Incidence and Reflection of Offshore Subinertial and Barotropic Pressure Signals in Wide Shelf Seas

Hui Wu aState Key Laboratory of Estuarine and Coastal Research and School of Marine Sciences, East China Normal University, Shanghai, China
bSchool of Mathematical Sciences, East China Normal University, Shanghai, China

Search for other papers by Hui Wu in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The response of a wide shelf to subinertial and barotropic offshore pressure signals from the shelf edge was investigated. By relaxing the semigeostrophic approximation, an elliptical wave structure equation was formulated and solved with the integral transform method. It was found that when the imposed offshore signal has an along-shelf length scale similar to the shelf width, it can efficiently break the potential vorticity barrier and propagate toward the coast, producing a significant coastal sea level setup. Thereafter, the pressure signal reflects from the coast or the sloping topography, producing a transient eddy and propagates to the downshelf. The intensities of the coastal setup and the eddy increase as the along-shelf scale of the subinertial signal decreases or when its time scale is close to the inertial period. For a signal with longer time scale, the eddy is insignificant. The nature of the shelf response is controlled by the shelf conductivity κr/(fsB), in which r is the Rayleigh friction coefficient, f is the Coriolis parameter, s is the shelf slope, and B is the shelf width, respectively. For a given offshore signal, coastal setup increases with κ. For large κ, the eddy energy is concentrated at low modes, producing a large eddy, whereas a small κ produces a small eddy. The proposed theory can explain coastal sea level fluctuations under eddy impingement in the Mid-Atlantic Bight or other similar areas.

Significance Statement

Coastal sea level and shelf circulation are greatly affected by offshore pressure signals, e.g., mesoscale eddy impingements or boundary current fluctuations. It is often assumed that the along-shelf length scale of the forcing is much larger than the shelf width, i.e., the semigeostrophic approximation. Here in this study, we found this approximation significantly underestimates the shelf–ocean interaction. A general shelf wave equation was developed that relaxed the semigeostrophic approximation and was solved analytically with a novel mathematical method. The solution can characterize the shelf response to subinertial offshore forcing at arbitrary spatiotemporal scales. It was found that for a subinertial signal with scale close to or smaller than the shelf width, significant coastal sea level setup and transient eddy can be formed, which was consistent with realistic phenomena. The new theory could promote the understanding of coastal sea level variations and along-/cross-shelf transports at synoptic and intermediate scales.

This article is included in the Oceanic Flow—Topography Interations Special Collection.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Hui Wu, hwu@sklec.ecnu.edu.cn

Abstract

The response of a wide shelf to subinertial and barotropic offshore pressure signals from the shelf edge was investigated. By relaxing the semigeostrophic approximation, an elliptical wave structure equation was formulated and solved with the integral transform method. It was found that when the imposed offshore signal has an along-shelf length scale similar to the shelf width, it can efficiently break the potential vorticity barrier and propagate toward the coast, producing a significant coastal sea level setup. Thereafter, the pressure signal reflects from the coast or the sloping topography, producing a transient eddy and propagates to the downshelf. The intensities of the coastal setup and the eddy increase as the along-shelf scale of the subinertial signal decreases or when its time scale is close to the inertial period. For a signal with longer time scale, the eddy is insignificant. The nature of the shelf response is controlled by the shelf conductivity κr/(fsB), in which r is the Rayleigh friction coefficient, f is the Coriolis parameter, s is the shelf slope, and B is the shelf width, respectively. For a given offshore signal, coastal setup increases with κ. For large κ, the eddy energy is concentrated at low modes, producing a large eddy, whereas a small κ produces a small eddy. The proposed theory can explain coastal sea level fluctuations under eddy impingement in the Mid-Atlantic Bight or other similar areas.

Significance Statement

Coastal sea level and shelf circulation are greatly affected by offshore pressure signals, e.g., mesoscale eddy impingements or boundary current fluctuations. It is often assumed that the along-shelf length scale of the forcing is much larger than the shelf width, i.e., the semigeostrophic approximation. Here in this study, we found this approximation significantly underestimates the shelf–ocean interaction. A general shelf wave equation was developed that relaxed the semigeostrophic approximation and was solved analytically with a novel mathematical method. The solution can characterize the shelf response to subinertial offshore forcing at arbitrary spatiotemporal scales. It was found that for a subinertial signal with scale close to or smaller than the shelf width, significant coastal sea level setup and transient eddy can be formed, which was consistent with realistic phenomena. The new theory could promote the understanding of coastal sea level variations and along-/cross-shelf transports at synoptic and intermediate scales.

