Weakly nonhydrostatic effects in compositionally-driven gravity flows

Studies in Applied Mathematics

Volumn 111, Issue 2, 2003, Pages 239-267

  Antar, N ^a   Moodie, T B ^b  

^a ISTANBUL TECHNICAL UNIVERSITY   (Turkey)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; HYDRAULICS; TWO PHASE FLOW;

DEPTH VARIATION; GOVERNING EQUATIONS; GRAVITY CURRENTS; GRAVITY FLOWS; HORIZONTAL VELOCITY; NONHYDROSTATIC EFFECT; PRESSURE-FIELD; SPACE AND TIME; TWO-LAYER FLOWS; VELOCITY FIELD;

ASPECT RATIO;

EID: 0037704464     PISSN: 00222526     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9590.t01-1-00233     Document Type: Article

References (39)

1. G. V. MIDDLETON, Sediment deposition from turbidity currents, Annu. Rev. Earth Planet. Sci. 21:89-114 (1993).
2. P. F. LINDEN, The fluid mechanincs of natural ventilation, Ann. Rev. Fluid Mech. 31:201-238 (1999).
3. S. J. D. D' ALESSIO, T. B. MOODIE, J. P. PASCAL, and G. E. SWATERS, Gravity currents produced by sudden release of a fixed volume of heavy fluid, Stud. Appl. Math. 96:359-385 (1996).
4. S. J. D. D' ALESSIO, T. B. MOODIE, J. P. PASCAL, and G. E. SWATERS, Intrusive gravity currents, Stud. Appl. Math. 98:19-46 (1997).
5. P. J. MONTGOMERY and T. B. MOODIE, Analytical and numerical results for flow and shock formation in two-layer models of gravity currents, J. Austral. Math. Soc. B 40:35-58 (1998).
6. P. J. MONTGOMERY and T. B. MOODIE, Two layer gravity currents with topography, Stud. Appl. Math. 102:221-266 (1999).
7. T. VON KÁRMÁN, The engineer grapples with nonlinear problems, Bull. Am. Math. Soc. 46:615-683 (1940).
8. T. B. BENJAMIN, Gravity currents and related phenomena, J. Fluid Mech. 31:209-248 (1968).
9. G. H. KEULEGAN, The motion of saline fronts in still water, US Nat. Bur. Stand. Technical Report 5831, 1958.
10. D. P. HOULT, Oil spreading on the sea, Ann. Rev. Fluid Mech. 4:341-368 (1972).
11. T. K. FANNELOP and G. D. WALDMAN, Dynamics of oil slicks, AIAA J. 10:506-510 (1972).
12. J. W. ROTTMAN and J. E. SIMPSON, Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel, J. Fluid Mech. 135:95-110 (1983).
13. R. J. LEVEQUE, Numerical methods for Conservation Laws, (2nd ed.), Birkhäuser, Basel, Switzerland, 1992.
14. R. E. GRUNDY and J. W. ROTTMAN, The approach to self-similarity of the solutions of the shallow-water equations representing gravity-current releases, J. Fluid Mech. 156:39-53 (1985).
15. R. T. BONNECAZE, H. E. HUPPERT, and J. R. LISTER, Particle-driven gravity currents, J. Fluid Mech. 250:339-369 (1993).
16. R. T. BONNECAZE, M. A. HALLWORTH, H.E. HUPPERT, and J. R. LISTER, Axisymmetric particle-driven gravity currents, J. Fluid Mech. 294:93-121 (1995).
17. R. T. BONNECAZE, H. E. HUPPERT, and J. R. LISTER, Patterns of sedimentation from polydispersed turbidity currents, Proc. Roy Soc. Land. A 452:2247-2261 (1996).
18. T. B. MOODIE, J. P. PASCAL, and G. E. SWATERS, Sediment transport and deposition from a two-layer fluid model of gravity currents on sloping bottoms, Stud. Appl. Math. 100:215-244 (1998).
19. T. B. MOODIE, J. P. PASCAL, and J. C. BOWMAN, Modelling sediment deposition patterns arising from suddenly released fixed-volume turbulent suspensions, Stud. Appl. Math. 105:333-359 (2000).
20. T. B. MOODIE, Hydraulic theory and particle-driven gravity currents, Stud. Appl. Math. 105:115-120 (2000).
21. T. B. MOODIE and J. P. PASCAL, Non-hydraulic effects in particle-driven gravity currents in deep surroundings, Stud. Appl. Math. 107:217-251 (2001).
22. D. Z. ZHU and G. A. LAWRENCE, Non-hydrostatic effects in layered shallow water flows, J. Fluid Mech. 355:1-16 (1998).
23. L. J. PRATT, Nonlinear flow over several obstacles, J. Atmos. Sci. 4:1212-1225 (1984).
24. N. S. SIVAKUMARAN, T. TINGSANCEALI, and R. J. HOSKING, Steady shallow flow over curved beds, J. Fluid Mech. 128:469-487 (1983).
25. G. A. LAWRENCE, The hydraulics of steady two-layer flow over a fixed obstacle, J. Fluid Mech. 254:605-633 (1993).
26. W. C. ULRICH, A comparison between hydrostatic and nonhydrostatic simulations of gravity currents and their interaction with orography, Meteorol. Atmos. Phys. 46:1-13 (1991).
27. W. C. ULRICH, Quasi-nonhydrostatic extensions in an anelastic model of gravity currents, Meteorol. Atmos. Phys. 52:137-145 (1993).
28. B. JOHNS, The modelling of the free surface flow of water over topography, Coastal Eng. 15:257-278 (1991).
29. P. K. STANSBY and J. G. ZHOU, Shallow-water flow solver with non-hydrostatic pressure: 2D vertical plane problems, Int. J. Numer. Meth. Fluids 28:541-563 (1998).
30. R. LISKA, L. MARGOLIN, and B. WENDROFF, Nonhydrostatic two-layer models of incompressible flow, Computers Math. Applic. 29:25-37 (1995).
31. A. E. GREEN and P. M. NAGHDI, A derivation of equations for wave propagation in water of variable depth, J. Fluid Mech. 78:237-246 (1976).
32. R. CAMASSA, D. D. HOLM, and C. D. LEVERMORE, Long-time effects of bottom topography in shallow water, Physica D 98:258-286 (1996).
33. W. CHOI and R. CAMASSA, Fully nonlinear internal waves in a two-fluid system, J. Fluid Mech. 396:1-36 (1999).
34. J. PEDLOSKY, Geophysical Fluid Dynamics, (2nd ed.) Springer, New York, 1986.
35. P. G. BAINES, Topographic Effects in Stratified Flows, Cambridge University Press, Cambridge, 1995.
36. S. JIN and Z. XIN, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Commun. Pure Appl. Math. 48:235-276 (1995).
37. P. J. MONTGOMERY and T. B. MOODIE, Generalization of a relaxation scheme for systems of forced nonlinear hyperbolic conservation laws with spatially dependent flux functions, Stud. Appl. Math., 110:1-19 (2003).
38. P. J. MONTGOMERY, Shallow-Water Models for Gravity Currents, Ph.D. Thesis, University of Alberta, Edmonton, 1999.
39. J. E. SIMPSON, Gravity Currents in the Environment and the Laboratory, (2nd ed)., Cambridge University Press, Cambridge. 1997.