Numerical studies of internal waves at a sill: Sensitivity to horizontal grid size and subgrid scale closure

Continental Shelf Research

Volumn 28, Issue 10-11, 2008, Pages 1376-1393

  Berntsen, Jarle ^a   Xing, Jiuxing ^b   Davies, Alan M ^b  

^a UNIVERSITY OF BERGEN   (Norway)

^b NATIONAL OCEANOGRAPHY CENTRE   (United Kingdom)

Author keywords

Grid resolution; Internal waves; Mixing; Non hydrostatic; Ocean modelling; Sills; Tides

Indexed keywords

BAROTROPIC TIDE; DIFFUSIVITY; INTERNAL WAVE; NUMERICAL MODEL; SENSITIVITY ANALYSIS; SILL; VERTICAL MIXING; VISCOSITY; WAVE BREAKING;

EID: 44649186210     PISSN: 02784343     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csr.2008.03.029     Document Type: Article

References (88)

1. Adcroft A., Hill C., and Marshall J. A new treatment of the coriolis terms in C-grid models at both high and low resolutions. Monthly Weather Review 127 (1999) 1928-1936
2. Afanasyev Y., and Peltier W. On breaking internal waves over the sill in Knight Inlet. Proceedings of the Royal Society of London A 457 (2001) 2799-2825
3. Afanasyev Y., and Peltier W. Reply to comment on the paper 'On breaking internal waves over the sill in Knight Inlet'. Proceedings of the Royal Society of London A 457 (2001) 2831-2834
4. Armi L. Some evidence for boundary mixing in the deep ocean. Journal of Geophysical Research 83 (1978) 1971-1979
5. Armi L., and Farmer D. Stratified flow over topography: bifurcation fronts and transition to the uncontrolled state. Proceedings of the Royal Society of London A 458 (2002) 513-538
6. Berntsen H., Kowalik Z., Sælid S., and Sørli K. Efficient numerical simulation of ocean hydrodynamics by a splitting procedure. Modeling, Identification and Control 2 (1981) 181-199
7. Berntsen, J., 2000. USERS GUIDE for a modesplit σ-coordinate numerical ocean model, Technical Report 135, Department of Applied Mathematics, University of Bergen, Johs. Bruns gt.12, N-5008 Bergen, Norway, 48p.
8. Berntsen J., and Furnes G. Internal pressure errors in sigma-coordinate ocean models- sensitivity of the growth of the flow to the time stepping method and possible non-hydrostatic effects. Continental Shelf Research 25 (2005) 829-848
9. Berntsen J., Xing J., and Alendal G. Assessment of non-hydrostatic ocean models using laboratory scale problems. Continental Shelf Research 26 (2006) 1433-1447
10. Blumberg A., and Mellor G. A description of a three-dimensional coastal ocean circulation model. In: Heaps N. (Ed). Three-Dimensional Coastal Ocean Models, Coastal and Estuarine Series vol. 4 (1987), American Geophysical Union 1-16
11. Bourgault D., and Kelley D. Wave-induced boundary mixing in a partially mixed estuary. Journal of Marine Research 61 (2003) 553-576
12. Burchard H. Applied turbulence modelling in marine waters, Lecture Notes in Earth Sciences (2002), Springer, Berlin
13. Casulli V. A semi-implicit finite difference method for non-hydrostatic, free-surface flows. International Journal for Numerical Methods in Fluids 30 (1999) 425-440
14. Cummins P. Stratified flow over topography: time-dependent comparisons between model solutions and observations. Dynamics of Atmospheres and Oceans 33 (2000) 43-72
15. Cummins P., Vagle S., Armi L., and Farmer D. Stratified flow over topography: upstream influence and generation of nonlinear waves. Proceedings of the Royal Society of London A 459 (2003) 1467-1487
16. Cushman-Roisin B., Tverberg V., and Pavia E. Resonance of internal waves in fjords: a finite difference model. Journal of Marine Research 47 (1989) 547-567
