Editorial Type:
Article
Article Type:
Research Article

The Effect of a Bottom Shelf Front upon the Generation and Propagation of Near-Inertial Internal Waves in the Coastal Ocean

Alan M. Davies Proudman Oceanographic Laboratory, Bidston Observatory, Birkenhead, Merseyside, United Kingdom

Search for other papers by Alan M. Davies in
Current site
Google Scholar
PubMed Close
and
Jiuxing Xing Proudman Oceanographic Laboratory, Bidston Observatory, Birkenhead, Merseyside, United Kingdom

Search for other papers by Jiuxing Xing in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Jun 2005
DOI:
https://doi.org/10.1175/JPO2732.1
Page(s):
976–990
Restricted access

Abstract

A three-dimensional nonlinear baroclinic model in cross-sectional form is used to study the generation and propagation of wind-forced near-inertial internal waves in a coastal region in the presence of a bottom front. Initially calculations are performed with the front in an infinite domain region. By this means coastal effects are removed. The initial response is in terms of inertial oscillations in the surface layer. However, in the frontal area these are modified by interaction through the nonlinear momentum terms with regions of positive and negative vorticity associated with the alongfront flow. This leads to a change in amplitude, phase, and frequency of the inertial current, and a resulting Ekman pumping that drives near-inertial internal waves in the frontal region. On the positive vorticity side of the front these waves are at the superinertial frequency and rapidly propagate away. On the negative side they are at the subinertial frequency and are trapped and inertial energy leaks to depth. Calculations with a coastal boundary and no front show that the offshore propagation of near-inertial waves is similar to that found on the positive vorticity side of the front. This shows that in terms of superinertial internal wave generation and propagation the front acts in a similar manner to a coastal boundary. However, with a coastal boundary, inertial currents below the thermocline are phase shifted by 180° from those above. This phase shift is only found in the frontal case when the front is adjacent to a coast and is due to the no-normal-flow condition at the coast. For the case of a stratified region between the coast and the front, near-inertial energy is trapped in this region and is dissipated at a rate depending upon the local value of vertical eddy viscosity. The offshore spatial distribution of near-inertial internal waves is found to be independent of whether the coastal region is represented by a vertical wall or a more realistic sloping seabed. However, in the case of a weak coastal front, the near-frontal distribution of near-inertial energy is influenced by the horizontal spatial variability of stratification within the front.

Corresponding author address: Dr. Alan M. Davies, Proudman Oceanographic Laboratory, Bidston Observatory, Birkenhead, Merseyside CH43 7RA, United Kingdom. Email: amd@pol.ac.uk

Abstract

A three-dimensional nonlinear baroclinic model in cross-sectional form is used to study the generation and propagation of wind-forced near-inertial internal waves in a coastal region in the presence of a bottom front. Initially calculations are performed with the front in an infinite domain region. By this means coastal effects are removed. The initial response is in terms of inertial oscillations in the surface layer. However, in the frontal area these are modified by interaction through the nonlinear momentum terms with regions of positive and negative vorticity associated with the alongfront flow. This leads to a change in amplitude, phase, and frequency of the inertial current, and a resulting Ekman pumping that drives near-inertial internal waves in the frontal region. On the positive vorticity side of the front these waves are at the superinertial frequency and rapidly propagate away. On the negative side they are at the subinertial frequency and are trapped and inertial energy leaks to depth. Calculations with a coastal boundary and no front show that the offshore propagation of near-inertial waves is similar to that found on the positive vorticity side of the front. This shows that in terms of superinertial internal wave generation and propagation the front acts in a similar manner to a coastal boundary. However, with a coastal boundary, inertial currents below the thermocline are phase shifted by 180° from those above. This phase shift is only found in the frontal case when the front is adjacent to a coast and is due to the no-normal-flow condition at the coast. For the case of a stratified region between the coast and the front, near-inertial energy is trapped in this region and is dissipated at a rate depending upon the local value of vertical eddy viscosity. The offshore spatial distribution of near-inertial internal waves is found to be independent of whether the coastal region is represented by a vertical wall or a more realistic sloping seabed. However, in the case of a weak coastal front, the near-frontal distribution of near-inertial energy is influenced by the horizontal spatial variability of stratification within the front.

