon, Oxford. Chanson, H., 1996. Air Bubble Entrainment in Free-Surface Turbulent Shear Flows. Academic Press, San Diego. Chanson, H., 1999. Critical flow constrains flow hydraulics in mobilebed streams: a new hypothesis—comment. Water Resources Research 35 (3), 903–907. Chanson, H., Toombes, L., 2004. Hydraulics of stepped chutes: the transition flow. Journal of Hydraulic Research 42 (1), 43–54. Chow, V.T., 1959. Open-Channel Hydraulics. McGraw-Hill, New York. 158 B.L. Vallé, G.B. Pasternack / Geomorphology 82 (2006) 146–159 Ohtsu, I., Yasuda, Y., 1991. Hydraulic jump in sloping channels. Journal of Hydraulic Engineering, ASCE 117 (7), 905–921. Ohtsu, I., Yasuda, Y., Ishikawa, M., 1999. Submerged hydraulic jumps below abrupt expansions. Journal of Hydraulic Engineering, ASCE 125 (5), 492–499. Parker, G., Izumi, N., 2000. Purely erosional cyclic and solitary steps created by flow over a cohesive bed. Journal of Fluid Mechanics 419, 203–238. Pasternack, G.B., Ellis, C., Leier, K.A., Valle, B.L., Marr, J.D., 2006-this issue. Convergent hydraulics at horseshoe steps in bedrock rivers. Geomorphology 82, 126–145. doi:10.1016/j.geomorph.2005. 08.022. Peterka, A.J., 1983. Hydraulic Design of Stilling Basins and Energy Dissipators. U.S. Dept. of the Interior Bureau of Reclamation, Washington, DC. Peterson, D.F., Mohanty, P.K., 1960. Flume studies of flow in steep, rough channels. Journal of Hydraulics Division 86 (9), 55–75. Rajaratnam, N., 1962. Profile equation for the hydraulic jump. Water Power 14, 324–327. Rajaratnam, N., 1965. Submerged hydraulic jump. Journal of the Hydraulics Division 91(HY4), 71–96. Rajaratnam, N., 1967. Hydraulic jumps. In: Chow, V.T. (Ed.), Advances in Hydroscience. Academic Press, New York, pp. 197–280. Rajaratnam, N., Subramanya, K., 1968. Profile of the hydraulic jump. Journal of the Hydraulics Division, ASCE 94(HY3), 663–673. Robinson, K.M., 1989. Hydraulic stresses on an overfall boundary. Transactions of the ASAE 32 (4), 1269–1274. Robinson, K.M., Cook, K.R., Hanson, G.J., 2000. Velocity field measurements at an overfall. Transactions of the ASAE 43 (3), 665–670. Rouse, H., 1936. Discharge characteristics of the free overfall. Civil Engineering 6, 257–260. Sarma, K.V.N., Newnham, D.A., 1973. Surface profiles of hydraulic jump for Froude numbers less than four. Water Power 25, 139–142. Seidl, M.A., Dietrich, W.E., Kirchner, J.W., 1994. Longitudinal profile development into bedrock: an analysis of Hawaiian channels. Journal of Geology 102, 457–474. Sentürk, F., 1994. Hydraulics of dams and reservoirs. Water Resources Publications. LLC, Highlands Ranch, Colorado. ISBN #0-91833480-2. 814 p. Tinkler, K.J., 1993. Fluvially sculpted rock bedforms in 20 Mile Creek, Niagara Peninsula, Ontario. Canadian Journal of Earth Sciences 30 (5), 945–953. Tinkler, K.J., 1997a. Critical flow in rockbed streams with estimated values for Manning 's n. Geomorphology 20 (1–2), 147–164. Tinkler, K.J., 1997b. Rockbed wear at a flow convergence zone in Fifteen Mile Creek, Niagara Peninsula, Ontario. Journal of Geology 105 (2), 263–274. Tinkler, K.J., 1997c. Indirect velocity measurement from standing waves in rockbed rivers. Journal of Hydraulic Engineering, ASCE 123 (10), 918–921. Tinkler, K.J., Wohl, E.E., 1998a. A primer on bedrock channels. In: Tinkler, K.J., Wohl, E.E. (Eds.), Rivers Over Rock: Fluvial Processes in Bedrock Channels. Geophysical Monograph, vol. 107. American Geophysical Union, Washington, DC, pp. 1–18. Tinkler, K.J., Wohl, E.E., 1998b. Field studies of bedrock channels. In: Tinkler, K.J., Wohl, E.E. (Eds.), Rivers Over Rock: fluvial Processes in Bedrock Channels. Geophysical Monograph, vol. 107. American Geophysical Union, Washington, DC, pp. 261–277. United States Bureau of Reclamation, 1948. Studies of Crests of Overfall Dams. U.S. Dept. of the Interior Bureau of Reclamation, Denver. Comiti, F., 2003. Erosione localizzata in strutture a gradinata naturali ed artificiali. PhD thesis, University of Padova, Italy. Crowder, D.W., Diplas, P., 2000. Using two-dimensional hydrodynamic models at scales of ecological importance. Journal of Hydrology 230 (3–4), 172–191. Crowe, C., Sommerfeld, M., Tsuji, Y., 1998. Multiphase Flows with Droplets and Particles. CRC Press, Boca Raton, FL. Davis, A.C., Ellett, B.G.S., Jacob, R.P., 1998. Flow measurement in sloping channels with rectangular free overfall. Journal of Hydraulic Engineering, ASCE 124, 