Two‐Layer Model of Saline Wedge. I: Entrainment and Interfacial Friction
Publication: Journal of Hydraulic Engineering
Volume 113, Issue 10
Abstract
The arrested saline wedge geometry is characterized by two major internal demarcation lines, the density interface and the zero velocity line (ZVL). As a complement to earlier two‐layer model formulations that are based upon the density interface, a two‐layer model using the ZVL is developed. The advantage of this model is that it divides the flow into an active upper zone with high kinetic energy content and a passive lower zone as suggested by detailed experiments. Net entrainment across the ZVL drives the flow in the passive salt zone. An entrainment model is developed on the basis of stability theory and similarity theory for turbulent buoyant shear flows but includes an empirical transition to purely laminar flow in the low Reynolds number range. The model depends on two local parameters, a bulk Richardson number (or densimetric Froude number) and a bulk Reynolds number. Predicted entrainment rates agree well with available data over the range of parameters. Furthermore, the model can be extended to predict the interfacial shear in the complementary formulation that is based on the density interface and, again, shows good agreement with published data. In part 2, the proposed model is applied to the prediction of overall wedge properties, i.e., length, shape, and internal circulation, in estuary flows.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abraham, G., and Eysink, W. (1985). “Magnitude of interfacial shear in exchange flow.” J. Hydr. Res., 9(2), 125–132.
2.
Abraham, G., Karelse, M., and Van Os, A. G. (1979). “On the magnitude of interfacial shear of subcritical stratified flows in relation with interfacial stability.” J. Hydr. Res., 17(4), 273–287.
3.
Arita, M., and Jirka, G. H. (1987). “Two‐layer model of saline wedge. II: Predictions of mean properties.” J. of Hydr. Engrg., ASCE, 113(10), 1249–1263.
4.
Arita, M., Jirka, G. H., and Tamai, N. (1986). “Classification and mixing of two‐dimensional buoyant surface discharges.” J. Hydr. Res., 24(5), 333–345.
5.
Balloffet, A., and Borah, P. (1985). “Lower Mississippi salinity analysis.” J. Hydr. Engrg., ASCE, 3(2), 300–315.
6.
Chu, V. H., and Vanvari, M. P. (1976). “Experimental study of turbulent stratified shearing flow.” J. Hydr. Div., ASCE, 102(6), 691–706.
7.
Dermissis, V., and Partheniades, E. (1984). “Interfacial flow structure and significant shear stresses in arrested saline wedges.” Tech. rep., Dept. Engr. Sci., U. Florida, Gainesville, Fla.
8.
Grubert, J. P. (1980). “Experiments on arrested saline wedge.” J. Hydr. Div., ASCE, 106(6), 945–960.
9.
Harleman, D. R. F., and Stolzenbach, D. D. (1972). “Fluid mechanics of heat disposal from power generation.” Ann. Rev. Fluid Mech., 4, 7–32.
10.
Hamada, T. (1966). “On density current (1).” Proc. 13th Japanese Conf. Coast. Engrg., JSCE, 259–262 (in Japanese).
11.
Hino, M. (1980). “Entrainment and friction of the interface of salt wedge.” Stratified flows, T. Carstens and T. McClimans, Eds., Tapir, Trondheim, Norway.
12.
Ippen, A. T., and Harleman, D. R. F. (1952). “Steady state characteristics of subsurface flow.” NBS circular 521, contribution no. 12, gravity waves, 79–93.
13.
Jirka, G. H. (1982). “Turbulent buoyant jets in shallow fluid layers.” Turbulent buoyant jets and plumes, W. Rodi, Ed., Pergamon Press, New York, N.Y., 69–119.
14.
Johnson, H., Boyd, M., and Keulegan, G. (1985). “A mathematical study of the impact on salinity intrusion of deepening the lower Mississippi River navigation channel.” Final rep., U.S. Army Wtrway Exp. Sta., Corps of Engrs., Vicksburg, Miss.
15.
Kaneko, Y. (1966). “An example of the interfacial drag coefficient of two‐layered flow.” Proc., 16th Japanese Conf. on Coast. Eng., 263–267 (in Japanese).
16.
Keulegan, G. (1966). “The mechanism of an arrested saline wedge.” Estuary and coastline hydrodynamics, ch. 11, A. T. Ippen, Ed., McGraw Hill Book Co., New York, N.Y., 546–574.
17.
Lofquist, K. (1960). “Flow and stress near an interface between stratified liquids.” Phys. of Fluids, 3(2), 158–175.
18.
Majewski, W. (1965). “The outfall of waste waters including the effect of density differences.” Lab. invest, arrested wedge, Proc., IAHR 11th Cong., Leningrad, USSR, 2, 1–9.
19.
Nakamura, H., and Abe, N. (1970). “Salt‐water wedge in Kuzuryu River estuary.” Rep. 2nd Tech. Lab., Central Res. Inst. of Electric Power Industry, no. 70519 (in Japanese).
20.
Morton, B. (1971). “The choice of conservation equations for plume models.” J. Geophys. Res., 76(39), 7409–7416.
21.
Pederson, B. (1980). “A monograph on turbulent entrainment and friction in two‐layer stratified flow.” Tech. Rep. 25, Tech. Univ. Denmark, Denmark.
22.
Rattay, M., and Mitsuda, E. (1974). “Theoretical analysis of conditions in a salt wedge.” Estuarine and Coast. Marine Sci., 2, 375–394.
23.
Riddell, J. F. (1970). “Densimetric exchange flow in rectangular channels—IV—The arrested saline wedge.” La Houille Blanche, 4, 317–329.
24.
Sargent, F. E., and Jirka, G. H. (1982). “A comparative study of density currents and density wedge (with application to intermediate field dynamics of ocean thermal energy conversion plants).” Tech. Rep., School of Civ. and Envir. Engrg., Cornell Univ., Ithaca, N.Y.
25.
Sargent, F. H., and Jirka, G. H. “Experiments on the saline wedge.” J. Hydr. Engrg., ASCE, 113(10), 1307–1324.
26.
Schlichting, H. (1986). Boundary layer theory. 6th ed., McGraw Hill, New York, N.Y., 288–335.
27.
Shi‐igai, H. (1965). “On the resistance coefficients at the interface between salt and fresh water.” Trans., JSCE, 123, 27–31.
28.
Schijf, J. B., and Schonfeld, J. C. (1953). “Theoretical considerations on the motion of salt and fresh water.” Proc. Minnesota Int. Hydr. Conv., ASCE and IAHR, held at Minneapolis, Minn.
29.
Suga, K., and Takahashi, A. (1976). “Entrainment coefficient of fresh and salt two‐layered flows.” Proc. 31 af annual meeting, JSCE, II, 383–384.
30.
Tamai, N. (1976). “Friction at the interface of two‐layered flows.” Proc., 15th coast. Engrg. Conf., Ch. 182, 4, Honolulu, Hawaii, 3169–3188.
31.
Tsubaki, T., and Komatsu, T. (1978). “Flow characteristics and entrainment of two‐dimensional surface jet,” Proc., JSCE, 273, 69–81.
32.
Turner, J. S. (1973). Buoyancy effects in fluids. Cambridge Univ. Press, Cambridge, U.K.
33.
U.S. Army Corps of Engineers (1928–1981). “Stage, discharge and salinity data, Mississippi at and below New Orleans, La.” Data Sheets, New Orleans District, New Orleans, La.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 113 • Issue 10 • October 1987
Pages: 1229 - 1246
Copyright
Copyright © 1987 ASCE.
History
Published online: Oct 1, 1987
Published in print: Oct 1987
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.