Effects of rotation and sloping terrain on the fronts of density currents

Journal of Fluid Mechanics

Volumn 537, Issue , 2005, Pages 285-315

  Hunt, J C R ^a,b,c   Pacheco, J R ^c   Mahalov, A ^d   Fernando, H J S ^c  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c Arizona State University   (United States)

^d ARIZONA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; NAVIER STOKES EQUATIONS; PERTURBATION TECHNIQUES; VORTEX FLOW;

FLOW REGIMES; KARMAN-BENJAMIN GRAVITY CURRENT; SHALLOW WATER EQUATIONS;

UNSTEADY FLOW;

FLUID MECHANICS; ROTATION;

EID: 23944468277     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112005005239     Document Type: Article

References (56)

1. Atkinson, B. W. 1981 Dynamical Meteorology: an Introductory Selection. Methuen.
2. Babin, A., Mahalov, A. & Nicolaenko, B. 1997a Global regularity and integrability of 3D Euler and Navier-Stokes equations for uniformly rotating fluids. Asymp. Anal. 15, 103-150.
3. Babin, A., Mahalov, A. & Nicolaenko, B. 1997b Global splitting and regularity of rotating shallow-water equations. Eur. J. Mech. B/Fluids 16, 725-754.
4. Babin, A., Mahalov, A. & Nicolaenko, B. 1997c Regularity and integrability of rotating shallow-water equations. In C. R. Acad. Sci. Paris, pp. 593-598.
5. Babin, A., Mahalov, A. & Nicolaenko, B. 1998 On nonlinear baroclinic waves and adjustment of pancake dynamics. Theor. Comput. Fluid Dyn. 11, 215-235.
6. Babin, A., Mahalov, A. & Nicolaenko, B. 2002 Fast Singular Oscillating Limits of Stably Stratified Three-Dimensional Euler-Boussinesq Equations and Ageostrophic Wave fronts. Cambridge University Press.
7. Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209-248.
8. Bonnecaze, R. T., Hallworth, M. A., Huppert, H. E. & Liter, J. R. 1995 Axi-symmetric particle-driven gravity currents. J. Fluid Mech. 294, 93-121.
9. Britter, J. E. & Linden, P. F. 1980 The motion of the front of a gravity current travelling down an incline. J. Fluid Mech. 99, 531-543.
10. Britter, J. E. & Simpson, J. E. 1978 Experiments on the dynamics of a gravity current head. J. Fluid Mech. 88, 223-240.
11. Charney, J. G. 1948 On the scale of atmospheric motions. Geofys. Publ. Oslo 17, 1-17.
12. Chen, R., Boyer, D. L. & Tao, L. 1993 Laboratory simulation of atmospheric motions in the vicinity of Antarctica. J. Atmos. Sci. 50, 4058-4079.
13. Chia, F., Griffiths, R. W. & Linden, P. F. 1982 Laboratory experiments on fronts. Part ii: The formation of cyclonic eddies at upwelling fronts. Geophys. Astrophys. Fluid Dyn. 19, 189-206.
14. Creswell, G. R. & Golding, T. G. 1986 Observations of south flowing currents in the southwestern Indian ocean. Deep-Sea Res. 27, 449-466.
15. Cullen, M. J. P. 2002 New mathematical developments in atmosphere and ocean dynamics and their application to computer simulations. In Large Scale Atmosphere Ocean Dynamics (ed. J. Norbury & I. Roulstone). Cambridge University Press.
16. Embid, P. F. & Majda, A. J. 1996 Averaging over fast gravity waves for geophysical flows with arbitrary potential vorticity. Commun. Part. Diff. Eqn. 21, 619-658.
17. Gill, A. E. 1982 Atmosphere-Ocean Dynamics. Academic.
18. Hallworth, M. A., Huppert, H. E. & Ungarish, M. 2001 Axisymmetric gravity currents in a rotating system: experimental and numerical investigations. J. Fluid Mech. 447, 1-29.
19. Haltiner, G. J. & Willaims, R. T. 1980 Numerical Prediction and Dynamic Meteorology. John Wiley.
20. Hoskins, B. J. & Bretherton, F. P. 1972 Atmospheric frontogenesis models: mathematical formulation and solution. J. Atmos. Sci. 29, 11-37.
21. Ivey, G. N. 1987 Boundary mixing in a rotating stratified fluid. J. Fluid Mech. 183, 25-44.
22. Jones, D. A., Mahalov, A. & Nicolaenko, B. 1998 A numerical study of an operator splitting method for rotating flows with large ageostrophic initial data. Theoret. Comput. Fluid Dyn. 13, 143-159.
23. von Kármán, T. 1940 The engineer graples with nonlinear problems. Bull. Am. Math. Soc. 46, 615-683.
24. Legeckis, R. & Creswell, G. 1981 Satellite observations of sea surface temperature off the coast of western and southern Australia. Deep-Sea Res. 28, 279-306.
25. Lentz, S. J. & Helfrich, K. R. 2002 Buoyant gravity current along a sloping bottom in a rotating fluid. J. Fluid Mech. 464, 251-278.