760–763. Fiorotto, V., Rinaldo, A., 1992. Fluctuating uplift and lining design in spillway stilling basins. Journal of Hydraulic Engineering, ASCE 118 (4), 578–596. Grant, G.E., 1997. Critical flow constrains flow hydraulics in mobilebed streams: A new hypothesis. Water Resources Research 33 (2), 349–358. Grant, G.E., Swanson, F.J., Wolman, M.G., 1990. Pattern and origin of stepped-bed morphology in high-gradient streams, Western Cascades, Oregon. Geological Society of America Bulletin 102 (3), 340–352. Hager, W.H., 1983. Hydraulics of the plane overfall. Journal of Hydraulic Engineering, ASCE 109 (12), 1683–1697. Hager, W.H., 1992. Energy Dissipators and Hydraulic Jump. Kluwer Academic Publishers, Dordrecht. Henderson, F.M., 1966. Open Channel Flow. Macmillan, New York. Jarrett, R.D., 1984. Hydraulics of high-gradient streams. Journal of Hydraulic Engineering, ASCE 110 (11), 1519–1539. Kells, J.A., Balachandar, R., Hagel, K.P., 2001. Effect of grain size on local channel scour below a sluice gate. Canadian Journal of Civil Engineering 28 (3), 440–451. Khan, A.A., Steffler, P.M., 1996. Physically based hydraulic jump model for depth-averaged computations. Journal of Hydraulic Engineering, ASCE 122 (10), 540–548. Kieffer, S.W., 1985. The 1983 hydraulic jump in Crystal Rapid— implications for river-running and geomorphic evolution in the Grand-Canyon. Journal of Geology 93 (4), 385–406. Kieffer, S.W., 1987. The rapids and eaves of the Colorado River, Grand Canyon, Arizona. U.S. Geological Survey Open-file Report 87–96. Kieffer, S.W., 1990. The hydraulics and geomorphology of the Colorado River in the Grand Canyon. In: Beus, S.S., Morales, M. (Eds.), Grand Canyon Geology. Oxford University Press, New York, pp. 333–383. Lenzi, M.A., Marion, A., Comiti, F., Gaudio, R., 2002. Local scouring in low and high gradient streams at bed sills. Journal of Hydraulic Research 40 (6), 731–739. Lenzi, M.A., Marion, A., Comiti, F., 2003. Local scouring at gradecontrol structures in alluvial mountain rivers. Water Resources Research 39 (7). Leutheusser, H.J., Birk, W.M., 1991. Drownproofing of low overflow structures. Journal of Hydraulic Engineering, ASCE 117 (2), 205–213. Leutheusser, H.K., Fan, J.J., 2001. Backward flow velocities of submerged hydraulic jumps. Journal of Hydraulic Engineering 127 (6), 514–517. Miller, J.R., 1991. The influence of bedrock geology on knickpoint development and channel-bed degradation along downcutting streams in South-Central Indiana. Journal of Geology 99 (4), 591–605. Montgomery, D.R., Buffington, J.M., 1997. Channel-reach morphology in mountain drainage basins. Geological Society of America Bulletin 109 (5), 596–611. B.L. Vallé, G.B. Pasternack / Geomorphology 82 (2006) 146–159 Vallé, B.L., 2005. Geomorphic Structure and Function of Hydraulic Jumps in Mountain River Channels. PhD thesis, University of California at Davis, USA. Vallé, B.L., Pasternack, G.B., 2002a. TDR measurements of hydraulic jump aeration in the South Fork of the American River, California. Geomorphology 42 (1–2), 153–165. Valle, B.L., Pasternack, G.B., 2002b. Assessment of the structure and function of natural hydraulic jumps. University of California Water Resources Center Technical Completion Report W944. Vallé, B.L., Pasternack, G.B., 2006. Field mapping and digital elevation modelling of submerged and unsubmerged hydraulic jump regions in a step-pool bedrock channel. Earth Surface Processes and Landforms 31 (6), 646–664. Vischer, D.L., Hager, W.H., 1998. Dam Hydraulics. John Wiley and Sons, New York. Whipple, K.X., Hancock, G.S., Anderson, R.S., 2000. River incision into bedrock: mechanics and relative efficacy of plucking, 159 abrasion, and cavitation. Geological Society of America Bulletin 112 (3), 490–503. Whitaker, S., 1992. Introduction to Fluid Mechanics. Krieger Publishing Company, Malabar. Wilson, P.J., Gallant, C.J. (Eds.), 2000. Terrain Analysis: Principles and Applications. John Wiley and Sons, New York. Wohl, E.E., 2000. Mountain Rivers. American Geophysical Union, Washington, DC. Wohl, E.E., Grodek, T., 1994. Channel bed-steps along Nahal-Yael, Negev Desert, Israel. Geomorphology 9 (2), 117–126. Wohl, E.E., 1998. Bedrock channel morphology in relation to erosional processes. In: Tinkler, K.J., Wohl, E.E. (Eds.), Rivers Over Rock: Fluvial Processes in Bedrock Channels. Geophysical Monograph, vol. 107. American Geophysical Union, Washington, DC, pp. 133–151.