This article is included in the Oceanic Flow—Topography Interations Special Collection.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Hui Wu, hwu@sklec.ecnu.edu.cn
Save
  • Brink, K. H., 2016: Cross-shelf exchange. Annu. Rev. Mar. Sci., 8, 5978, https://doi.org/10.1146/annurev-marine-010814-015717.

  • Brink, K. H., and J. S. Allen, 1978: On the effect of bottom friction on barotropic motion over the continental shelf. J. Phys. Oceanogr., 8, 919922, https://doi.org/10.1175/1520-0485(1978)008<0919:OTEOBF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chapman, D. C., and K. H. Brink, 1987: Shelf and slope circulation induced by fluctuating offshore forcing. J. Geophys. Res., 92, 11 74111 759, https://doi.org/10.1029/JC092iC11p11741.

    • Search Google Scholar
    • Export Citation
  • Cherian, D. A., and K. H. Brink, 2018: Shelf flows forced by deep-ocean anticyclonic eddies at the shelf break. J. Phys. Oceanogr., 48, 11171138, https://doi.org/10.1175/JPO-D-17-0237.1.

    • Search Google Scholar
    • Export Citation
  • Clarke, A. J., and C. Shi, 1991: Critical frequencies at ocean boundaries. J. Geophys. Res., 96, 10 73110 738, https://doi.org/10.1029/91JC00933.

    • Search Google Scholar
    • Export Citation
  • Csanady, G. T., 1978: The arrested topography wave. J. Phys. Oceanogr., 8, 4762, https://doi.org/10.1175/1520-0485(1978)008<0047:TATW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Csanady, G. T., and P. T. Shaw, 1983: The “insulating” effect of a steep continental slope. J. Geophys. Res., 88, 75197524, https://doi.org/10.1029/JC088iC12p07519.

    • Search Google Scholar
    • Export Citation
  • Ezer, T., 2016: Can the Gulf Stream induce coherent short-term fluctuations in sea level along the US East Coast? A modeling study. Ocean Dyn., 66, 207220, https://doi.org/10.1007/s10236-016-0928-0.

    • Search Google Scholar
    • Export Citation
  • Hetland, R. D., Y. Hsueh, R. R. Leben, and P. P. Niiler, 1999: A loop current-induced jet along the edge of the West Florida shelf. Geophys. Res. Lett., 26, 22392242, https://doi.org/10.1029/1999GL900463.

    • Search Google Scholar
    • Export Citation
  • Higginson, S., K. R. Thompson, P. L. Woodworth, and C. W. Hughes, 2015: The tilt of mean sea level along the east coast of North America. Geophys. Res. Lett., 42, 14711479, https://doi.org/10.1002/2015GL063186.

    • Search Google Scholar
    • Export Citation
  • Hopkins, T. S., 1982: On the sea level forcing of the Mid-Atlantic Bight. J. Geophys. Res., 87, 19972006, https://doi.org/10.1029/JC087iC03p01997.

    • Search Google Scholar
    • Export Citation
  • Hughes, C. W., I. Fukumori, S. M. Griffies, J. M. Huthnance, S. Minobe, P. Spence, K. R. Thompson, and A. Wise, 2019: Sea level and the role of coastal trapped waves in mediating the influence of the open ocean on the coast. Surv. Geophys., 40, 14671492, https://doi.org/10.1007/s10712-019-09535-x.

    • Search Google Scholar
    • Export Citation
  • Huthnance, J. M., 2004: Ocean-to-shelf signal transmission: A parameter study. J. Geophys. Res., 109, C12029, https://doi.org/10.1029/2004JC002358.

    • Search Google Scholar
    • Export Citation
  • Johnston, P. R., 1994: A solution method for the Graetz problem for non-Newtonian fluids with Dirichlet and Neumann boundary conditions. Math. Comput. Modell., 19, 119, https://doi.org/10.1016/0895-7177(94)90045-0.

