Using the Incomplete Self-Similarity Method for Estimation of the Conjugate Depth Ratio of Density Jumps on Smooth and Rough Beds
Subject Areas :
Subjects
N. Barahmand
1
(گروه مهندسی عمران، واحد لارستان، دانشگاه آزاد اسلامی، لارستان، ایران.)
Received: 2016-03-02
Accepted : 2016-03-02
Published : 2016-02-20
Keywords:
density current,
Density jump,
incomplete self-similarity method,
sequent depth ratio,
relative roughness,
Abstract :
Density current is produced because of a density contrast with the ambient fluid. This density difference can result from dissolved solids, suspended materials, temperature, etc. Density jumps significantly influence the quality characteristics of the gravity currents and the ambient fluid (e.g., lakes and reservoirs). In this research, using dimensional analysis and incomplete self-similarity method, these jumps were studied and a new equation was obtained for calculating the sequent depth ratio. This equation was validated using experimental results. Therefore, these experiments were carried out on both smooth and rough beds. The results indicate that the new relationship is more accurate than the classical equation; it was shown that the effects of both the entrainment ratio and the bed roughness are not negligible, even for their small amount.
References:
برهمند، ن. 1389. بررسی آزمایشگاهی پرشهای چگالی ایجادی بر روی بسترهای صاف و زبر. پایان نامه کارشناسی ارشد. دانشگاه آزاد اسلامی، واحد علوم و تحقیقات تهران.
Alavian, V. 1986. Behavior of density currents on an incline. J. Hydraul. Eng. 112: 27–42.
Baddour, R.E., and H. Abbink. 1983. Turbulent underflow in a short channel of limited depth. J. Hydraul. Eng. 109: 722–740.
Barahmand, N., and A. Shamsai. 2010. Experimental and theoretical study of density jumps on smooth and rough beds. Lakes and Resrvoirs: Res. Manage. 4: 285-306.
Barenblatt, G.I. 1979. Similarity, self-similarity, and intermediate asymptotics. Consultants Bureau, N.Y.
Barenblatt, G.I. 1987. Dimensional analysis. Gordon and Breach, Newark, N.J.
Barenblatt, G.I. 1993. Scaling laws for fully developed turbulent shear flows. 1: Basic hypothesis and analysis. J. Fluid Mech. 248: 513–520.
Carollo, F.G., V. Ferro, and V. Pampalone. 2007. Hydraulic jumps on rough beds. J. Hydraul. Eng. 133: 989-999.
Carollo, F.G., V. Ferro, and D. Termini. 2005. Flow resistance law in channels with flexible submerged vegetation. Hydraul. Eng. 131: 554-564.
D’Agostino, V., and V. Ferro. 2004. Scour on alluvial bed downstream of grade-control structures. J. Hydraul. Eng. 130: 24-37.
Dallimore, C.J., J. Imberger, and T. Ishikawa. 2001. Entrainment and turbulence in a saline underflow in Lake Ogawara. J. Hydraul. Eng. 127: 937–948.
Daly, R.A. 1936. Origin of submarine canyons. Am. J. Sci. 31: 401-420.
Di Stefano, C., and V. Ferro. 1998. Calculating average filing rock diameter for gabion-mattresss channel design. J. Hydraul. Eng. 124(9): 975-978.
De Cesare, G., A. Schleiss, and F. Hermann. 2001. Impact of turbidity currents on reservoir sedimentation. J. Hydraul. Eng. 127: 6-16.
Fan, J., and G.L. Morris. 1992. Reservoir sedimentation. I: Delta and density current deposits. J. Hydraul. Eng. 118: 354–369.
Ferro, V. 1997. Applying hypothesis of self-similarity for flow resistance law of small-diameter plastic pipes. J. Irrig. Drain. Eng. 123: 175–179.
Ferro, V. 2006. La sistemazione dei bacini idrografici – seconda edizione. McGraw-Hill, Milano, 848 pp. (in Italian).
Ferro, V., and R. Pecoraro. 2000. Incomplete self-similarity and flow velocity in gravel-bed channels. Water Resour. Res. 36: 2761–2769.
Fozdar, F.M., G. Parker, and J. Imberger. 1985. Matching temperature and conductivity sensor response characteristics. J. Phys. Oceanogr. 15: 1557–1569.
Garcia, M.H. 1993. Hydraulic jumps in sediment-driven bottom currents. J. Hydraul. Eng. 119: 1094-1117.
Hager, W.H., and R. Bremen. 1989. Classical hydraulic jump: Sequent depths. J. Hydraul. Res. 27: 565-585.
