• Adcroft, A., Hill C. , and Marshall J. , 1997: Representation of topography by shaved cells in a height coordinate ocean model. Mon. Wea. Rev, 125 , 22932315.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Afanasyev, Y. D., and Peltier W. R. , 2001: On the breaking internal waves over the skill in Knight Inlet. Proc. Roy. Soc. London, A457 , 27992825.

    • Search Google Scholar
    • Export Citation
  • Arakawa, A., 1966: Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. Part I. J. Comput. Phys, 1 , 119143.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Armi, L., and Farmer D. , 1986: Maximal two-layer exchange through a contraction with barotropic net flow. J. Fluid Mech, 164 , 2751.

  • Armi, L., 1987: A generalization of the concept of maximal exchange in a strait. J. Geophys. Res, 92 , 1467914680.

  • Blumberg, A. F., 1977: A two-dimensional numerical model for the simulation of partially mixed estuaries. Estuarine Processes. Volume II: Circulation, Sediments, and Transfer of Material in the Estuary, M. Wiley, Ed., Academic Press, 1–16.

    • Search Google Scholar
    • Export Citation
  • Bogucki, D., and Garrett C. , 1993: A simple model for shear-induced decay of an internal solitary wave. J. Phys. Oceanogr, 23 , 17671776.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bourgault, D., and Kelley D. E. , 2003: Wave-induced boundary mixing in a partially mixed estuary. J. Mar. Res, 61 , 553576.

  • 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
  • Cummins, P. F., 2000: Stratified flow over topography: Time-dependent comparisons between model solutions and observations. Dyn. Atmos. Oceans, 33 , 4372.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cummins, P. F., Vagle S. , Armi L. , and Farmer D. M. , 2003: Stratified flow over topography: Upstream influence and generation of nonlinear internal waves. Proc. Roy. Soc. London, A459 , 14671487.

    • Search Google Scholar
    • Export Citation
  • Dronkers, J. J., 1964: Tidal Computations in Rivers and Coastal Waters. North-Holland, 518 pp.

  • Farmer, D. M., and Smith J. D. , 1980: Tidal interaction of stratified flow with a sill in Knight Inlet. Deep-Sea Res, 27A , 239254.

  • Farmer, D. M., and Freeland H. , 1983: The physical oceanography of fjords. Progress in Oceanography, Vol. 12, Pergamon, 147–220.

  • Farmer, D. M., and Armi L. , 1986: Maximal two-layer exchange over a sill and through the combination of a sill and contraction with barotropic flow. J. Fluid Mech, 164 , 5376.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Farmer, D. M., and Armi L. , 1999a: The generation and trapping of internal solitary waves over topography. Science, 283 , 188190.

  • Farmer, D. M., and Armi L. , 1999b: Stratified flow over topography: The role of small-scale entrainment and mixing in flow establishment. Proc. Roy. Soc. London, A455 , 32213258.

    • Search Google Scholar
    • Export Citation
  • Farmer, D. M., and Armi L. , 2001: Stratified flow over topography: Models versus observations. Proc. Roy. Soc. London, A457 , 28272830.

    • Search Google Scholar
    • Export Citation
  • Ferziger, J. H., and Perić M. , 1996: Computational Methods for Fluid Dynamics. Springer, 364 pp.

  • Ford, M., Wang J. , and Cheng R. T. , 1990: Predicting the vertical structure of tidal current and salinity in San Francisco Bay, California. Water Resour. Res, 26 , 10271045.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Geyer, W. R., and Smith J. D. , 1987: Shear instability in a highly stratified estuary. J. Phys. Oceanogr, 17 , 16681679.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.

  • Gillibrand, P. A., Turrell W. R. , and Elliott A. J. , 1995: Deep-water renewal in the upper basin of Loch Sunart, a Scottish fjord. J. Phys. Oceanogr, 25 , 14881503.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Haidvogel, D. B., and Beckmann A. , 1999: Numerical Ocean Circulation Modeling. Imperial College Press, 320 pp.

  • Hamilton, P., 1975: A numerical model of the vertical circulation of tidal estuaries and its application to the Rottardam waterway. Geophys. J. Roy. Astron. Soc, 40 , 121.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hibiya, T., Niwa Y. , and Fujiwara K. , 1998: Numerical experiments of nonlinear energy transfer within the oceanic internal wave spectrum. J. Geophys. Res, 103 (C9) 1871518722.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jankowski, J. A., 1999: A non-hydrostatic model for free surface flows. Ph.D. thesis, University of Hannover, 231 pp.

  • Klymak, J. M., and Gregg M. C. , 2001: The three-dimensional nature of flow near a sill. J. Geophys. Res, 106 , 2229522311.

  • Klymak, J. M., and Gregg M. C. , 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 , 14461461.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kundu, P. K., 1990: Fluid Mechanics. Academic Press, 638 pp.

  • Lamb, K. G., 1994: Numerical experiments of internal wave generation by strong tidal flow across a finite amplitude bank edge. J. Geophys. Res, 99 , 843864.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lane-Serff, G. F., Smeed D. A. , and Postlethwaite C. R. , 2000: Multi-layer hydraulic exchange flows. J. Fluid Mech, 416 , 269296.

