Abstract
The effect of the upstream conditions on propagation of gravity current over a slope is investigated using three-dimensional numerical simulations. The current produced by constant buoyancy flux, is simulated using a large eddy simulation solver. The dense saline solution used at the inlet is the driving force of the flow. Higher replenishment of the current is possible either by a high inflow discharge or high initial fractional density excess. In the simulations, it is observed that these two parameters affect the flow in different ways. Results show that the front speed of the descending current is proportional to the cube root of buoyancy flux, \((g_o^{\prime } Q)^{1/3}\), which agrees with the previous experimental and numerical observations. The height of the tail of the current grows linearly in the streamwise direction. Formation of a strong shear layer at the boundary of mixed upper layer and dense lower layer is observed within the body and the tail of the current. Over the tail of the current far enough from the inlet, the vertical velocity and density profiles are compared to the ones from an experimental study. Distance from the bed to the point of maximum velocity increases with an increase in inflow discharge, while it remains practically unchanged with increasing initial fractional excess density in the simulations. Even though the velocity profiles are in good agreement, some discrepancies are observed in fractional excess density profiles among experimental and numerical results. Possible reasons for these discrepancies are discussed. Generally, gravity current type of flows could be expressed in layer-integrated formulation of governing equations. However, layer integration introduces several constants, commonly known as shape factors, to the equations of motion. The values of these shape factors are calculated based on simulation results and compared to the values from experiments and to the favorably used ‘top hat’ assumption.
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References
Adduce C, Sciortino G, Proietti S (2012) Gravity currents produces by lock-exchangeq: experiments and simulations with a two-layer shallow-water model with entrainment. J Hydraul Eng 138(2):111–121
Altinakar MS, Graf WH, Hopfinger EJ (1996) Flow structure in turbidity currents. J Hydraul Res 34:713–718
An S, Julien PY, Venayagamoorthy SK (2012) Numerical simulation of particle-driven gravity currents. Environ Fluid Mech 12:495–513
Ansys Fluent (2009) User’s guide 12.0. ANSYS Inc., Canonsburg
Benjamin TB (1968) Gravity currents and related phenomena. J Fluid Mech 31:209–248
Blanchette F, Strauss M, Meiburg E, Kneller B, Glinsky ME (2005) High-resolution numerical simulations of resuspending gravity currents: conditions for self-sustainment. J Geophys Res Ocean 110(C12). doi:10.1029/2005JC002927
Bournet PE, Dartus D, Tassin B, Vincon-Leite B (1999) Numerical investigation of plunging density current. J Hydraul Eng 125(6):584–594
Britter RE, Linden PF (1980) The motion of the front of a gravity current travelling down an incline. J Fluid Mech 99(3):531–543
Cantero MI, Balachandar S, Garcia MH (2007) High-resolution simulations of cylindrical density currents. J Fluid Mech 590:437–469
Cantero MI, Lee JR, Balachandar S, Garcia MH (2007) On the front velocity of gravity currents. J Fluid Mech 586:1–39
Cantero M, García MH, Balachandar S (2008) An Eulerian–Eulerian model for gravity currents driven by inertial particles. Int J Multiph Flow 34(5):484–501
Cantero M, García M, Balachandar S (2008) Effect of particle inertia on depositional particulate gravity currents. Comput Geosci 34(10):1308–1318
Cantero MI, Balachandar S, García MH, Bock D (2008) Turbulent structures in planar gravity currents and their influence on the flow dynamics. J Geophys Res Ocean 113(C8). doi:10.1029/2007JC004645
Chen G, Lee JHW (2001) Turbulent lock release gravity current. Sci China E 44(5):449–462
Choi SU, García MH (2002) k-\(\varepsilon \) Turbulence modelling of density currents developing two dimensionally on a slope. J Hydraul Eng 128(1):55–63
Dai A (2012) Gravity currents propagating on sloping boundaries. J Hydraul Eng. doi:10.1061/(ASCE)HY.1943-7900.0000716
Dai A, Ozdemir C, Cantero M, Balachandar S (2012) Gravity currents from instantaneous sources down a slope. J Hydraul Eng 138(3):237–246
Ellison TH, Turner JS (1959) Turbulent entrainment in stratified flows. J Fluid Mech 6:423–448
García MH (1993) Hydraulic jumps in sediment-driven bottom currents. J Hydraul Eng 119(10):1094–1117
García MH (1994) Depositional turbidity currents laden with poorly sorted sediment. J Hydraul Eng 120(11):1240–1263
García MH (2008) Sedimentation engineering—processes, measurements, modeling, and practice. ASCE Manuals and Reports on Engineering Practice No. 110
García MH, Parker G (1993) Experiments on the entrainment of sediment into suspension by a dense bottom current. J Geophys Res Ocean 98(C3):4793–4807
Georgoulas AN, Angelidis PB, Panagiotidis TG, Kotsovinos NE (2010) 3D numerical modeling of turbidity currents. Environ Fluid Mech 10:603–635
Gerber G, Diedericks G, Basson GR (2011) Particle image velocimetry measurements and numerical modeling of saline density currents. J Hydraul Eng 137(3):333–342
Gonzalez-Juez E, Meiburg E, Constantinescu GS (2009) Gravity currents impinging on bottom mounted square cylinders: flow fields and associated forces. J Fluid Mech 631:65–102
