Numerical studies of flow over a sill: Sensitivity of the non-hydrostatic effects to the grid size

Ocean Dynamics

Volumn 59, Issue 6, 2009, Pages 1043-1059

  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; Non hydrostatic; Ocean modelling; Sills; Tides

Indexed keywords

GRID RESOLUTION; GRID SIZE; HIGH RESOLUTION; HORIZONTAL GRID; HYDROSTATIC OCEAN; INTERNAL WAVE ACTIVITY; INTERNAL WAVES; LENGTH SCALE; NON-HYDROSTATIC; NON-HYDROSTATIC PRESSURE; NONHYDROSTATIC MODEL; NUMERICAL RESULTS; NUMERICAL SOLUTION; NUMERICAL STUDIES; SEPARATION POINTS; SUPER-CRITICAL; SYSTEMATIC STUDY; TEMPERATURE FIELD; TIME AND SPACE; TIME MEAN VELOCITY;

FLOW OF WATER; HYDRAULICS; HYDRODYNAMICS; HYDROSTATIC PRESSURE; PRESSURE EFFECTS; SEPARATION; SURFACE DISCHARGES; TIDES;

EXPERIMENTS;

HYDROSTATIC PRESSURE; INTERNAL WAVE; LEE WAVE; SHALLOW WATER; SILL; TEMPERATURE PROFILE; TIDAL MODELING; VORTEX FLOW;

EID: 71149113184     PISSN: 16167341     EISSN: 16167228     Source Type: Journal    
DOI: 10.1007/s10236-009-0227-0     Document Type: Conference Paper

References (68)

