The Influence of Open versus Periodic Alongshore Boundaries on Circulation near Submarine Canyons

Michael S. Dinniman Center for Coastal Physical Oceanography, Old Dominion University, Norfolk, Virginia

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John M. Klinck Center for Coastal Physical Oceanography, Old Dominion University, Norfolk, Virginia

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Abstract

It is impractical to create gridded numerical models of coastal circulation with sufficient resolution around small topographic features, such as submarine canyons, and still have the alongshore boundaries placed beyond the decay distance of coastal trapped waves. Two solutions to this problem are to make the alongshore boundaries either open or periodic. Numerical simulations were performed with upwelling and downwelling winds to compare the effects of these different choices for boundary conditions.

Several open boundary formulations were tried and three are discussed in detail. The offshore boundary was specified as “no gradient” for all variables with no serious effect. The “modified” Orlanski radiation condition is used for all variables at the alongshore boundaries, except the vertically integrated flow that has the strongest effect on the model solution.

An alongshore pressure gradient, opposing the wind, develops in the model if the modified Orlanski radiation condition is applied to the barotropic flow, causing slower currents near the surface and deep undercurrents away from the shelf. The other cases, which combined either a radiation or a relaxation boundary condition with a local solution of the barotropic equations on the boundary, were at least initially similar to the periodic case but with slower alongshore flow. The initial impact of these differences on the circulation within the canyon was small. The models with the open boundaries were more stable (did not develop strong flow meanders) than the cases with periodic conditions as initial transients are not trapped, and amplified, within the domain. Thus, open cases, especially with the upwelling winds, could run for extended times.

Corresponding author address: Mr. Michael S. Dinniman, Center for Coastal Physical Oceanography, Old Dominion University, Norfolk, VA 23529. Email: msd@ccpo.odu.edu

Abstract

It is impractical to create gridded numerical models of coastal circulation with sufficient resolution around small topographic features, such as submarine canyons, and still have the alongshore boundaries placed beyond the decay distance of coastal trapped waves. Two solutions to this problem are to make the alongshore boundaries either open or periodic. Numerical simulations were performed with upwelling and downwelling winds to compare the effects of these different choices for boundary conditions.

Several open boundary formulations were tried and three are discussed in detail. The offshore boundary was specified as “no gradient” for all variables with no serious effect. The “modified” Orlanski radiation condition is used for all variables at the alongshore boundaries, except the vertically integrated flow that has the strongest effect on the model solution.

An alongshore pressure gradient, opposing the wind, develops in the model if the modified Orlanski radiation condition is applied to the barotropic flow, causing slower currents near the surface and deep undercurrents away from the shelf. The other cases, which combined either a radiation or a relaxation boundary condition with a local solution of the barotropic equations on the boundary, were at least initially similar to the periodic case but with slower alongshore flow. The initial impact of these differences on the circulation within the canyon was small. The models with the open boundaries were more stable (did not develop strong flow meanders) than the cases with periodic conditions as initial transients are not trapped, and amplified, within the domain. Thus, open cases, especially with the upwelling winds, could run for extended times.

Corresponding author address: Mr. Michael S. Dinniman, Center for Coastal Physical Oceanography, Old Dominion University, Norfolk, VA 23529. Email: msd@ccpo.odu.edu

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  • Allen, J. S., and Newberger P. A. , 1996: Downwelling circulation on the Oregon continental shelf. Part I: Response to idealized forcing. J. Phys. Oceanogr., 26 , 20112035.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Allen, J. S., Newberger P. A. , and Federiuk J. , 1995: Upwelling circulation on the Oregon continental shelf. Part I: Response to idealized forcing. J. Phys. Oceanogr., 25 , 18431866.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Allen, S. E., 1996: Topographically generated, subinertial flows within a finite length canyon. J. Phys. Oceanogr., 26 , 16081632.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ardhuin, F., Pinot J-M. , and Tintoré J. , 1999: Numerical study of the circulation in a steep canyon off the Catalan coast (western Mediterranean). J. Geophys. Res., 104 , 1111511135.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bennett, A. F., and Kloeden P. E. , 1978: Boundary conditions for limited-area forecasts. J. Atmos. Sci., 35 , 355375.

