Idealised flow past an island in a dynamically adaptive finite element model

Ocean Dynamics

Volumn 60, Issue 4, 2010, Pages 835-850

  Munday, David R ^a   Marshall, David P ^a   Piggott, Matthew D ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Dynamic adaptivity; Finite elements; Flow separation; Island wakes; Secondary circulations

Indexed keywords

ADAPTIVE FINITE ELEMENT; DYNAMIC ADAPTIVITY; FINITE ELEMENT; FLOW CURVATURE; FRICTIONAL BOUNDARIES; ISLAND WAKES; NUMERICAL EXPERIMENTS; SECONDARY CIRCULATION; SEPARATED FLOWS; SEPARATED SHEAR LAYERS; SHEAR LAYER; UNSTRUCTURED MESHES; VERTICAL MOTIONS;

BOUNDARY LAYERS; EXPERIMENTS; FLOW SEPARATION; OCEAN STRUCTURES; WAKES;

FINITE ELEMENT METHOD;

EDDY; FINITE ELEMENT METHOD; MATHEMATICAL ANALYSIS; NUMERICAL MODEL; RESOLUTION; WAKE;

EID: 77956228475     PISSN: 16167341     EISSN: 16167228     Source Type: Journal    
DOI: 10.1007/s10236-010-0291-5     Document Type: Article

References (46)