1. A Adcroft C Hill J Marshall 1999 A new treatment of the coriolis terms in c-grid models at both high and low resolutions Mon Weather Rev 127 1928 1936 10.1175/1520-0493(1999)127<1928:ANTOTC>2.0.CO;2
2. Y Afanasyev W Peltier 2001 On breaking internal waves over the sill in Knight Inlet Proc R Soc Lond A 457 2799 2825 10.1098/rspa.2000.0735
3. Y Afanasyev W Peltier 2001 Reply to comment on the paper 'On breaking internal waves over the sill in Knight Inlet' Proc R Soc Lond A 457 2831 2834 10.1098/rspa.2001.0801
4. L Armi D Farmer 2002 Stratified flow over topography: bifurcation fronts and transition to the uncontrolled state Proc R Soc Lond A 458 513 538 10.1098/rspa.2001.0887
5. H Avlesen J Berntsen T Espelid 2001 A convergence study of two prognostic, sigma coordinate ocean models on a density driven flow in a quadratic basin Int J Numer Model Fluids 36 639 657 10.1002/fld.149 (Pubitemid 32710700)
6. H Berntsen Z Kowalik S Sælid K Sørli 1981 Efficient numerical simulation of ocean hydrodynamics by a splitting procedure Model Identif Contro 2 181 199
7. Berntsen J (2000) USERS GUIDE for a modesplit σ-coordinate numerical ocean model. Technical report 135, Dept. of Applied Mathematics, University of Bergen, Bergen, 48 p
8. J Berntsen D Aksnes A Foldvik 2002 Production enhancement by artificial upwelling: a simulation study Hydrobiologia 484 177 190 10.1023/A:1021317424276 (Pubitemid 36128494)
9. J Berntsen G Furnes 2005 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 Cont Shelf Res 25 829 848 10.1016/j.csr.2004.09.025 (Pubitemid 40406147)
10. J Berntsen J Xing G Alendal 2006 Assessment of non-hydrostatic ocean models using laboratory scale problems Cont Shelf Res 26 1433 1447 10.1016/j.csr.2006.02.014 (Pubitemid 44164309)
11. J Berntsen J Xing A Davies 2008 Numerical studies of internal waves at a sill: sensitivity to horizontal size and subgrid scale closure Cont Shelf Res 28 1376 1393 10.1016/j.csr.2008.03.029
12. Blumberg A, Mellor G (1987) 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. American Geophysical Union, Washington, DC, pp 1-16
13. G Carnevale M Briscolini P Orlandi 2001 Buoyancy- to inertial-range transition in forced stratified turbulence J Fluid Mech 427 205 239 10.1017/S002211200000241X (Pubitemid 32257365)
14. P Cummins 2000 Stratified flow over topography: time-dependent comparisons between model solutions and observations Dyn Atmos Ocean 33 43 72 10.1016/S0377-0265(00)00044-0 (Pubitemid 30845128)
15. P Cummins S Vagle L Armi D Farmer 2003 Stratified flow over topography: upstream influence and generation of nonlinear waves Proc R Soc Lond A 459 1467 1487 10.1098/rspa.2002.1077 (Pubitemid 38337428)
16. Cushman-Roisin B (1994) Introduction to geophysical fluid dynamics. Prentice Hall, Englewood Cliffs. ISBN-0-13-353301-8
17. A Davies J Xing 2007 On the influence of stratification and tidal forcing upon mixing in sill regions Ocean Dyn 57 431 451 10.1007/s10236-007-0114-5 (Pubitemid 350003525)
18. A Dörnbrack 1998 Turbulent mixing by breaking gravity waves J Fluid Mech 375 113 141 10.1017/S0022112098002833
19. D Farmer L Armi 1999 Stratified flow over topography: the role of small-scale entrainment and mixing in flow establishment Proc R Soc Lond A 455 3221 3258 10.1098/rspa.1999.0448
20. D Farmer L Armi 2001 Stratified flow over topography: models versus observations Proc R Soc Lond A 457 2827 2830 10.1098/rspa.2001.0802
21. D Farmer H Freeland 1983 The physical oceanography of fjords Prog Oceanogr 12 147 220 10.1016/0079-6611(83)90004-6
22. Fringer O (2009) Towards nonhydrostatic ocean modeling with large-eddy simulation. In: Glickson D (ed) Oceanography in 2025: proceedings of a workshop. National Academic Press, Washington, DC, pp 81-83
23. O Fringer R Street 2003 The dynamics of breaking progressive interfacial waves J Fluid Mech 494 319 353 10.1017/S0022112003006189 (Pubitemid 37497098)
24. Griffies S (2004) Fundamentals of ocean climate models. Princeton University Press, Princeton
25. Haidvogel D, Beckmann A (1999) Numerical ocean circulation modeling. Series on environmental science and management, vol 2. Imperial College Press, London
26. R Haney 1991 On the pressure gradient force over steep topography in sigma coordinate ocean models J Phys Oceanogr 21 610 619 10.1175/1520-0485(1991) 021<0610:OTPGFO>2.0.CO;2
27. Y Heggelund F Vikebø J Berntsen G Furnes 2004 Hydrostatic and non-hydrostatic studies of gravitational adjustment over a slope Cont Shelf Res 24 2133 2148 10.1016/j.csr.2004.07.005 (Pubitemid 39568468)
28. B Hodges B Laval B Wadzuk 2006 Numerical error assessment and a temporal horizon for internal waves in a hydrostatic model Ocean Model 13 44 64 10.1016/j.ocemod.2005.09.005 (Pubitemid 43231383)
29. M Inall F Cottier C Griffiths T Rippeth 2004 Sill dynamics and energy transformation in a jet fjord Ocean Dyn 54 307 314 10.1007/s10236-003-0059-2
30. M Inall T Rippeth C Griffiths P Wiles 2005 Evolution and distribution of TKE production and dissipation within stratified flow over topography Geophys Res Lett 32 8607 10.1029/2004GL022289 10.1029/2004GL022289 (Pubitemid 41043270)
31. Y Kanarska V Maderich 2003 A non-hydrostatic numerical model for calculating free-surface stratified flows Ocean Dyn 53 176 185 10.1007/s10236-003-0039-6 10.1007/s10236-003-0039-6
32. Y Kanarska A Shchepetkin J McWilliams 2007 Algorithm for non-hydrostatic dynamics in the regional oceanic modeling system Ocean Model 18 143 174 10.1016/j.ocemod.2007.04.001 (Pubitemid 47010234)
33. Kantha L, Clayson C (2000) Numerical models of oceans and oceanic processes. International geophysics series, vol 66. Academic, London
