Reynolds number dependence of mixing in a lock-exchange system from direct numerical and large eddy simulations

Ocean Modelling

Volumn 30, Issue 2-3, 2009, Pages 190-206

  Özgökmen, Tamay M ^a   Iliescu, Traian ^b   Fischer, Paul F ^c  

^a UNIVERSITY OF MIAMI   (United States)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^c ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

DNS; LES; Mixing; Reynolds number

Indexed keywords

APPROXIMATE DECONVOLUTION; COMPUTATIONAL TOOLS; DIRECT-NUMERICAL-SIMULATION; DNS; EDDY VISCOSITY; EXCHANGE PROBLEMS; LES; OCEAN CIRCULATION; OCEANIC FLOW; POSTERIORI; THREE ORDERS OF MAGNITUDE; TURBULENT MIXING; UNAM-BIGOUS; WATER MASS;

COMPUTER SIMULATION LANGUAGES; INTERNET PROTOCOLS; MIXING; OCEANOGRAPHY; POTENTIAL ENERGY; REYNOLDS NUMBER; SIMULATORS; TURBULENT FLOW;

LARGE EDDY SIMULATION;

LARGE EDDY SIMULATION; MIXING; NUMERICAL MODEL; POTENTIAL ENERGY; REYNOLDS NUMBER; WATER MASS;

EID: 68749099676     PISSN: 14635003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ocemod.2009.06.013     Document Type: Article

References (93)