  • Camerlengo, A. L., and O'Brien J. J. , 1980: Open boundary conditions in rotating fluids. J. Comput. Phys., 35 , 1235.

  • Cannon, G. A., Reed R. K. , and Pullen P. E. , 1985: Comparison of El Niño events off the Pacific Northwest. El Niño North: Niño Effects in the Eastern Subartic Pacific Ocean, W. S. Wooster and D. L. Fluharty, Eds., Washington Sea Grant Program, 75–84.

    • Search Google Scholar
    • Export Citation
  • Chapman, D. C., 1985: Numerical treatment of cross-shelf open boundaries in a barotropic coastal ocean model. J. Phys. Oceanogr., 15 , 10601075.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Church, J. A., Cresswell G. R. , and Godfrey J. S. , 1989: The Leeuwin Current. Poleward Flows along Eastern Ocean Boundaries, S. J. Neshyba et al., Eds., Coastal and Estuarine Studies, Vol. 34, Springer-Verlag, 230–254.

    • Search Google Scholar
    • Export Citation
  • Csanady, G. T., 1988: Ocean currents over the continental slope. Advances in Geophysics, Vol. 30, Academic Press, 95–203.

  • Flather, R. A., 1976: A tidal model of the northwest European continental shelf. Mem. Soc. Roy. Sci. Liege, Ser. 6, 10 , 141164.

  • Garvine, R. W., 2001: The impact of model configuration in studies of buoyant coastal discharge. J. Mar. Res., 59 , 193225.

  • Haidvogel, D. B., and Beckmann A. , 1998: Numerical models of the coastal ocean. The Sea, K. H. Brink and A. R. Robinson, Eds., the Global Coastal Ocean, Vol. 10, John Wiley and Sons, 457–482.

    • Search Google Scholar
    • Export Citation
  • Haidvogel, D. B., . 1999: Numerical Ocean Circulation Modeling. Series on Environmental Science and Management, Vol. 2, Imperial College Press, 319 pp.

    • Search Google Scholar
    • Export Citation
  • Hedström, K. S., 1997: (DRAFT) User's manual for an S-Coordinate Primitive Equation Ocean Circulation Model (SCRUM) Version 3.0. Institute of Marine and Coastal Sciences, Rutgers University Contribution 97-10, 116 pp.

    • Search Google Scholar
    • Export Citation
  • Hickey, B., 1989: Poleward flow near the northern and southern boundaries of the U.S. West Coast. Poleward Flows along Eastern Ocean Boundaries, S. J. Neshyba et al., Eds., Coastal and Estuarine Studies, Vol. 34, Springer-Verlag, 160–175.

    • Search Google Scholar
    • Export Citation
  • Hickey, B., . 1995: Coastal submarine canyons. Topographic Interactions in the Ocean: Proc. ‘Aha Huliko’ a Hawaiian Winter Workshop, Honolulu, HI, University of Hawaii at Manoa, 95–110.

    • Search Google Scholar
    • Export Citation
  • Hickey, B., . 1997: The response of a steep-sided, narrow canyon to time-variable wind forcing. J. Phys. Oceanogr., 27 , 697726.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huthnance, J. M., 1992: Extensive slope currents and the ocean-shelf boundary. Progress in Oceanography, Vol. 29, Pergamon, 161–196.

  • Huthnance, J. M., Mysak L. A. , and Wang D-P. , 1986: Coastal trapped waves. Baroclinic Processes on Continental Shelves, C. N. K. Mooers, Ed., Coastal and Estuarine Series, Vol. 3, Amer. Geophys. Union, 1–18.