34. J Klymak M Gregg 2001 Three-dimensional nature of flow near a sill J Geophys Res 106 22295 22311 10.1029/2001JC000933
35. J Klymak M Gregg 2003 The role of upstream waves and a downstream density pool in the growth of lee waves: stratified flow over the Knight Inlet sill J Phys Oceanogr 33 1446 1461 10.1175/1520-0485(2003)033<1446:TROUWA>2.0.CO;2 (Pubitemid 37084541)
36. J Klymak M Gregg 2004 Tidally generated turbulence over the Knight Inlet sill J Phys Oceanogr 34 1135 1151 10.1175/1520-0485(2004)034<1135: TGTOTK>2.0.CO;2 (Pubitemid 38762953)
37. Kowalik Z, Murty T (1993) Numerical modeling of ocean dynamics. Advanced series on ocean engineering, vol 5. World Scientific, Singapore
38. Kundu P, Cohen I (2008) Fluid mechanics. Elsevier Academic, Amsterdam
39. E Kunze S Llewellyn Smith 2004 The role of small-scale topography in turbulent mixing of the global ocean Oceanogr 17 55 64
40. K Lamb 2004 On boundary-layer separation and internal wave generation at the Knight Inlet sill Proc R Soc Lond A 460 2305 2337 10.1098/rspa.2003.1276 (Pubitemid 40268440)
41. K Lamb 2007 Energy and pseudoenergy flux in the internal wave field generated by tidal flow over topography Cont Shelf Res 27 1208 1232 10.1016/j.csr.2007.01.020 (Pubitemid 46778946)
42. S Legg A Adcroft 2003 Internal wave breaking at concave and convex continental slopes J Phys Oceanogr 33 2224 2246 10.1175/1520-0485(2003) 033<2224:IWBACA>2.0.CO;2 (Pubitemid 38184948)
43. J Marshall A Adcroft C Hill L Perelman C Heisey 1997 A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers J Geophys Res 102 C3 5753 5766 10.1029/96JC02775
44. J Marshall C Hill L Perelman A Adcroft 1997 Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling J Geophys Res 102 C3 5733 5752 10.1029/96JC02776
45. E Martinsen H Engedahl 1987 Implementation and testing of a lateral boundary scheme as an open boundary condition in a barotropic ocean model Coast Eng 11 603 627 10.1016/0378-3839(87)90028-7
46. Mellor G (1996) Users guide for a three-dimensional, primitive equation, numerical ocean model. Technical report, Princeton University
47. G Mellor L-Y Oey T Ezer 1998 Sigma coordinate pressure gradient errors and the seamount problem J Atmos Ocean Technol 15 1122 1131 10.1175/1520- 0426(1998)015<1122:SCPGEA>2.0.CO;2
48. W Munk C Wunsch 1998 Abyssal recipes II: energetics of tidal and wind mixing Deep-Sea Res 45 1978 2010
49. K Polzin J Toole J Ledwell R Schmitt 1997 Spatial variability of turbulent mixing in the abyssal ocean Science 276 93 96 10.1126/science.276. 5309.93 (Pubitemid 27161250)
50. G Rickard J O'Callaghan S Popinet 2009 Numerical simulations of internal solitary waves interacting with uniform slopes using an adaptive model Ocean Model 30 16 28 10.1016/j.ocemod.2009.05.008
51. R Samelson 1998 Large scale circulation with locally enhanced vertical mixing J Phys Oceanogr 28 712 726 10.1175/1520-0485(1998)028<0712: LSCWLE>2.0.CO;2
52. W Smyth J Nash J Moum 2005 Differential diffusion in breaking Kelvin-Helmholtz Billows J Phys Oceanogr 35 1004 1022 10.1175/JPO2739.1 (Pubitemid 41065470)
53. M Spall 2001 Large-scale circulations forced by localized mixing over a sloping bottom J Phys Oceanogr 31 2369 2384 10.1175/1520-0485(2001)031<2369: LSCFBL>2.0.CO;2
54. M Stacey 1985 Some aspects of the internal tide in Knight Inlet, British Columbia J Phys Oceanogr 15 1652 1661 10.1175/1520-0485(1985)015<1652: SAOTIT>2.0.CO;2
55. M Stacey Y Gratton 2001 The energetics and tidally induced reverse renewal in a two-silled Fjord J Phys Oceanogr 31 1599 1615 10.1175/1520- 0485(2001)031<1599:TEATIR>2.0.CO;2
56. N Stashchuk M Inall V Vlasenko 2007 Analysis of supercritical stratified tidal flow in a Scottish Fjord J Phys Oceanogr 37 1793 1810 10.1175/JPO3087.1 (Pubitemid 47278506)
57. A Stigebrandt 1976 Vertical diffusion driven by internal waves in a sill fjord J Phys Oceanogr 6 486 495 10.1175/1520-0485(1976)006<0486:VDDBIW>2. 0.CO;2
58. A Stigebrandt 1999 Resistance to barotropic tidal flow in straits by baroclinic wave drag J Phys Oceanogr 29 191 197 10.1175/1520-0485(1999) 029<0191:RTBTFI>2.0.CO;2
59. A Stigebrandt J Aure 1989 vertical mixing in basin waters of Fjords J Phys Oceanogr 19 917 926 10.1175/1520-0485(1989)019<0917:VMIBWO>2.0.CO;2
60. V Vlasenko N Stashchuk K Hutter 2002 Water exchange in fjords induced by tidally generated internal lee waves Dyn Atmos Ocean 35 63 89 10.1016/S0377-0265(01)00085-9 (Pubitemid 34206986)
61. Wadzuk B, Hodges B (2004) Hydrostatic and non-hydrostatic internal wave models. Technical report CRWR online report 04-09, University of Texas at Austin
62. C Wunsch 1970 On oceanic boundary mixing Deep-Sea Res 17 293 301
63. C Wunsch R Ferrari 2004 Vertical mixing, energy, and the general circulation of the oceans Annu Rev Fluid Mech 36 281 314 10.1146/annurev.fluid. 36.050802.122121
64. J Xing A Davies 2001 A three-dimensional baroclinic model of the Irish sea: formation of the thermal fronts and associated circulation J Phys Oceanogr 31 94 114 10.1175/1520-0485(2001)031<0094:ATDBMO>2.0.CO;2
65. J Xing A Davies 2006 Processes influencing tidal mixing in the region of sills Geophys Res Lett 33 4603 10.1029/2005GL025226 10.1029/2005GL025226
66. J Xing A Davies 2006 Influence of stratification and topography upon internal wave spectra in the region of sills Geophys Res Lett 33 23606 10.1029/2006GL028092 10.1029/2006GL028092 (Pubitemid 47407879)
67. J Xing A Davies 2007 On the importance of non-hydrostatic processes in determining tidally induced mixing in sill regions. Cont Shelf Res 27 2162 2185 10.1016/j.csr.2007.05.012 (Pubitemid 47379477)
68. H Yang A Przekwas 1992 A comparative study of advanced shock-capturing schemes applied to Burgers equation J Comput Phys 102 139 159 10.1016/S0021-9991(05)80012-9