1. Baumert H., and Peters H. Turbulence closure, steady state, and collapse into waves. J. Phys. Oceanogr. 34 (2004) 505-512
2. Baumert H., Simpson J., and Sündermann J. Marine Turbulence (2005), Cambridge University Press, Cambridge, UK
3. Benjamin T.B. Gravity currents and related phenomena. J. Fluid Mech. 31 (1968) 209-248
4. Berselli L., Iliescu T., and Layton W. Mathematics of Large Eddy Simulation of Turbulent Flows (2005), Springer-Verlag
5. Britter R.E., and Simpson J.E. Experiments on the dynamics of a gravity current head. J. Fluid Mech. 88 (1978) 223-240
6. Burchard H., and Baumert H. On the performance of a mixed-layer model based on the k - ε turbulence closure. J. Geophys. Res. 100 (1995) 8523-8540
7. Burchard H., and Bolding K. Comparative analysis of four second-moment turbulence closure models for the oceanic mixed layer. J. Phys. Oceanogr. 31 (2001) 1943-1968
8. Cantero M.I., Balachandar S., Garcia M., and Ferry J.R. Direct numerical simulations of planar and cylindrical density currents. J. Appl. Mech. 73 (2006) 923-930
9. Cantero M.I., Lee J.R., Balachandar S., and Garcia M. On the front velocity of gravity currents. J. Fluid Mech. 586 (2007) 1-39
10. Canuto V., Cheng Y., and Howard A. Non-local ocean mixing mode and a new plume model for deep convection. Ocean Modell. 16 (2007) 28-46
11. Canuto V.M., Howard A.M., Cheng Y., and Esau I.N. Stably stratified flows: a model with no Ri(cr). J. Atmos. Sci. 65 (2008) 2437-2447
12. Canuto V.M., Howard A., Cheng Y., and Dubovikov M.S. Ocean turbulence. Part I: one-point closure model momentum and heat vertical diffusivities. J. Phys. Oceanogr. 31 (2001) 1413-1426
13. Cao C., Holm D.D., and Titi E.S. On the Clark-α model of turbulence: global regularity and long-time dynamics. J. Turbul., 1468-5248 6 (2005) 11 (Electronic)
14. Carati D., Winckelmans G., and Jeanmart H. On the modeling of the subgrid-scale and filtered-scale stress tensors in large-eddy simulation. J. Fluid Mech. 441 (2001) 119-138
15. Chang Y., Xu X., Özgökmen T., Chassignet E., Peters H., and Fischer P. Comparison of gravity current mixing parameterizations and calibration using a high-resolution 3d nonhydrostatic spectral element model. Ocean Modell. 10 (2005) 342-368
16. Clark R., Ferziger J., and Reynolds W. Evaluation of subgrid scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91 (1979) 1-16
17. Deville M., Fischer P., and Mund E. High-order Methods for Incompressible Fluid Flow, vol. 9 of Cambridge Monographs on Applied and Computational Mathematics (2002), Cambridge University Press, Cambridge. 0-521-45309-7
18. Dörnbrack A. Turbulent mixing by breaking gravity waves. J. Fluid Mech. 375 (1998) 113-141
19. Dryja, M., Widlund, O.B., 1987. An additive variant of the Schwarz alternating method for the case of many subregions. Technical Report Technical Report 339. Dept. Computer Science, Courant Institute.
20. Ferron B., Mercier H., Speer K., Gargett A., and Poltzin K. Mixing in the romanche fracture zone. J. Phys. Oceanogr. 28 (1998) 1929-1945
21. Fischer P., and Gottlieb D. On the optimal number of subdomains for hyperbolic problems on parallel computers. Int. J. Supercomp. Appl. High Perf. Comp. 11 (1997) 65-76
22. Fischer P., and Mullen J. Filter-based stabilization of spectral element methods. C. R. Acad. Sci. Paris Sér. I Math., 0764-4442 332 3 (2001) 265-270
23. Fischer P.F. An overlapping Schwarz method for spectral element solution of the incompressible Navier-Stokes equations. J. Comp. Phys. 133 (1997) 84-101
24. Fischer P.F., Miller N.I., and Tufo H.M. An overlapping Schwarz method for spectral element simulation of three-dimensional incompressible flows. In: Luskin P.B.M. (Ed). Parallel Solution of Partial Differential Equations (2000), Springer-Verlag 159-181
25. Fischer P.F., and Ronquist E.M. Spectral element methods for large scale parallel Navier-Stokes calculation. Comput. Methods Appl. Mech. Eng. 116 (1994) 69
26. Frisch U. Turbulence, The Legacy of A.N. Kolmogorov (1995), Cambridge University Press, Cambridge
27. Galdi G., and Layton W. Approximation of the larger eddies in fluid motions. II. A model for space-filtered flow. Math. Models Methods Appl. Sci., 0218-2025 10 3 (2000) 343-350
28. Germano M., Piomelli U., Moin P., and Cabot W. A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (1991) 1760-1765
29. Gibson C., Nabatov V., and Ozmidov R. Measurements of turbulence and fussil turbulence near Ampere seamount. Dyn. Atmos. Oceans 19 (1993) 175-204
30. Hacker J., Linden P.F., and Dalziel S.B. Mixing in lock-release gravity currents. Dyn. Atmos. Oceans 24 1-4 (1996) 183-195