Corresponding author address: Dr. Alan M. Davies, Proudman Oceanographic Laboratory, Bidston Observatory, Birkenhead, Merseyside CH43 7RA, United Kingdom. Email: amd@pol.ac.uk

Save
Cover Journal of Physical Oceanography
Journal of Physical Oceanography

  • Csanady, G. T., 1996: Circulation in the Coastal Ocean. Reidel, 300 pp.

  • Dale, A. C., J. M. Huthnance, and T. J. Sherwin, 2001: Coastal-trapped waves and tides at near-inertial frequencies. J. Phys. Oceanogr., 31 , 2958–2970.

    • Search Google Scholar
    • Export Citation

  • Davies, A. M., 1989a: Application of a sigma coordinate sea model to the calculation of wind-induced currents. Cont. Shelf Res., 4 , 389–423.

    • Search Google Scholar
    • Export Citation

  • Davies, A. M., 1989b: A three-dimensional modal model of wind induced flow in a sea region. Progress in Oceanography, Vol. 15, Pergamon, 71–128.

  • Davies, A. M., and S. C. M. Kwong, 2000: Tidal energy fluxes and dissipation on the European continental shelf. J. Geophys. Res., 105 , 21969–21989.

    • Search Google Scholar
    • Export Citation

  • Davies, A. M., and J. Xing, 2003: Processes influencing wind induced current profiles in near coastal stratified regions. Cont. Shelf Res., 23 , 1379–1400.

    • Search Google Scholar
    • Export Citation

  • Davies, A. M., P. Hall, J. M. Howarth, P. Knight, and R. Player, 2001: A detailed comparison of measured and modelled wind driven currents in the North Channel of the Irish Sea. J. Geophys. Res., 106 , 19683–19713.

    • Search Google Scholar
    • Export Citation

  • De Young, B., and C. L. Tang, 1990: Storm-forced baroclinic near-inertial currents on the Grand Bank. J. Phys. Oceanogr., 20 , 1725–1741.

    • Search Google Scholar
    • Export Citation

  • Federiuk, J., and J. S. Allen, 1996: Model studies of near-inertial waves in flow over the Oregon continental shelf. J. Phys. Oceanogr., 26 , 2053–2075.

    • Search Google Scholar
    • Export Citation

  • Gemmrich, J. R., and H. Van Haren, 2002: Internal wave band eddy fluxes above a continental slope. J. Mar. Res., 60 , 227–253.

  • Greatbatch, R. J., 1983: On the response of the ocean to a moving storm. The non-linear dynamics. J. Phys. Oceanogr., 13 , 357–367.

  • Hill, A. E., 1996: Spin-down and the dynamics of dense pool gyres in shallow seas. J. Mar. Res., 54 , 471–486.

  • Hill, A. E., R. Durazo, and D. A. Smeed, 1994: Observations of a cyclonic gyre in the western Irish Sea. Cont. Shelf Res., 14 , 479–490.

    • Search Google Scholar
    • Export Citation

  • Horsburgh, K. J., and A. E. Hill, 2003: A three-dimensional model of density-driven circulation in the Irish Sea. J. Phys. Oceanogr., 33 , 343–365.

    • Search Google Scholar
    • Export Citation

  • Inall, M. E., T. P. Rippeth, and T. J. Sherwin, 2000: Impact of nonlinear waves on the dissipation of internal tidal energy at a shelf break. J. Geophys. Res., 105 , 8687–8705.

    • Search Google Scholar
    • Export Citation

  • Knight, P. J., M. J. Howarth, and T. P. Rippeth, 2002: Inertial currents in the northern North Sea. J. Sea Res., 47 , 269–284.

  • Kunze, E., 1985: Near-inertial wave propagation in geostrophic shear. J. Phys. Oceanogr., 15 , 544–565.

  • Kunze, E., and T. B. Sanford, 1984: Observations of near-inertial waves in a front. J. Phys. Oceanogr., 14 , 566–581.