26. Linden, P. F. & Simpson, J. E. 1989 Self-similar solutions of the shallow-water equations representing gravity current with variable inflow. J. Fluid Mech. 202, 1-16.
27. Maas, L. R. M. & van Haren, J. J. M. 1987 Observations on the vertical structure of tidal and inertial currents in central North Sea. J. Mar. Res. 45, 293-318.
28. McWilliams, J. C. 1985 Submesoscale coherent vortices in the ocean. Rev. Geophys. 23, 165-254.
29. Mahalov, A., Pacheco, J. R., Voropayev, S. I., Fernando, H. J. S. & Hunt, J. C. R. 2000 Effects of rotation on fronts of density currents. Phys. Letters A 270, 149-156.
30. Manins, P. C. & Sawford, B. L. 1979 Katabatic winds - field case-study. Q. J. R. Met. Soc. 105, 1011-1025.
31. Margules, M. 1906 Über Temperaturschichtung in stationär bewegter und ruhender Luft. Met. Z. 23, 165-254.
32. Milne-Thompson, L. M. 1968 Theoretical Hydrodynamics. Macmillan.
33. Noh, Y. & Fernando, H. J. S. 1992 The motion of a buoyant cloud along an incline in the presence of boundary mixing. J. Fluid Mech. 235, 557-577.
34. Noh, Y. & Fernando, H. J. S. 1993 A numerical model of the fluid motion at a density front in the presence of background turbulence. J. Phys. Oceanogr. 23, 1142-1153.
35. Norbury, J. & Roulstone, I. 2002 Large Scale Ocean Dynamics. Cambridge University Press.
36. Pacheco, J. R. 2001 The solution of viscous incompressible jet flows using non-staggered boundary fitted coordinate methods. Intl J. Numer. Meth. Fluids 35, 71-91.
37. Pacheco, J. R. & Pacheco-Vega, A. 2003 Analysis of thin film flows using a flux vector splitting. J. Fluids Engng. 125, 365-374.
38. Pacheco, J. R. & Peck, R. E. 2000 Non-staggered grid boundary-fitted coordinate method for free surface flows. Numer. Heat Transfer B 37, 267-291.
39. Parker, D. J. 2000 Frontal theory. Weather 55, 120-134.
40. Peregrine, D. H. 1967 Long waves on a beach. J. Fluid Mech. 27, 815-827.
41. Qiu, B. & Imasato, N. 1988 Baroclinic instability of buoyancy driven coastal density current. J. Geophys. Res. 93, 5037-5050.
42. Reznik, G. M., Zeitlin, V. & Jelloul, M. B. 2001 Nonlinear theory of geostrophic adjustment. Part 1. Rotating shallow-water model. J. Fluid Mech. 445, 93-120.
43. Rottman, J. W., Hunt, J. C. R. & Mercer, A. 1985 The initial and gravity spreading phases of heavy gas dispersion: comparison of models with Phase I data. J. Hazard. Mat. 11, 261-279.
44. Rottman, J. W. & Simpson, J. E. 1983 Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel. J. Fluid Mech. 135, 95-110.
45. Rottuno, R. 1983 On the linear theory of the land and sea breeze. J. Atmos. Sci. 40, 1999-2009.
46. Samah, A. A. & Thorpe, A. J. 1993 Gravity wave propagation in a frontal environment. In Waves and Turbulence in Stably Stratified Flows (ed. S. D. Morh & J. C. King). Clarendon.
47. Sidi, J. & Barat, J. 1986 Observational evidence of an inertial wind structure in the stratosphere. J. Geophys. Res. 91, 1209-1217.
48. Simpson, J. E. 1997 Gravity Currents. Cambridge University Press.
49. Stegner, A., Bouruet-Aubertot, P. & Pinchon, T. 2004 Nonlinear adjustment of density fronts. Part 1. The Rossby scenario and the experimental reality. J. Fluid Mech. 502, 335-360.
50. Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
51. Ungarish, M. & Huppert, H. E. 1998 The effects of rotation on axisymmetric gravity currents. J. Fluid Mech. 362, 17-51.
52. Vreugdenhill, C. B. 1993 Numerical Methods for Shallow-Water Flows. Kluwer.
53. Westerweel, J., Hofmann, T., Fukushima, C. & Hunt, J. C. R. 2002 The turbulent/non-turbulent interface at the outer boundary of a self-similar turbulent jet. Exps. Fluids 33, 873-878.
54. Zang, Y., Street, R. I. & Koseff, J. R. 1994 A non-staggered grid, fractional step method for time dependent incompressible Navier-Stokes equations in curvilinear coordinates. J. Comput. Phys. 114, 18-33.
55. Zeitlin, V., Medvedev, S. B. & Plougonven, R. 2003 Frontal geostrophic adjustment, slow manifold and nonlinear wave phenomena in one-dimensional rotating shallow water. Part 1. Theory. J. Fluid Mech. 481, 269-290.
56. Zukoski, E. E. 1966 Influence of viscosity, surface terrain, and inclination angle on motion of long bubbles in closed tubes. J. Fluid Mech. 25, 821-837.