User menu

Accès à distance ? S'identifier sur le proxy UCLouvain

Capturing the residence time boundary layer - Application to the Scheldt Estuary

Primary tabs

Blaise, Sébastien [UCL] de Brye, Benjamin [UCL] Debrauwere, Anouk [UCL] Deleersnijder, Eric [UCL] Delhez, Eric J. M. [ULg] Comblen, Richard [UCL]

At high Peclet number, the residence time exhibits a boundary layer adjacent to incoming open boundaries. In a Eulerian model, not resolving this boundary layer can generate spurious oscillations that can propagate into the area of interest. However, resolving this boundary layer would require an unacceptably high spatial resolution. Therefore, alternative methods are needed in which no grid refinement is required to capture the key aspects of the physics of the residence time boundary layer. An extended finite element method representation and a boundary layer parameterisation are presented and tested herein. It is also explained how to preserve local consistency in reversed time simulations so as to avoid the generation of spurious residence time extrema. Finally, the boundary layer parameterisation is applied to the computation of the residence time in the Scheldt Estuary (Belgium/The Netherlands). This timescale is simulated by means of a depth-integrated, finite element, unstructured mesh model, with a high space-time resolution. It is seen that the residence time temporal variations are mainly affected by the semi-diurnal tides. However, the spring-neap variability also impacts the residence time, particularly in the sandbank and shallow areas. Seasonal variability is also observed, which is induced by the fluctuations over the year of the upstream flows. In general, the residence time is an increasing function of the distance to the mouth of the estuary. However, smaller-scale fluctuations are also present: they are caused by local bathymetric features and their impact on the hydrodynamics.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2010
Language Anglais
Journal information "Ocean Dynamics : theoretical, computational oceanography and monitoring" - Vol. 60, no. 3, p. 535-554 (2010)
Peer reviewed yes
Publisher Springer Heidelberg (Heidelberg)
issn 1616-7341
e-issn 1616-7228
Publication status Publié
Affiliation UCL - SST/IMMC - Institute of Mechanics, Materials and Civil Engineering
Keywords Residence time ; Boundary layer ; Parameterisation ; X-FEM ; Finite elements ; Diagnostic ; Adjoint modelling ; Local consistency
Links
  1. Alexe M, Sandu A (2009) Forward and adjoint sensitivity analysis with continuous explicit Runge–Kutta schemes. Appl Math Comput 208(2):328–346
  2. Allen CM (1982) Numerical simulation of contaminant dispersion in estuary flows. In: Royal society of London proceedings series A, vol 381, pp 179–194
  3. Arega F, Armstrong S, Badr A (2008) Modeling of residence time in the East Scott Creek Estuary, South Carolina, USA. Journal of Hydro-environment Research 2(2):99–108
  4. Arminjon P, Dervieux A (1993) Construction of TVD-like artificial viscosities on two-dimensional arbitrary FEM grids. J Comput Phys 106(1):176–198
  5. Black KP, Gay SL (1987) Eddy formation in unsteady flows. J Geophys Res 92(C9):9514–9522
  6. Blumberg Alan F., Mellor George L., A description of a three-dimensional coastal ocean circulation model, Three-Dimensional Coastal Ocean Models (1987) ISBN:0875902537 p.1-16, 10.1029/co004p0001
  7. Bolin B, Rhode H (1973) A note on the concepts of age distribution and residence time in natural reservoirs. Tellus 25:58–62
  8. Burchard H (2002) Applied turbulence modelling in marine waters. Lecture notes in earth science, vol 100. Springer, Heidelberg
  9. Cockburn Bernardo, Shu Chi-Wang, The Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V, 10.1006/jcph.1998.5892
  10. Combescure A., Gravouil A., Baietto-Dubourg M.-C., Elguedj E., Ribeaucourt R., Ferrié Emilie, Extended finite element method for numerical simulation of 3D fatigue crack growth, Life Cycle Tribology (2005) ISBN:9780444516879 p.323-328, 10.1016/s0167-8922(05)80034-3
  11. Comblen R, Lambrechts J, Remacle J-F, Legat V (2009) Practical evaluation of five part-discontinuous finite element pairs for the non-conservative shallow water equations. Int J Numer Methods Fluids. doi: 10.1002/fld.2094
  12. de Brye B, de Brauwere A, Gourgue O, Kärna T, Lambrechts J, Comblen R, Deleersnijder E (2009) A finite-element, multi-scale model of the Scheldt Tributaries, River, Estuary and ROFI. Coast Eng (under revision)
  13. Deleersnijder E (1993) Numerical mass conservation in a free-surface sigma coordinate marine model with mode splitting. J Mar Syst 4:365–370
  14. Deleersnijder E, Campin J-M, Delhez EJM (2001) The concept of age in marine modelling: I. Theory and preliminary model results. J Mar Syst 28(3–4):229–267
  15. Deleersnijder E, Delhez EJ (eds) (2007) Timescale- and tracer-based methods for understanding the results of complex marine models. Estuar Coast Shelf Sci 74:585–776 (special issue)
  16. Delhez EJM (2006) Transient residence and exposure times. Ocean Sci 2(1):1–9