Gray TE, Alexander J, Leeder MR (2006) Quantifying velocity and turbulence structure in depositing sustained turbidity currents across breaks in slope. Sedimentology 52:467–488
Hartel C, Carlsson F, Thunblom M (2000) 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, Meiburg E, Necker F (2000) 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
Hinze JO (1975) Turbulence. McGraw-Hill Publishing Co., New York
Huang H, Imran J, Pirmez C (2005) Numerical model of turbidity currents with a deforming bottom boundary. J Hydraul Eng 131(4):283–293
Huang H, Imran J, Pirmez C (2007) Numerical modeling of poorly sorted depositional turbidity currents. J Geophys Res 112:1–15
Huang H, Imran J, Pirmez C (2009) Nondimensional parameters of depth-average gravity flow models. J Hydraul Res 47(4):455–465
Ilicak M, Özgökmen TM, Özsoy E, Fischer PF (2009) Non-hydrostatic modeling of exchange flows across complex geometries. Ocean Model 29:159–175
Imran J, Kassem A, Khan SM (2004) Three-dimensional modeling of density current. I. Flow in straight confined and unconfined channels. J Hydraul Res 42(6):578–590
Johnson G, Massoudi M, Rajagopal KR (1991) Flow of a fluid–solid mixture between flat plates. Chem Eng Sci 46(7):1713–1723
Kneller B, Bennett SJ, McCaffrey WD (1999) Velocity structure, turbulence and fluid stresses in experimental gravity currents. J Geophys Res Ocean 104(C3):5381–5391
Martin JE, Sun T, García MH (2012) Chapter 18: Optical methods in the laboratory: an application to density currents over bedforms. IAHR Monograph. In: Rodi W, Uhlman M (eds) Environmental fluid mechanics: memorial volume in honour of Prof. Gerhard H. Jirka. CRC Press (Taylor & Francis Group), Boca Raton, pp 333–346
Middleton GV (1966) Experiments on density and turbidity currents: II. Uniform flow of density currents. Can J Earth Sci 3:627–637
Ooi SK, Constantinescu SG, Weber L (2009) Numerical simulations of lock exchange compositional gravity currents. J Fluid Mech 635:361–388
Özgökmen TM, Chassignet EP (2002) Dynamics of two-dimensional turbulent bottom gravity current. J Phys Oceanogr 32:1460–1478
Özgökmen TM, Fischer PF, Duan J, Iliescu T (2004) Three-dimensional turbulent bottom density currents from a high-order nonhydrostatic spectral element model. J Phys Oceanogr 34:2006–2026
Özgökmen TM, Fischer PF, Johns WE (2006) Product water mass formation by turbulent density current from a high-order nonhydrostatic spectral element model. Ocean Model 12:237–267
Özgökmen TM, Iliescu T, Fischer PF, Srinivasan A, Duan J (2007) Large eddy simulation of stratified mixing in two-dimensional dam-break problem in a rectangular enclosed domain. Ocean Model 16:106–140
Özgökmen TM, Fischer PF (2008) On the role of bottom roughness in overflows. Ocean Model 20:336–361
Özgökmen TM, Iliescu T, Fischer PF (2009) Large eddy simulation of stratified mixing in a three-dimensional lock-exchange system. Ocean Model 26:134–155
Özgökmen TM, Iliescu T, Fischer PF (2009) Reynolds number dependence of mixing in a lock-exchange system from direct numerical and large eddy simulations. Ocean Model 30:190–206
Parker G, Fukushima Y, Pantin H (1986) Self-accelerating turbidity currents. J Fluid Mech 171:145–181
Sequeiros OE, Spinewine B, Beaubouef RT, Sun T, García MH, Parker G (2010) Characteristics of velocity and excess density profiles of saline underflows and turbidity currents flowing over a mobile bed. J Hydraul Eng 136(7):412–433
Shin J, Dalziel S, Linden PF (2004) Gravity currents produced by lock exchange. J Fluid Mech 521:1–34
Simpson JE, Britter RE (1979) The dynamics of the head of a gravity current advancing over a horizontal surface. J Fluid Mech 94(3):477–495
Simpson JE (1997) Gravity currents in the environment and the laboratory, 2nd edn. Cambridge University Press, Cambridge
Smagorinsky J (1963) General circulation experiments with the primitive equations. I. The basic experiment. Mon Weather Rev 164:91–99
Tokyay T, Constantinescu G, Meiburg E (2011) Lock exchange gravity currents with a high volume of release propagating over periodic array of obstacles. J Fluid Mech 672:570–605
Tokyay T, Constantinescu G, Gonzalez-Juez E, Meiburg E (2011) Gravity currents propagating over periodic arrays of blunt obstacles: effect of the obstacle size. J Fluids Struct. doi:10.1016/j.jfluidstructs.2011.01.006
Tokyay T, Constantinescu G, Meiburg E (2012) Tail structure and bed friction velocity distribution of gravity currents propagating over an array of obstacles. J Fluid Mech. doi:10.1017/jfm.2011.542
Turner JS (1973) Buoyancy effects in fluids. Cambridge University Press, Cambridge
Turner J (1986) Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J Fluid Mech 173:431–471
Ungarish M (2012) Gravity currents and intrusions of stratified fluids into a stratified ambient. Environ Fluid Mech 12:115–132
Von Karman T (1940) The engineer grapples with nonlinear problems. Bull Am Math Soc 46:615–683
Yam K, McCaffrey WD, Ingham DB, Burns AD (2011) CFD modeling of selected laboratory turbidity currents. J Hydraul Res 49(5):657–666
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Tokyay, T.E., García, M.H. Effect of initial excess density and discharge on constant flux gravity currents propagating on a slope. Environ Fluid Mech 14, 409–429 (2014). https://doi.org/10.1007/s10652-013-9317-0
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DOI: https://doi.org/10.1007/s10652-013-9317-0