31. Hallworth M.A., Huppert H.E., Phillips J.C., and Sparks R.S.J. Entrainment into two-dimensional and axisymmetric turbulent gravity currents. J. Fluid Mech. 308 (1996) 289-311
32. Hallworth M.A., Phillips J.C., Huppert H.E., and Sparks R.S.J. Entrainment in turbulent gravity currents. Nature 362 (1993) 829-831
33. Härtel C., Meiburg E., and Necker F. 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 (2000) 189-212
34. Huppert H.E., and Simpson J.E. The slumping of gravity currents. J. Fluid Mech. 99 (1980) 785-799
35. Ilicak M., Özgökmen T., Özsoy E., and Fischer P. Non-hydrostatic modeling of exchange flows across complex geometries. Ocean Modell. 29 (2009) 159-175
36. Ili{dotless}cak M., Özgökmen T.M., Peters H., Baumert H.Z., and Iskandarani M. Performance of two-equation turbulence closures in three-dimensional simulations of the Red Sea overflow. Ocean Modell. 24 (2008) 122-139
37. Iliescu T., and Fischer P. Large Eddy Simulation of turbulent channel flows by the Rational LES model. Phys. Fluids 15 10 (2003) 3036-3047
38. Iliescu T., and Fischer P. Backscatter in the Rational LES model. Comput. Fluids 35 5-6 (2004) 783-790
39. John V. Analytical and numerical results for a class of LES models. Large Eddy Simulation of Turbulent Incompressible Flows, vol. 34 of Lecture Notes in Computational Science and Engineering (2004), Springer-Verlag, Berlin. 3-540-40643-3
40. John V. An assessment of two models for the subgrid scale tensor in the Rational LES model. J. Comp. Appl. Math. 173 (2005) 57-80
41. Kantha L.H., and Clayson C.A. An improved mixed layer model for geophysical applications. J. Geophys. Res. 99 (1994) 252355-252366
42. Kantha L.H., and Clayson C.A. Small Scale Processes in Geophysical Flows (2000), Academic Press, New York
43. Katopodes F., Street R., and Ferziger J. Subfilter-scale scalar transport for large-eddy simulation. 14th Symposium on Boundary Layer and Turbulence (2000), American Meteorological Society 472-475
44. Klaassen G.P., and Peltier W.R. The role of transverse secondary instabilities in the evolution of free shear layers. J. Fluid Mech. 202 (1989) 367-402
45. Klaassen G.P., and Peltier W.R. The influence of stratification on secondary instability in free shear layers. J. Fluid Mech. 227 (1991) 71-106
46. Kunze E., and Toole J. Tidally driven vorticity, diurnal shear, and turbulence atop Fieberling Seamount. J. Phys. Oceanogr. 27 (1997) 2663-2693
47. Lavelle J., Lozovatsky I., and Smith D. Tidally induced turbulent mixing at Irving Seamount - Modeling and measurements. Geopys. Res. Lett. 31 L10308 (2004) 10.1029/2004GL019706
48. Ledwell J., Montgomery E., Polzin K., Schmitt R., St. Laurent L., and Toole J. Evidence for enhanced mixing over rough topography in the abyssal ocean. Nature 403 (2000) 179-182
49. Leonard A. Energy cascade in large eddy simulations of turbulent fluid flows. Adv. Geophys. 18A (1974) 237-248
50. Lottes J.W., and Fischer P.F. Hybrid multigrid/Schwarz algorithms for the spectral element method. J. Sci. Comput. 24 1 (2005) 45-78
51. Lueck R., and Mudge T. Topographically induced mixing around a shallow seamount. Science 276 (1997) 1831-1833
52. Maday Y., and Patera A.T. Spectral element methods for the Navier-Stokes equations. In: Noor A.K. (Ed). State of the Art Surveys in Computational Mechanics (1989), ASME 71-143
53. Maday Y., Patera A.T., and Rønquist E.M. An operator-integration-factor splitting method for time-dependent problems: application to incompressible fluid flow. J. Sci. Comput. 10 (1990) 496-508
54. Mellor G.L., and Yamada T. Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. 30 (1982) 851-875
55. Meneveau C., Lund T., and Cabot W. A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319 (1996) 353-385
56. Miles J.W. On the stability of heterogeneous shear flows. J. Fluid Mech. 10 (1961) 496-508
57. Moum J., Caldwell D., Nash J., and Gunderson G. Observations of boundary mixing over the continental slope. J. Phys. Oceanogr. 32 (2002) 2113-2130
58. Nabatov V., and Ozmidov R. A study of turbulence over underwater mountains in the Atlantic Ocean. Oceanology 28 (1988) 210-217 (in Russian)
59. Özgökmen T., and Fischer P. On the role of bottom roughness in overflows. Ocean Modell. 20 (2008) 336-361
60. Özgökmen T., Fischer P., and Johns W. Product water mass formation by turbulent density currents from a high-order nonhydrostatic spectral element model. Ocean Modell. 12 (2006) 237-267
61. Özgökmen T., Iliescu T., and Fischer P. Large eddy simulation of stratified mixing in a three-dimensional lock-exchange system. Ocean Modell. 26 (2009) 134-155
62. Özgökmen T., Iliescu T., Fischer P., Srinivasan A., and Duan J. Large eddy simulation of stratified mixing in two-dimensional dam-break problem in a rectangular enclosed domain. Ocean Modell. 16 (2007) 106-140
