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Proudman resonance with tides, bathymetry and variable atmospheric forcings

Author

Listed:
  • David A. Williams

    (University of Liverpool)

  • Kevin J. Horsburgh

    (National Oceanography Centre)

  • David M. Schultz

    (University of Manchester)

  • Chris W. Hughes

    (University of Liverpool)

Abstract

Proudman resonance is a primary amplification mechanism for meteotsunamis, which are shallow-water waves generated by atmospheric forcings. The effect of tides, sloping bathymetry and the speed, amplitude and aspect ratio of the atmospheric forcing on Proudman resonant wave growth are investigated using analytical approximations and numerical models. With tides included, maximum wave growth through Proudman resonance occurred when the atmospheric-forcing speed matched the tidal-wave speed. Growth greater than Proudman resonance occurred with a positive tidal elevation together with a tidal current in the opposite direction to wave propagation, due to linear growth combined with further amplification from wave-flux conservation. Near-Proudman resonant growth occurred when the forced-wave speed or free-wave speed varied by either a small amount, or varied rapidly, around a speed appropriate for Proudman resonance. For a forcing moving at Proudman resonant speed, resultant wave growth was proportional to the total, time-integrated forcing amplitude. Finally, Proudman resonant wave growth was lower for forcings with lower aspect ratios (AP), partly because forced-wave heights are proportional to 1 + A P 2 , but also because free waves could spread in two dimensions. Whilst the assumptions of strict Proudman resonance are never met, near-Proudman resonant growth may occur over hundreds of kilometres if the effective Froude number is near 1 and the resultant wave propagates predominantly in one dimension.

Suggested Citation

  • David A. Williams & Kevin J. Horsburgh & David M. Schultz & Chris W. Hughes, 2021. "Proudman resonance with tides, bathymetry and variable atmospheric forcings," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 106(2), pages 1169-1194, March.
    • Handle: RePEc:spr:nathaz:v:106:y:2021:i:2:d:10.1007_s11069-020-03896-y
    DOI: 10.1007/s11069-020-03896-y
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    References listed on IDEAS

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    1. Kristian Horvath & Ivica Vilibić, 2014. "Atmospheric mesoscale conditions during the Boothbay meteotsunami: a numerical sensitivity study using a high-resolution mesoscale model," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 74(1), pages 55-74, October.
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    Cited by:

    1. Ivica Vilibić & Alexander B. Rabinovich & Eric J. Anderson, 2021. "Special issue on the global perspective on meteotsunami science: editorial," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 106(2), pages 1087-1104, March.

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