We study the variation of the Froude number at the front of gravity currents developed in uniform channels whose cross-section shape depends on a parameter usually used in many numerical and theoretical models. The thickness and front velocity of the dense currents running on the bottom are greater for all the cases studied, resulting in a Froude number greater than that corresponding to the rectangular cross-section shape. The light currents developing along the upper boundary show the opposite trend. It is found that the results are not related to the depth and width of the channel. The relationships obtained agree with the results of laboratory experiments in which open and closed channels of different cross-section shapes are used.
Issue Section:
Fundamental Issues and Canonical Flows
Keywords:
channel flow
1.
Simpson
, J. E.
, 1997, Gravity Currents: In the Environment and the Laboratory
, Cambridge University
, Cambridge
, p. 258
.2.
Imberger
, J.
, and Hamblin
, P. F.
, 1982, “Dynamics of Lakes, Reservoirs and Cooling Pounds
,” Annu. Rev. Fluid Mech.
0066-4189, 14
, pp. 153
–187
.3.
Farrell
, G.
, and Stefan
, H.
, 1988, “Mathematical Modeling of Plunging Reservoir Flows
,” J. Hydraul. Res.
, 26
, pp. 525
–537
. 0022-16864.
Britter
, R. E.
, and Linden
, P. F.
, 1980, “The Motion of the Front of a Gravity Current Travelling Down an Incline
,” J. Fluid Mech.
0022-1120, 99
, pp. 531
–543
.5.
Alavian
, V.
, Jirka
, G. H.
, Denton
, R. A.
, Johnson
, M. C.
, and Stefan
, H. G.
, 1992, “Density Currents Entering Lakes and Reservoirs
,” J. Hydrol. Eng.
, 118
, pp. 1464
–1489
. 1084-06996.
Akiyama
, J.
, and Stefan
, G.
, 1987, “Onset of Underflow in Slightly Diverging Channels
,” J. Hydrol. Eng.
, 113
, pp. 825
–844
. 1084-06997.
Johnson
, T. R.
, Farell
, G. J.
, Ellis
, C. R.
, and Stefan
, H. G.
, 1987, “Negatively Buoyant Flow in a Diverging Channel. I: Flow Regimes
,” J. Hydrol. Eng.
, 113
, pp. 716
–730
. 1084-06998.
Johnson
, T. R.
, Ellis
, C. R.
, Farell
, G. J.
, and Stefan
, H. G.
, 1987, “Negatively Buoyant Flow in a Diverging Channel. II: 3-d Flow Field Descriptions
,” J. Hydrol. Eng.
, 113
, pp. 731
–742
. 1084-06999.
Johnson
, T.
, Ellis
, C.
, and Stefan
, H.
, 1989, “Negatively Buoyant Flow in Diverging Channel. IV: Entrainment and Dilution
,” J. Hydrol. Eng.
, 115
, pp. 437
–456
. 1084-069910.
Stefan
, H.
, and Johnson
, T.
, 1989, “Negatively Buoyant Flow in Diverging Channel. III: Onset of Underflow
,” J. Hydrol. Eng.
, 115
, pp. 423
–436
. 1084-069911.
Bournet
, P. E.
, Dartus
, D.
, Tassin
, B.
, and Vinçon-Leite
, B.
, 1999, “Numerical Investigation of Plunging Density Current
,” J. Hydrol. Eng.
1084-0699, 125
, pp. 584
–594
.12.
Monaghan
, J. J.
, 2007, “Gravity Current Interaction With Interfaces
,” Annu. Rev. Fluid Mech.
0066-4189, 39
, pp. 245
–261
.13.
Britter
, R. E.
, and Simpson
, J. E.
, 1978, “Experiments on the Dynamics of a Gravity Current
,” J. Fluid Mech.
0022-1120, 88
, pp. 223
–240
.14.
Zhou
, M.
, 1998, “Influence of the Bottom Stress on the Two-Layer Flow Induced by Gravity Currents in Estuaries
,” Estuarine Coastal Shelf Sci.
, 46
, pp. 811
–825
. 0272-771415.
Nunes
, R. A.
, and Simpson
, J. H.
, 1985, “Axial Convergence in a Well Mixed Estuary
,” Estuarine Coastal Shelf Sci.
0272-7714, 20
, pp. 637
–649
.16.
Wong
, K. C.
, 1994, “On the Nature of Transverse Variability in a Coastal Plain Estuary
,” J. Geophys. Res.
, 99
, pp. 209
–222
. 0148-022717.
Wong
, K. C.
, and Munchow
, A.
, 1995, “Buoyancy Forced Interaction Between Estuary and Inner Shelf-Observation
,” Cont. Shelf Res.
0278-4343, 15
, pp. 59
–88
.18.
Valle-Levinson
, A.
, and Lwiza
, K. M. M.
, 1995, “The Effects of Channels and Shoals on Exchange Between the Chesapeake Bay and the Adjacent Ocean
,” J. Geophys. Res.
0148-0227, 100
, pp. 18551
–18563
.19.
Engqvist
, A.
, and Hogg
, A.
, 2004, “Unidirectional Stratified Flow Through a Non-Rectangular Channel
,” J. Fluid Mech.
, 509
, pp. 83
–92
. 0022-112020.
Thomas
, L. P.
, and Marino
, B. M.
, 2004, “Lock-Exchange Flows in Non-Rectangular Cross-Section Channels
,” ASME J. Fluids Eng.
0098-2202, 126
, pp. 290
–292
.21.
Benjamin
, T. B.
, 1968, “Gravity Currents and Related Phenomena
,” J. Fluid Mech.
0022-1120, 31
, pp. 209
–248
.22.
von Karman
, T.
, 1940, “The Engineer Grapples With Non-Linear Problems
,” Bull. Am. Math. Soc.
0002-9904, 46
, pp. 615
–683
.23.
Lowe
, R. J.
, Rottman
, J. W.
, and Linden
, P. F.
, 2002, “A Laboratory Study of the Velocity Structure in an Intrusive Gravity Current
,” J. Fluid Mech.
0022-1120, 456
, pp. 33
–48
.24.
Birman
, V. K.
, Martin
, J. E.
, and Meiburg
, E.
, 2005, “The Non-Boussinesq Lock-Exchange Problem. Part 2. High Resolution Simulation
,” J. Fluid Mech.
0022-1120, 537
, pp. 125
–144
.25.
Marino
, B. M.
, Thomas
, L. P.
, and Linden
, P. F.
, 2005, “The Front Condition for Gravity Currents
,” J. Fluid Mech.
, 536
, pp. 49
–78
. 0022-112026.
Shin
, J. O.
, Dalziel
, S. B.
, and Linden
, P. F.
, 2004, “Gravity Currents Produced by Lock Exchange
,” J. Fluid Mech.
0022-1120, 521
, pp. 1
–34
.27.
Simpson
, J. E.
, and Britter
, R. E.
, 1979, “The Dynamics of the Head of a Gravity Current Advancing Over a Horizontal Surface
,” J. Fluid Mech.
0022-1120, 94
, pp. 477
–495
.28.
Hartel
, C.
, Meiburg
, E.
, and 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.
0022-1120, 418
, pp. 189
–212
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