17. Davies A., and Xing J. On the influence of stratification and tidal forcing upon mixing in sill regions. Ocean Dynamics 57 (2007) 431-451
18. Dörnbrack A. Turbulent mixing by breaking gravity waves. Journal of Fluid Mechanics 375 (1998) 113-141
19. Eliassen I., Heggelund Y., and Haakstad M. A numerical study of the circulation in Saltfjorden, Saltstraumen and Skjerstadfjorden. Continental Shelf Research 21 (2001) 1669-1689
20. Farmer D., and Armi L. Stratified flow over topography: the role of small-scale entrainment and mixing in flow establishment. Proceedings of the Royal Society of London A 455 (1999) 3221-3258
21. Farmer D., and Armi L. Stratified flow over topography: models versus observations. Proceedings of the Royal Society of London A 457 (2001) 2827-2830
22. Farmer D., and Freeland H. The physical oceanography of fjords. Progress in Oceanography 12 (1983) 147-220
23. Fer I. Scaling turbulent dissipation in an Arctic fjord. Deep-Sea Research II 53 (2006) 77-95
24. Fer I., and Widell K. Early spring turbulent mixing in an ice-covered Arctic fjord during transition to melting. Continental Shelf Research 27 (2007) 1980-1999
25. Fer I., Skogseth R., Haugan P., and Jaccard P. Observations of the Storfjorden overflow. Deep-Sea Research I 50 (2003) 1283-1303
26. Galperin B., Kantha L., Hassid S., and Rosati A. A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci. 45 (1988) 55-62
27. Gill A. Atmosphere-Ocean Dynamics (1982), Academic Press, New York
28. Griffies S. Fundamentals of Ocean Climate Models (2004), Princeton University Press, Princeton, NJ
29. Guo Y., and Davies P. Laboratory modelling experiments on the flow generated by the tidal motion of a stratified ocean over a continental shelf. Continental Shelf Research 23 (2003) 193-212
30. Guo Y., Sveen J., Davies P., Grue J., and Dong P. Modelling the motion of an internal solitary wave over a bottom ridge in a stratified fluid. Environmental Fluid Mechanics 4 (2005) 415-441
31. Haidvogel D., and Beckmann A. Numerical ocean circulation modeling, Series on Environmental Science and Management vol. 2 (1999), Imperial College Press
32. Haney R. On the pressure gradient force over steep topography in sigma coordinate ocean models. Journal of Physical Oceanography 21 (1991) 610-619
33. Heggelund Y., Vikebø F., Berntsen J., and Furnes G. Hydrostatic and non-hydrostatic studies of gravitational adjustment over a slope. Continental Shelf Research 24 (2004) 2133-2148
34. Helfrich K., and Melville W. Long nonlinear internal waves. Annual Review of Fluid Mechanics 38 (2006) 395-425
35. Inall M., Cottier F., Griffiths C., and Rippeth T. Sill dynamics and energy transformation in a jet fjord. Ocean Dynamics 54 (2004) 307-314
36. Inall M., Rippeth T., Griffiths C., and Wiles P. Evolution and distribution of TKE production and dissipation within stratified flow over topography. Geophysical Research Letters 32 (2005) L08607 10.1029/2004GL022289
37. Kanarska Y., and Maderich V. A non-hydrostatic numerical model for calculating free-surface stratified flows. Ocean Dynamics 53 (2003) 176-185 10.1007/s10236-003-0039-6
38. Kantha L., and Clayson C. Small scale processes in geophysical fluid flows. International Geophysics Series vol. 67 (2000), Academic Press, New York
39. Klymak J., and Gregg M. Three-dimensional nature of flow near a sill. Journal of Geophysical Research 106 (2001) 22295-22311
40. Klymak J., and Gregg M. The role of upstream waves and a downstream density pool in the growth of lee waves: stratified flow over the knight inlet sill. Journal of Physical Oceanography 33 (2003) 1446-1461