    • Search Google Scholar
    • Export Citation
  • Jensen, T. G., 1998: Open boundary conditions in stratified ocean models. J. Mar. Sys., 16 , 297322.

  • Klinck, J. M., 1988: The influence of a narrow transverse canyon on initially geostrophic flow. J. Geophys. Res., 93 , 509515.

  • Klinck, J. M., . 1996: Circulation near submarine canyons: A modeling study. J. Geophys. Res., 101 , 12111223.

  • Large, W. G., McWilliams J. C. , and Doney S. C. , 1994: Oceanic vertical mixing: A review and model with a nonlocal boundary layer parameterization. Rev. Geophys., 32 , 363403.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marchesiello, P., McWilliams J. C. , and Shchepetkin A. , 2001: Open boundary condition for long-term integration of regional oceanic models. Ocean Modell., 3 , 120.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Martinsen, E. H., and Engedahl H. , 1987: Implementation and testing of a lateral boundary scheme as an open boundary condition in a barotropic ocean model. Coastal Eng., 11 , 603627.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McCreary, J. P., and Chao S-Y. , 1985: Three-dimensional shelf circulation along an eastern ocean boundary. J. Mar. Res., 43 , 1336.

  • Middleton, J. F., and Cirano M. , 1999: Wind-forced downwelling slope currents: A numerical study. J. Phys. Oceanogr., 29 , 17231743.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Neshyba, S. J., Mooers C. N. K. , Smith R. L. , and Barber R. T. , Eds.,. 1989: Poleward Flows along Eastern Ocean Boundaries. Coastal and Estuarine Studies, Vol. 34, Springer-Verlag, 374 pp.

    • Search Google Scholar
    • Export Citation
  • Oliger, J., and Sündstrom A. , 1978: Theoretical and practical aspects of some initial boundary value problems in fluid dynamics. SIAM J. Appl. Math., 35 , 419446.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Orlanski, I., 1976: A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys., 21 , 251269.

  • Palma, E. D., and Matano R. P. , 1998: On the implementation of passive open boundary conditions for a general circulation model: The barotropic mode. J. Geophys. Res., 103 , 13191341.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Palma, E. D., . 2000: On the implementation of open boundary conditions for a general circulation model: The three-dimensional case. J. Geophys. Res., 105 , 86058627.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pérenne, N., Verron J. , Renouard D. , Boyer D. L. , and Zhang X. , 1997: Rectified barotropic flow over a submarine canyon. J. Phys. Oceanogr., 27 , 18681893.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raymond, W. H., and Kuo H. L. , 1984: A radiation boundary condition for multi-dimensional flows. Quart. J. Roy. Meteor., Soc., 110 , 535551.

  • Reed, R. K., 1984: Oceanographic conditions off the Pacific Northwest following the 1982 El Niño event. Mar. Fish. Rev., 46 , 712.

  • Røed, L. P., and Smedstad O. M. , 1984: Open boundary conditions for forced waves in a rotating fluid. SIAM J. Sci. Stat. Comput., 5 , 414426.

  • Røed, L. P., and Cooper C. , 1987: A study of various open boundary conditions for wind-forced barotropic numerical models. Three-dimensional Models of Marine and Estuarine Dynamics, J. C. J. Nihoul and B. N. Jamart, Eds., Elsevier, 305–335.

    • Search Google Scholar
    • Export Citation
  • She, J., and Klinck J. M. , 2000: Flow near submarine canyons driven by constant winds. J. Geophys. Res., 105 , 2867128694.

  • Suginohara, N., 1982: Coastal upwelling: Onshore–offshore circulation, equatorward coastal jet and poleward undercurrent over a continental shelf-slope. J. Phys. Oceanogr., 12 , 272284.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wilkin, J. L., 1987: A computer program for calculating frequencies and modal structures of free coastal-trapped waves. Tech. Rep. WHOI 87-53, Woods Hole Oceanographic Institute, Woods Hole, MA, 50 pp.

    • Search Google Scholar
    • Export Citation
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