    • Search Google Scholar
    • Export Citation
  • Lin, W., H. Lin, and J. Hu, 2021: The tilt of mean dynamic topography and its seasonality along the coast of the Chinese Mainland. J. Geophys. Res. Oceans, 126, e2020JC016778, https://doi.org/10.1029/2020JC016778.

    • Search Google Scholar
    • Export Citation
  • Marshall, D. P., and H. L. Johnson, 2013: Propagation of meridional circulation anomalies along western and eastern boundaries. J. Phys. Oceanogr., 43, 26992717, https://doi.org/10.1175/JPO-D-13-0134.1.

    • Search Google Scholar
    • Export Citation
  • Munk, W., F. Snodgrass, and G. Carrier, 1956: Edge waves on the continental shelf. Science, 123, 127132, https://doi.org/10.1126/science.123.3187.127.

    • Search Google Scholar
    • Export Citation
  • Mysak, L. A., 1980: Recent advances in shelf wave dynamics. Rev. Geophys., 18, 211241, https://doi.org/10.1029/RG018i001p00211.

  • Özısık, M. N., 1993: Heat Conduction. 2nd ed. John Wiley and Sons, 692 pp.

  • Pedlosky, J., 1987: Geophysical Fluid Dynamics. 2nd ed. Springer, 710 pp.

  • Power, S. B., R. H. J. Grimshaw, and J. H. Middleton, 1990: Large-scale, low-frequency barotropic circulation on continental margins. J. Phys. Oceanogr., 20, 769785, https://doi.org/10.1175/1520-0485(1990)020<0769:LSLFBC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Robinson, A. R., 1964: Continental shelf waves and the response of the sea level to weather systems. J. Geophys. Res., 69, 367368, https://doi.org/10.1029/JZ069i002p00367.

    • Search Google Scholar
    • Export Citation
  • Ursell, F., 1952: Edge waves on a sloping beach. Proc. Roy. Soc. London, 214A, 7997, https://doi.org/10.1098/rspa.1952.0152.

  • Wang, D.-P., 1982: Effects of continental slope on the mean shelf circulation. J. Phys. Oceanogr., 12, 15241526, https://doi.org/10.1175/1520-0485(1982)012<1524:EOCSOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wise, A., C. W. Hughes, and J. Polton, 2018: Bathymetric influence on the coastal sea level response to ocean gyres at western boundaries. J. Phys. Oceanogr., 48, 29492964, https://doi.org/10.1175/JPO-D-18-0007.1.

    • Search Google Scholar
    • Export Citation
  • Wise, A., C. W. Hughes, J. A. Polton, and J. M. Huthnance, 2020: Leaky slope waves and sea level: Unusual consequences of the beta effect along western boundaries with bottom topography and dissipation. J. Phys. Oceanogr., 50, 217237, https://doi.org/10.1175/JPO-D-19-0084.1.

    • Search Google Scholar
    • Export Citation
  • Wu, H., 2021: Beta-plane arrested topographic wave as a linkage of open ocean forcing and mean shelf circulation. J. Phys. Oceanogr., 51, 879893, https://doi.org/10.1175/JPO-D-20-0195.1.

    • Search Google Scholar
    • Export Citation
  • Xu, F.-H., and L.-Y. Oey, 2011: The origin of along-shelf pressure gradient in the Middle Atlantic Bight. J. Phys. Oceanogr., 41, 17201740, https://doi.org/10.1175/2011JPO4589.1.

    • Search Google Scholar
    • Export Citation
  • Yang, D., B. Yin, Z. Liu, and X. Feng, 2011: Numerical study of the ocean circulation on the East China Sea shelf and a Kuroshio bottom branch northeast of Taiwan in summer. J. Geophys. Res., 116, C05015, https://doi.org/10.1029/2010JC006777.

    • Search Google Scholar
    • Export Citation
  • Yankovsky, A. E., 2009: Large-scale edge waves generated by hurricane landfall. J. Geophys. Res., 114, C03014, https://doi.org/10.1029/2008JC005113.

    • Search Google Scholar
    • Export Citation
  • Zhang, W. G., and J. Partida, 2018: Frontal subduction of the Mid-Atlantic Bight shelf water at the onshore edge of a warm-core ring. J. Geophys. Res. Oceans, 123, 77957818, https://doi.org/10.1029/2018JC013794.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 850 850 20
Full Text Views 314 314 11
PDF Downloads 337 337 10