  17. Delhez EJM, Deleersnijder E (2006) The boundary layer of the residence time. Ocean Dyn 56:139–150
  18. Delhez EJ, Lacroix G, Deleersnijder E (2004a) The age as a diagnostic of the dynamics of marine ecosystem models. Ocean Dyn 54(2):221–231
  19. Delhez EJM, Heemink AW, Deleersnijder E (2004b) Residence time in a semi-enclosed domain from the solution of an adjoint problem. Estuar Coast Shelf Sci 61:691–702
  20. Egbert GD, Benett AF, Foreman MGG (1994) TOPEX/ POSEIDON tides estimated using a global inverse model. J Geophys Res 99:24,821–24,852
  21. Elden L (1982) Time discretization in the backward solution of parabolic equations. II. Math Comput 39(159):69–84
  22. Garabedian PR (1964) Partial differential equations. Wiley, New York
  23. Gourgue Olivier, Deleersnijder Eric, White Laurent, Toward a generic method for studying water renewal, with application to the epilimnion of Lake Tanganyika, 10.1016/j.ecss.2007.05.009
  24. Hanert E, Deleersnijder E, Blaise S, Remacle J-F (2007) Capturing the bottom boundary layer in finite element ocean models. Ocean Model 17:153–162
  25. Kalnay E, Kanamitsu M, Kistler R, Collins W, Deaven D, Gandin L, Iredell M, Saha S, White G, Woollen J, Zhu Y, Leetmaa A, Reynolds B, Chelliah M, Ebisuzaki W, Higgins W, Janowiak J, Mo KC, Ropelewski C, Wang J, Jenne R, Joseph D (1996) The NCEP/NCAR 40-year reanalysis project. Bull Am Meteorol Soc 77:437–472
  26. Kuzmin D, Löhner R, Turek S (eds) (2005) Flux-corrected transport. Principles, algorithms and applications. Springer, Heidelberg
  27. Liu Chein-Shan, Chang Chih-Wen, Chang Jiang-Ren, The backward group preserving scheme for 1D backward in time advection-dispersion equation, 10.1002/num.20415
  28. Liu W-C, Chen W-B, Kuo J-T, Wu C (2008b) Numerical determination of residence time and age in a partially mixed estuary using three-dimensional hydrodynamic model. Cont Shelf Res 28(8):1068–1088
  29. Luther KH, Haitjema HM (1998) Numerical experiments on the residence time distributions of heterogeneous groundwatersheds. J Hydrol 207(1–2):1–17
  30. Meyers SD, Luther ME (2008) A numerical simulation of residual circulation in Tampa Bay. Part II: Lagrangian residence time. Estuar Coast 31:815–827
  31. Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150
  32. Monsen Nancy E., Cloern James E., Lucas Lisa V., Monismith Stephen G., A comment on the use of flushing time, residence time, and age as transport time scales, 10.4319/lo.2002.47.5.1545
  33. Nauman EB (1981) Residence time distributions in systems governed by the dispersion equation. Chem Eng Sci 36(6):957–966
  34. Pawlowicz R, Beardsley B, Lentz S (2002) Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE. Comput Geosci 28:929–937
  35. Payne LE (1975) Improperly posed problems in partial differential equations. In: Regional conference series in applied mathematics. Society for Industrial and Applied Mathematics
  36. Soetaert K, Herman PMJ (1995) Estimating estuarine residence times in the Westerschelde (The Netherlands) using a box model with fixed dispersion coefficients. Hydrobiologia 311:215–224
  37. Spivakovskaya D, Hemink AW, Deleersnijder E (2007) Lagrangian modelling of multi-dimensional advection–diffusion with space-varying diffusivities: theory and idealized test cases. Ocean Dyn 57:189–203
  38. Steen RJ, Evers EH, Hattum BV, Cofino WP, Brinkman TUA (2002) Net fluxes of pesticides from the Scheldt Estuary into the North Sea: a model approach. Environ Pollut 116(1):75–84
  39. Takeoka H (1984) Fundamental concepts of exchange and transport time scales in a coastal sea. Cont Shelf Res 3(3):311–326
  40. Tartinville B, Deleersnijder E, Rancher J (1997) The water residence time in the Mururoa atoll lagoon: sensitivity analysis of a three-dimensional model. Coral Reefs 16:193–203
  41. Thuburn J, Haine TWN (2001) Adjoints of nonoscillatory advection schemes. J Comput Phys 171:616–631
  42. Wang C-F, Hsu M-H, Kuo AY (2004) Residence time of the Danshuei River estuary, Taiwan. Estuar Coast Shelf Sci 60(3):381–393
  43. White L, Legat V, Deleersnijder E (2008) Tracer conservation for three-dimensional, finite-element, free-surface, ocean modeling on moving prismatic meshes. Mon Weather Rev 136:420–442
  44. Wyart E, Duflot M, Coulon D, Martiny P, Pardoen T, Remacle J-F, Lani F (2008) Substructuring FE-XFE approaches applied to three-dimensional crack propagation. J Comput Appl Math 215(2):626–638
  45. Zimmerman JTF (1976) Mixing and flushing of tidal embayments in the western dutch Wadden Sea. Part I: distribution of salinity and calculation of mixing time scales. Neth J Sea Res 10:149–191
Bibliographic reference Blaise, Sébastien ; de Brye, Benjamin ; Debrauwere, Anouk ; Deleersnijder, Eric ; Delhez, Eric J. M. ; et. al. Capturing the residence time boundary layer - Application to the Scheldt Estuary. In: Ocean Dynamics : theoretical, computational oceanography and monitoring, Vol. 60, no. 3, p. 535-554 (2010)
Permanent URL http://hdl.handle.net/2078.1/33725