  • Lavelle, J. W., Cokelet E. D. , and Cannon G. A. , 1991: A model study of density intrusions into and circulation within a deep, silled estuary: Puget Sound. J. Geophys. Res, 96 (C9) 1677916800.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, C-Y., and Beardsley R. C. , 1974: The generation of long nonlinear internal waves in a weakly stratified shear flow. J. Geophys. Res, 79 , 453462.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lu, Y., Wright D. G. , and Brickman D. , 2001: Internal tide generation over topography: Experiments with a free-surface z-level ocean model. J. Atmos. Oceanic Technol, 18 , 10761091.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J., Adcroft A. , Hill C. , Perelman L. , and Heisey C. , 1997a: A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J. Geophys. Res, 102 (C3) 57535766.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J., Hill C. , Perelman L. , and Adcroft A. , 1997b: Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modelling. J. Geophys. Res, 102 (C3) 57335752.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Michallet, H., and Ivey G. N. , 1999: Experiments on mixing due to internal solitary waves breaking on uniform slopes. J. Geophys. Res, 104 (C6) 1346713477.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miles, J., 1961: On the stability of heterogeneous shear flows. J. Fluid Mech, 10 , 496508.

  • Pacanowski, R. C., and Philander S. G. H. , 1981: Parameterization of vertical mixing in numerical models of the tropical oceans. J. Phys. Oceanogr, 11 , 14431451.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pietrzak, J., 1998: The use of TVD limiters for forward-in-time upstream-biased advection schemes in ocean modeling. Mon. Wea. Rev, 126 , 812830.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Porté-Agel, F., Meneveau C. , and Parlange M. B. , 2000: A scale-dependent dynamic model for large-eddy simulation: Application to a neutral atmospheric boundary layer. J. Fluid Mech, 415 , 261284.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Press, W., Teukolsky S. , Vetterling W. , and Flannery B. , 1992: Numerical Recipes in FORTRAN: The Art of Scientific Computing. 2d ed. Cambridge University Press, 963 pp.

    • Search Google Scholar
    • Export Citation
  • Roache, P. J., 1998: Fundamentals of Computational Fluid Dynamics. Hermosa, 648 pp.

  • Smagorinsky, J., 1963: General circulation experiments with primitive equations. I. The basic experiment. Mon. Wea. Rev, 91 , 99164.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stacey, M. W., Pond S. , and Nowak Z. P. , 1995: A numerical model of the circulation in Knight Inlet, British Columbia, Canada. J. Phys. Oceanogr, 25 , 10371062.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 1968: A method of producing a shear flow in a stratified fluid. J. Fluid Mech, 32 , 693704.

  • Turner, J. S., 1973: Buoyancy Effects in Fluids. Cambridge University Press, 367 pp.

  • Wang, D-P., and Kravitz D. W. , 1980: A semi-implicit two-dimensional model of estuarine circulation. J. Phys. Oceanogr, 10 , 441454.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, J., 1998: A two-channel laterally averaged estuarine circulation model (laecim). J. Geophys. Res, 103 (C9) 1838118391.

  • Winters, K. B., and Seim H. E. , 2000: The role of dissipation and mixing in exchange flow through a contracting channel. J. Fluid Mech, 407 , 265290.

    • Crossref
    • Search Google Scholar
    • Export Citation
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A Laterally Averaged Nonhydrostatic Ocean Model

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  • 1 Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's, Newfoundland, Canada
  • | 2 Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada
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Abstract

A laterally averaged nonhydrostatic model for stratified flow in dynamically narrow domains is presented. Averaging laterally yields the computational efficiency of a two-dimensional model, while retaining some effects associated with variable domain width, such as flow acceleration through contracting channels. The model may be run in both hydrostatic and nonhydrostatic modes, and in the latter case it converges rapidly if the flow is approximately hydrostatic. The model's strengths and weaknesses are illustrated with a series of test cases of increasing complexity. Side-by-side comparisons with laboratory observations show the ability of the model to simulate the structures of nonhydrostatic flows, including shear instabilities and overturning internal waves, with discrepancies becoming apparent mainly for transition to three-dimensional turbulence. Similar results are demonstrated in an application to the stratified sill flow in Knight Inlet, British Columbia. The model reproduces nonhydrostatic features thought to be dynamically important to this system, including the generation of large-amplitude lee waves and shear instabilities.

Corresponding author address: Dr. Daniel Bourgault, Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's, NL A1B 3X7, Canada. Email: danielb@physics.mun.ca

Abstract

A laterally averaged nonhydrostatic model for stratified flow in dynamically narrow domains is presented. Averaging laterally yields the computational efficiency of a two-dimensional model, while retaining some effects associated with variable domain width, such as flow acceleration through contracting channels. The model may be run in both hydrostatic and nonhydrostatic modes, and in the latter case it converges rapidly if the flow is approximately hydrostatic. The model's strengths and weaknesses are illustrated with a series of test cases of increasing complexity. Side-by-side comparisons with laboratory observations show the ability of the model to simulate the structures of nonhydrostatic flows, including shear instabilities and overturning internal waves, with discrepancies becoming apparent mainly for transition to three-dimensional turbulence. Similar results are demonstrated in an application to the stratified sill flow in Knight Inlet, British Columbia. The model reproduces nonhydrostatic features thought to be dynamically important to this system, including the generation of large-amplitude lee waves and shear instabilities.

Corresponding author address: Dr. Daniel Bourgault, Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's, NL A1B 3X7, Canada. Email: danielb@physics.mun.ca

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