41. Klymak J., and Gregg M. Tidally generated turbulence over the knight inlet sill. Journal of Physical Oceanography 34 (2004) 1135-1151
42. Kowalik Z., and Murty T. Numerical Modeling of Ocean Dynamics, Advanced Series on Ocean Engineering vol. 5 (1993), World Scientific, Singapore
43. Kundu P., and Beardsley R. Evidence of a critical Richardson number in moored measurements during the upwelling season off Northern California. Journal of Geophysical Research 96 (1991) 4855-4868
44. Kundu P., and Cohen I. Fluid Mechanics (2008), Elsevier Academic Press, Amsterdam
45. Kunze E., and Llewellyn Smith S. The role of small-scale topography in turbulent mixing of the global Ocean. Oceanography 17 (2004) 55-64
46. Lamb K. On boundary-layer separation and internal wave generation at the Knight Inlet sill. Proceedings of the Royal Society of London A 460 (2004) 2305-2337
47. Lamb K. Energy and pseudoenergy flux in the internal wave field generated by tidal flow over topography. Continental Shelf Research 27 (2007) 1208-1232
48. Legg S., and Adcroft A. Internal wave breaking at concave and convex continental slopes. Journal of Physical Oceanography 33 (2003) 2224-2246
49. Marshall J., Adcroft A., Hill C., Perelman L., and Heisey C. A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. Journal of Geophysical Research 102 C3 (1997) 5753-5766
50. Marshall J., Hill C., Perelman L., and Adcroft A. Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling. Journal of Geophysical Research 102 C3 (1997) 5733-5752
51. McCabe R., MacCready P., and Pawlak G. Form drag due to flow separation at a headland. Journal of Physical Oceanography 36 (2006) 2136-2152
52. Mellor, G., 1996. Users guide for a three-dimensional, primitive equation numerical ocean model. Technical Report, Princeton University, Princeton, NJ.
53. Mellor G., and Yamada T. Development of a turbulence closure model for geophysical fluid problems. Reviews of Geophysics and Space Physics 20 (1982) 851-875
54. Mellor G., Oey L.-Y., and Ezer T. Sigma coordinate pressure gradient errors and the seamount problem. Journal of Atmospheric and Oceanic Technology 15 (1998) 1122-1131
55. Munk W., and Wunsch C. Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Research I 45 (1998) 1978-2010
56. Pacanowski R., and Philander S. Parameterization of vertical mixing in numerical models of tropical oceans. Journal of Physical Oceanography 11 (1981) 1443-1451
57. Parsmar R., and Stigebrandt A. Observed damping of barotropic seiches through baroclinic wave drag in the gullmar fjord. Journal of Physical Oceanography 27 (1997) 849-857
58. Pierrehumbert R., and Wyman B. Upstream effects of mesoscale mountains. Journal of the Atmospheric Sciences 42 (1985) 977-1003
59. Polzin K., Toole J., Ledwell J., and Schmitt R. Spatial variability of turbulent mixing in the abyssal ocean. Science 276 (1997) 93-96
60. Samelson R. Large scale circulation with locally enhanced vertical mixing. Journal of Physical Oceanography 28 (1998) 712-726
61. Shchepetkin A., and McWilliams J. A method for computing horizontal pressure-gradient force in an oceanic model with a non-aligned vertical coordinate. Journal of Geophysical Research 108 C3, 3090 (2003) 10.1029/2001C001047
62. Skogseth R., Haugan P., and Jakobsson M. Watermass transformations in Storfjorden. Continental Shelf Research 25 (2005) 667-695
63. Skogseth R., Sandvik A., and Asplin L. Wind and tidal forcing on the meso-scale circulation in Storfjorden, Svalbard. Continental Shelf Research 27 (2007) 208-227
64. Smagorinsky J. General circulation experiments with the primitive equations, I. The basic experiment. Monthly Weather Review 91 (1963) 99-164