63. Özgökmen T.M., Fischer P.F., Duan J., and Iliescu T. Three-dimensional turbulent bottom density currents from a high-order nonhydrostatic spectral element model. J. Phys. Oceanogr. 34 9 (2004) 2006-2026
64. Özgökmen T.M., Fischer P.F., Duan J., and Iliescu T. Entrainment in bottom gravity currents over complex topography from three-dimensional nonhydrostatic simulations. Geophys. Res. Lett. 31 L13212 (2004) 10.1029/2004GL020186
65. Patera A. A spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comp. Phys. 54 (1984) 468-488
66. Peters H., Gregg M., and Sanford T. Detail and scaling of turbulent overturns in the Pacific Equatorial Undercurrent. J. Geophys. Res. 100 (1995) 18349-18368
67. Peters H., and Johns W.E. Mixing and entrainment in the Red Sea outflow plume. Part ii: turbulence characteristics. J. Phys. Oceanogr. 35 (2005) 584-600
68. Poltzin K., Toole J., Ledwell J., and Schmitt R. Spatial variability of turbulent mixing in the abyssal ocean. Science 276 (1997) 93-96
69. Pope S. Turbulent Flows (2000), Cambridge University Press, Cambridge. 0-521-59886-9
70. Porté-Agel F., Meneveau C., and Parlange M.B. A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J. Fluid Mech., 0022-1120 415 (2000) 261-284
71. Price J.F., and Baringer M.O. Outflows and deep water production by marginal seas. Prog. Oceanogr. 33 (1994) 161-200
72. Rohr J.J., Itsweire E.C., Helland K.N., and Atta C.W.V. Growth and decay of turbulence in stably stratified shear flow. J. Fluid Mech. 195 (1988) 77-111
73. Rottman J.W., and Simpson J.E. Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel. J. Fluid Mech. 135 (1983) 95-110
74. Sagaut P. Large Eddy Simulation for Incompressible Flows. Scientific Computation (2006), Springer-Verlag, Berlin
75. Schlatter P., Stolz S., and Kleiser L. LES of transitional flows using the approximate deconvolution model. Int. J. Heat Fluid Flow 25 (2004) 549-558
76. Schumann U. Subgrid scale model of finite difference simulations of turbulent flows in plane channels and annuli. J. Comp. Phys. 18 (1975) 376-404
77. Shin J.O., Dalziel S.B., and Linden P.F. Gravity currents produced by lock exchange. J. Fluid Mech. 521 (2004) 1-34
78. Simpson J.E. The dynamics of the head of a gravity current advancing over a horizontal surface. J. Fluid Mech. 94 (1979) 477-495
79. Smagorinsky J. General circulation experiments with the primitive equations. Mon. Weather Rev. 91 (1963) 99-164
80. Stevens B., Moeng C.-H., and Sullivan P. Entrainment and subgrid lengthscales in large-eddy simulations of atmospheric boundary layer flows. In: Kerr R.M., and Kimura Y. (Eds). Developments in Geophysical Turbulence (1998), Kluwer 253-269
81. Stolz S., and Adams N. An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids 11 7 (1999) 1699-1701
82. Stolz S., Schlatter P., and Kleiser L. High-pass filtered eddy-viscosity models for large-eddy simulations of transitional and turbulent flow. Phys. Fluids 17 (2005) 065103
83. Thorpe S. The Turbulent Ocean (2005), Cambridge University Press, New York
84. Thurnherr A. Diapycnal mixing associated with an overflow in a deep submarine canyon. Deep Sea Res. II 53 (2006) 194-206
85. Thurnherr A., Laurent L.S., Speer K., Toole J., and Ledwell J. Mixing associated with sills in a canyon on the mid-ocean ridge flank. J. Phys. Oceanogr. 35 (2004) 1370-1381
86. Thurnherr A., and Speer K. Boundary mixing and topographic blocking on the Mid-Atlantic Ridge in the South Atlantic. J. Phys. Oceanogr. 33 (2003) 848-862
87. Tseng Y., and Ferziger J. Mixing and available potential energy in stratified flows. Phys. Fluids 13 (2001) 1281-1293
88. Tufo H.M., and Fischer P. Fast parallel direct solvers for coarse grid problems. J. Par. Dist. Comput. 173 (2001) 431-471
89. Umlauf L., and Burchard H. Second-order turbulence closure models for geophysical boundary layers: a review of recent work. Cont. Shelf Res. 25 (2005) 795-827
90. Warner J.C., Sherwood C.R., Arango H.G., and Signell R.P. Performance of four turbulence closure methods implemented using a generic length scale method. Ocean Modell. 8 (2005) 81-113
91. Winckelmans G., Wray A., Vasilyev O., and Jeanmart H. Explicit-filtering large-eddy simulations using the tensor-diffusivity model supplemented by a dynamic Smagorinsky term. Phys. Fluids 13 (2001) 1385-1403
92. Winters K.B., Lombard P.N., Riley J.J., and D'Asaro E.A. Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289 (1995) 115-128
93. Xu X., Chang Y., Peters H., Özgökmen T., and Chassignet E. Parameterization of gravity current entrainment for ocean circulation models using a high-order 3d nonhydrostatic spectral element model. Ocean Modell. 14 (2006) 19-44