1. MJ Alaee G Ivey C Pattiaratchi 2004 Secondary circulation induced by flow curvature and Coriolis effects around headlands and islands Ocean Dyn 54 27 38 10.1007/s10236-003-0058-3 (Pubitemid 38407788)
2. I Babuška 1971 Error bounds for finite element methods Numer Math 16 322 333 10.1007/BF02165003
3. RA Barkley 1972 Johnston Atoll's wake J Mar Res 30 201 216
4. E Berger R Wille 1972 Periodic flow phenomena Annu Rev Fluid Mech 4 313 340 10.1146/annurev.fl.04.010172.001525
5. KP Black SL Gay 1987 Eddy formation in unsteady flows J Geophys Res 92 9514 9522 10.1029/JC092iC09p09514
6. E Blayo L Debreu 1999 Adaptive mesh refinement for finite-difference ocean models: first experiments J Phys Oceanogr 29 1239 1250 10.1175/1520-0485(1999)029<1239:AMRFFD>2.0.CO;2
7. F Brezzi 1974 On the existence, uniqueness and approximation of saddle point problems arising from Lagrangian multipliers Rev Francaise d'Automatique Inform Rech Oper: Anal Numer 8 129 151
8. DC Chapman DB Haidvogel 1992 Formation of Taylor caps over a tall isolated seamount in a stratified ocean Geophys Astrophys Fluid Dyn 64 31 65 10.1080/03091929208228084
9. DC Chapman DB Haidvogel 1993 Generation of internal lee waves trapped over a tall isolated seamount Geophys Astrophys Fluid Dyn 69 33 54 10.1080/03091929308203573
10. KP Chopra 1973 Atmospheric and oceanic flow problems introduced by islands Adv Geophys 16 297 421
11. CJ Cotter DA Ham CC Pain S Reich 2009 LBB stability of a mixed Galerkin finite element pair for fluid flow simulations J Comp Physiol 228 336 348
12. E Deleersnijder A Norro E Wolanski 1992 A three-dimensional model of the water circulation around an island in shallow water Cont Shelf Res 12 891 906 10.1016/0278-4343(92)90050-T
13. T Denniss JH Middleton 1994 Effects of viscosity an bottom friction on recirculating flows J Geophys Res 99 10183 10192 10.1029/93JC03588
14. A Einstein 1926 Die Ursache der Mäanderbildung der Fluäufe und des sogenannten Baerschen Gesetzes Naturwiss 14 223 224 10.1007/BF01510300
15. RA Falconer Wolanski L Mardapitta-Hadjipandeli 1986 Modeling tidal circulation in an island's wake J Waterw, Port, Coast, Ocean Eng Div Am Soc Civ Eng 112 234 254 10.1061/(ASCE)0733-950X(1986)112:2(234)
16. PE Farrell MD Piggott CC Pain GJ Gorman CR Wilson 2009 Conservative interpolation between unstructured meshes via supermesh construction Comput Methods Appl Mech Engrg 198 2632 2642 10.1016/j.cma.2009.03.004
17. R Ford CC Pain MD Piggott AJH Goddard CRE de Oliveira AP Umpleby 2004 A non-hydrostatic finite element model for three-dimensional stratified oceanic flows. Part I: model formulation Mon Weather Rev 132 2816 2831 10.1175/MWR2824.1 (Pubitemid 40099009)
18. R Ford CC Pain MD Piggott AJH Goddard CRE de Oliveira AP Umpleby 2004 A non-hydrostatic finite element model for three-dimensional stratified oceanic flows. Part II: model validation Mon Weather Rev 132 2832 2844 10.1175/MWR2825.1 (Pubitemid 40099010)
19. K Furukawa E Wolanski 1998 Shallow-water frictional effects in island wakes Estuar Coast Shelf Sci 46 599 608 10.1006/ecss.1997.0301 (Pubitemid 28205573)
20. Gresho PM, Sani RL (1998) Incompressible flow and the finite element method. In: Advection-diffusion, vol 1. Wiley, New York, 445 pp
21. 0 element. Numerical Analysis Report No 257, Department of Mathematics, University of Manchester, UK
22. D Hasegawa H Yamazaki RG Lueck L Seuront 2004 How islands stir and fertilize the upper ocean Geophys Res Lett 31 16303 10.1029/2004GL020143 (Pubitemid 39428481)
23. KJ Heywood ED Barton JH Simpson 1990 The effects of flow disturbance by an oceanic island J Mar Res 48 55 73 10.1357/002224090784984623
24. A Huerta A Rodríguez-Ferran P Díez J Sarrate 1999 Adaptive finite element strategies based on error assessment Int J Numer Methods Eng 46 1803 1818 10.1002/(SICI)1097-0207(19991210)46:10<1803::AID-NME725>3.0. CO;2-3
25. RG Ingram VH Chu 1987 Flow around islands in Rupert Bay: an investigation of the bottom friction effect J Geophys Res 92 14521 14533 10.1029/ JC092iC13p14521
26. Ladyzhenskaya OA (1969) The mathematical theory of viscous incompressible flow. Gordon and Breach, 224 pp
27. SP Neill AJ Elliott 2004 In situ measurements of spring-neap variations to unsteady island wake development in the Firth of Forth, Scotland Estuar Coast Shelf Sci 60 229 239 10.1016/j.ecss.2004.01.001 (Pubitemid 38681939)
28. SP Neill AJ Elliott 2004 Observations and simulations of an unsteady island wake in the Firth of Forth, Scotland Ocean Dyn 54 324 332 10.1007/s10236-003-0084-1
29. CC Pain AP Umpleby CRE de Oliveira 2001 Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations Comput Methods Appl Mech Eng 190 3771 3796 10.1016/S0045-7825(00)00294-2
30. CC Pain MD Piggott AJH Goddard F Fang GJ Gorman DP Marshall MD Eaton PW Power CRE De Oliveira 2005 Three-dimensional unstructured mesh ocean modelling Ocean Model 10 5 33 10.1016/j.ocemod.2004.07.005 (Pubitemid 40335010)
31. C Pattiaratchi A James M Collins 1986 Island wakes and headland eddies: a comparison between remotely sensed data and laboratory experiments J Geophys Res 92 783 794 10.1029/JC092iC01p00783
32. HJ Perkins 1970 The formation of streamwise vorticity in turbulent flow J Fluid Mech 44 721 740 10.1017/S0022112070002112
33. MD Piggott CC Pain GJ Gorman PW Power AJH Goddard 2006 h, r, and hr adaptivity with applications in numerical ocean modelling Ocean Model 10 95 113 10.1016/j.ocemod.2004.07.007
34. MD Piggott GJ Gorman CC Pain PA Allison AS Candy BT Martin MR Wells 2008 A new computational framework for multi-scale ocean modelling based on adapting ustructured meshes Int J Numer Methods Fluids 56 103 1015 10.1002/fld.1663 (Pubitemid 351385436)
35. FT Smith 1982 On the high Reynolds number theory of laminar flows IMA J Appl Math 28 207 281 10.1093/imamat/28.3.207
36. IM Suthers CT Taggart D Kelley D Rissik JH Middleton 2004 Entrainment and advection in and island's tidal wake, as revealed by attenuanc, zooplankton, and ichthyoplankton Limnol Oceanogr 49 283 296 10.4319/lo.2004.49.1.0283
37. M Tatsuno PW Bearman 1990 A visual study of the flow around an oscillating circular cylinder at low Keulegan-Carpenter number and low Stokes numbers J Fluid Mech 211 157 182 10.1017/S0022112090001537
38. M Tomczak 1988 Island wakes in deep and shallow water J Geophys Res 93 5153 5154 10.1029/JC093iC05p05153
39. L White E Wolanski 2008 Flow separation and vertical motion in a tidal flow interacting with a shallow-water island Estuar Coast Shelf Sci 10.1016/j.ecss.2007.10.003 (Pubitemid 351400315)
40. CHK Williamson 1985 Sinusoidal flow relative to circular cylinders J Fluid Mech 155 141 174 10.1017/S0022112085001756
41. E Wolanski 1988 Island wakes in shallow waters J Geophys Res 93 1335 1336 10.1029/JC093iC02p01335
42. E Wolanski WM Hamner 1988 Topographically controlled fronts in the ocean and their biological influence Science 241 177 181 10.1126/science.241.4862.177
43. E Wolanski J Imberger ML Heron 1984 Islands wakes in shallow coastal waters J Geophys Res 10 10553 10569 10.1029/JC089iC06p10553
44. E Wolanski T Asaeda A Tanaka E Deleersnijder 1996 Three-dimensional island wakes in the field, laboratory experiments and numerical models Cont Shelf Res 16 1437 1452 10.1016/0278-4343(95)00087-9
45. Wolanski E, Brinkman R, Spagnol S, McAllister F, Steinberg C, Skirving W, Deleersnijder E (2003) Merging scales in models of water circulation: perspectives from the Great Barrier Reef. In: Lakhan VC (ed) Advances in coastal modeling. Elsevier Oceanography Series, vol 67. Elsevier Science, pp 411-429
46. J Xing AM Davies 1996 Internal lee waves and turbulence mixing over an isolated seamount: results from turbulence energy models Int J Num Meth Fluids 23 1043 1072 10.1002/(SICI)1097-0363(19961130)23:10<1043::AID-FLD451>3.0. CO;2-S (Pubitemid 27071021)