65. Smyth W., Nash J., and Moum J. Differential diffusion in breaking Kelvin-Helmholtz billows. Journal of Physical Oceanography 35 (2005) 1004-1022
66. Spall M. Large-scale circulations forced by localized mixing over a sloping bottom. Journal of Physical Oceanography 31 (2001) 2369-2384
67. Stacey M. Some aspects of the internal tide in knight, inlet British Columbia. Journal of Physical Oceanography 15 (1985) 1652-1661
68. Stacey M., and Gratton Y. The energetics and tidally induced reverse renewal in a two-silled fjord. Journal of Physical Oceanography 31 (2001) 1599-1615
69. Stashchuk N., and Vlasenko V. Numerical modelling of stratified tidal flow over a fjord sill. Ocean Dynamics 57 (2007) 325-338
70. Stashchuk N., Inall M., and Vlasenko V. Analysis of supercritical stratified tidal flow in a scottish fjord. Journal of Physical Oceanography 37 (2007) 1793-1810
71. Stigebrandt A. Vertical diffusion driven by internal waves in a sill fjord. Journal of Physical Oceanography 6 (1976) 486-495
72. Stigebrandt A. Resistance to barotropic tidal flow in straits by baroclinic wave drag. Journal of Physical Oceanography 29 (1999) 191-197
73. Stigebrandt A., and Aure J. Vertical mixing in basin waters of fjords. Journal of Physical Oceanography 19 (1989) 917-926
74. Sveen J., Guo Y., Davies P., and Grue J. On the breaking of internal solitary waves at a ridge. Journal of Fluid Mechanics 469 (2002) 161-188
75. Thiem Ø., and Berntsen J. Internal pressure errors in sigma-coordinate ocean models due to anisotropy. Ocean Modelling 12 (2006) 140-156
76. Thorpe S. The Turbulent Ocean (2005), Cambridge University Press, Cambridge
77. Tverberg V., Cushman-Roisin B., and Svendsen H. Modeling of internal tides in fjords. Journal of Marine Research 49 (1991) 635-658
78. Vlasenko V., and Stashchuk N. Amplification and suppression of internal waves by tides over variable bottom topography. Journal of Physical Oceanography 36 (2006) 1959-1973
79. Vlasenko V., Stashchuk N., and Hutter K. Water exchange in fjords induced by tidally generated internal lee waves. Dynamics of Atmospheres and Oceans 35 (2002) 63-89
80. Vlasenko V., Stashchuk N., and Hutter K. Baroclinic tides: theoretical modeling and observational evidence. Cambridge Monographs on Mechanics (2005), Cambridge University Press, Cambridge
81. Wang D.-P. Tidally generated internal waves in partially mixed estuaries. Continental Shelf Research 26 (2006) 1469-1480
82. Wunsch C. On oceanic boundary mixing. Deep-Sea Research 17 (1970) 293-301
83. Wunsch C., and Ferrari R. Vertical mixing, energy, and the general circulation of the Oceans. Annual Review of Fluid Mechanics 36 (2004) 281-314
84. Xing J., and Davies A. Processes influencing tidal mixing in the region of sills. Geophysical Research Letters 33 (2006) L04603 10.1029/2005GL025226
85. Xing J., and Davies A. Influence of stratification and topography upon internal wave spectra in the region of sills. Geophysical Research Letters 33 (2006) L23606 10.1029/2005GL025226
86. Xing J., and Davies A. On the importance of non-hydrostatic processes in determining tidally induced mixing in sill regions. Continental Shelf Research 27 (2007) 2162-2185
87. Yang H., and Przekwas A. A comparative study of advanced shock-capturing schemes applied to Burgers equation. Journal of Computational Physics 102 (1992) 139-159
88. Zhao L., Chen C., and Cowles G. Tidal flushing and eddy shedding in Mount Hope Bay and Narragansett Bay: an application of FVCOM. Journal of Geophysical Research 111 (2006) C10015 10.1029/2005JC003135