  • Luyten, P. J., E. Deleersnijder, J. Ozer, and K. G. Ruddick, 1996: Presentation of a family of turbulence closure models for stratified shallow water flows and preliminary application to the Rhine outflow region. Cont. Shelf Res., 16 , 101–130.

    • Search Google Scholar
    • Export Citation

  • Millot, C., and M. Crepon, 1981: Inertial oscillations on the continental shelf of the Gulf of Lions—Observations and theory. J. Phys. Oceanogr., 11 , 639–657.

    • Search Google Scholar
    • Export Citation

  • Mooers, C. N. K., 1975: Several effects of a baroclinic current on the cross-stream propagation of inertial–internal waves. Geophys. Fluid Dyn., 6 , 245–275.

    • Search Google Scholar
    • Export Citation

  • Oey, L-Y., and P. Chen, 1992: A nested-grid ocean model: With application for the simulation of meanders and eddies in the Norwegian coastal current. J. Geophys. Res., 97 , 20063–20086.

    • Search Google Scholar
    • Export Citation

  • Orlic, M., 1987: Oscillations at the inertial period on the Adriatic Sea shelf. Cont. Shelf Res., 7 , 577–598.

  • Rippeth, T. P., J. H. Simpson, R. J. Player, and M. Garcia, 2002: Current oscillations in the diurnal-inertial band on the Catalunyan shelf. Cont. Shelf Res., 22 , 247–266.

    • Search Google Scholar
    • Export Citation

  • Salat, J., J. Tintore, J. Font, D-P. Wang, and M. Vieira, 1992: Near-inertial motion on the shelf-slope front off northeast Spain. J. Geophys. Res., 97 , 7277–7281.

    • Search Google Scholar
    • Export Citation

  • Tintore, J., D-P. Wang, E. Garcia, and A. Viudez, 1995: Near-inertial motions in the coastal ocean. J. Mar. Syst., 6 , 301–312.

  • Van Haren, H., L. Maas, J. T. F. Zimmermann, H. Ridderinkhof, and H. Malschaert, 1999: Strong inertial currents and marginal internal wave stability in the central North Sea. Geophys. Res. Lett., 26 , 2993–2996.

    • Search Google Scholar
    • Export Citation

  • Van Haren, H., L. Maas, and H. Van Aken, 2002: On the nature of internal wave spectra near a continental slope. Geophys. Res. Lett., 29 .1615, doi:10.1029/2001GL014341.

    • Search Google Scholar
    • Export Citation

  • Wang, D-P., 1991: Generation and propagation of inertial waves in the subtropical front. J. Mar. Res., 49 , 619–633.

  • Weller, R. A., 1982: The relation of near-inertial motions observed in the mixed layer during the JASIN (1978) experiment to the local wind stress and to the quasigeostrophic flow field. J. Phys. Oceanogr., 12 , 1122–1136.

    • Search Google Scholar
    • Export Citation

  • Xing, J., and A. M. Davies, 1998: A three-dimensional model of internal tides on the Malin-Hebrides shelf and shelf edge. J. Geophys. Res., 103 , 27821–27847.

    • Search Google Scholar
    • Export Citation

  • Xing, J., and A. M. Davies, 2001a: A three-dimensional baroclinic model of the Irish Sea: Formation of the thermal fronts and associated circulation. J. Phys. Oceanogr., 31 , 94–114.

    • Search Google Scholar
    • Export Citation

  • Xing, J., and A. M. Davies, 2001b: Non-linear effects of internal tides on the generation of the tidal mean flow at the Hebrides shelf edge. Geophys. Res. Lett., 28 , 3939–3942.

    • Search Google Scholar
    • Export Citation

  • Xing, J., and A. M. Davies, 2002: Processes influencing the non-linear interaction between inertial oscillations, near-inertial internal waves and internal tides. Geophys. Res. Lett., 29 .1067, doi:10.1029/2001GL014199.

    • Search Google Scholar
    • Export Citation

  • Xing, J., and A. M. Davies, 2003: Influence of coastal effects, bottom topography, stratification, wind period, and mixing upon the propagation of internal waves and the profile of wind induced currents. J. Geophys. Res., 108 .3052, doi:10.1029/2002JC001377.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 229 120 8
PDF Downloads 96 46 1