Hartel, C., F. Carlsson, and M. Thunblom. 2000a. Analysis and direct numerical simulation of the flow at a gravity-current head. Part 2: The Lobe-and-cleft instability. J. Fluid Mech. 418: 213-229.
Hartel, C., E. Meiburg, and F. Necker. 2000b. Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1: Flow topology and front speed for slip and no-slip boundaries. J. Fluid Mech. 418: 189-212.
Hay, A.E. 1987. Turbidity currents and submarine channel formation in Rupert Inlet, British Columbia, 2. The roles of continuous and surge-type flow. J. Geophys. Res. 92: 2883-2900.
Huang, H., J. Imran, C. Pirmez, Q. Zhang, and G. Chen. 2009. The critical densimetric Froude number of subaqueous gravity currents can be non-unity or non-existent. J. Sediment. Res. 79: 479–485.
Hughes, W.C., and J.E. Flack. 1984. Hydraulic jump properties over a rough bed. J. Hydraul. Eng. 110: 1755-1771.
Inman, D.L., C.E. Nordstrom, and R.E. Flick. 1976. Currents in submarine canyons: An air-sea-land interaction. Annu. Rev. Fluid Mech. 8: 275–310.
Koh, R.C.Y. 1971. Two-dimensional surface warm jets. J. Hydraul. Div., ASCE. 97(HY6): 819-836.
Kostic, S., and G. Parker. 2007. Conditions under which a supercritical turbidity current traverses an abrupt transition to vanishing bed slope without a hydraulic jump. J. Fluid Mech. 586: 119-145.
Kostic, S., and G. Parker. 2006. The response of turbidity currents to a canyon-fan transition: Internal hydraulic jumps and depositional signatures. J. Hydraul. Res. 44: 631-653.
Krause, D.C., W.C. White, D.J.W. Piper, and B.C. Heezen. 1970. Turbidity currents and cable breaks in the western New Britain Trench. Geol. Soc. Am. Bull. 81: 2153–2160.
La Rocca, M., C. Adduce, and G. Sciortino. 2008. Experimental and numerical simulation of three-dimensional gravity currents on smooth and rough bottom. Phys. Fluids. 20: 106603(1-15).
Long, R.R. 1953. Some aspects of the flow of stratified fluids I. A theoretical investigation. Tellus, 5: 42-58.
Long, R.R. 1954. Some aspects of the flow of stratified fluids II. Experiments with a two-fluid system. Tellus 6: 97-115.
Macagno, E.O., and M.C. Macagno. 1975. Mixing in interfacial hydraulic jumps. Proc., 16th Cong. IAHR, São Paulo, Brazil.
Mahmood, K. 1987. Reservoir sedimentation: Impact, extent and mitigation. Technical paper No.71, The World Bank, Washington D.C.
Mehrotra, S.C., and R.E. Kelly. 1973. On the question of non-uniqueness of internal hydraulic jumps and drops in a two-fluid system. Tellus. 25: 560-567.
Parker, G., Y. Fukushima, and H.M. Pantin. 1986. Self-accelerating turbidity currents. J. Fluid Mech. 171: 145-181.
Rajaratnam, N. 1965. The hydraulic jump as a wall jet. J. Hydraul. Division. 91: 107-132.
Rajaratnam, N. 1967. Hydraulic jumps. Adv. Hydrosci. 4: 197–280.
Regev, A., S. Hassid, and M. Poreh. 2004. Density jumps in smoke flow along horizontal ceilings. Fire Safety J. 39: 465–479.
Regev, A., S. Hassid, and M. Poreh. 2006. Calculation of entrainment in density jumps. J. Environ Fluid Mech. 6: 407–424.
Simpson, J.E. 1982. Gravity currents in the laboratory, atmosphere, and ocean. Ann. Rev. Fluid Mech. 14: 213-234.
Simpson, J.E. 1992. Effects of the lower boundary on the head of a gravity current. J. Fluid Mech. 53: 759-768.
Simpson, J.E. 1997. Gravity currents in the environment and in the laboratory, 2nd ed., Cambridge University Press, Cambridge, U.K.
Turner, J.S. 1973. Buoyancy effects in fluids. Cambridge Univ. Press, London, UK.
Wilkinson, D.L., and I.R. Wood. 1971. A rapidly varied flow phenomenon in a two-layer flow. J. Fluid Mech. 47: 241-256.
Wood, I.R., and J.E. Simpson. 1984. Jumps in layered miscible fluids. J. Fluid Mech. 140: 329–342.
Yih, C.S., and C.R. Guha. 1955. Hydraulic jump in a fluid system of two layers. Tellus, 7: 358-366.
