Proudman resonance with tides, bathymetry and variable atmospheric forcings

• Published in: Natural hazards (Dordrecht) Vol. 106; no. 2; pp. 1169 - 1194
• Main Authors: Williams, David A., Horsburgh, Kevin J., Schultz, David M., Hughes, Chris W.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.03.2021; Springer Nature B.V
• Subjects: Amplification; Amplitude; Amplitudes; Approximation; Aspect ratio; Atmospheric forcing; Atmospheric models; Atmospheric pressure; Bathymeters; Bathymetry; Boundary conditions; Case studies; Civil Engineering; Conservation; Dimensions; Earth and Environmental Science; Earth Sciences; Environmental Management; Froude number; Geophysics/Geodesy; Geotechnical Engineering & Applied Earth Sciences; Growth; Hydrogeology; Mathematical models; Natural Hazards; Numerical models; Original Paper; Propagation; Resonance; Shallow water; Tidal currents; Tidal effects; Tidal range; Tides; Water waves; Wave height; Wave propagation; Meteotsunami; Bathymetry; Synthetic model; Tides; Variable atmospheric forcing; Proudman resonance
• DOI: 10.1007/s11069-020-03896-y
• ISSN: 0921-030X

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 ( A P ), 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.