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Resonance of long waves generated by storms obliquely crossing shelf topography in a rotating ocean

Published online by Cambridge University Press:  07 July 2011

S. THIEBAUT  and
R. VENNELL
S. THIEBAUT*
Affiliation:
Ocean Physics Group, Department of Marine Science, University of Otago, Dunedin 9054, New Zealand
R. VENNELL
Affiliation:
Ocean Physics Group, Department of Marine Science, University of Otago, Dunedin 9054, New Zealand
*
†Email address for correspondence: [email protected]
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Abstract

The oceanic forced wave beneath a moving atmospheric disturbance is amplified by Proudman resonance. When modified by the Earth's rotation this classical resonance only occurs if the disturbance time scale is smaller than the inertial period. With or without Coriolis effects, free transients generated by storm forced waves obliquely crossing step changes in water depth at particular angles are shown to resonate by exciting a range of long barotropic free waves. Rotationally influenced slow atmospherically forced waves crossing a vertical coast at a critical angle lead to a form of subcritical resonance, which occurs only when the component of the disturbances' phase velocities along the coast matches that of a free Kelvin wave (KW). In a rotating ocean, transients generated by disturbances crossing a step at a particular angle are shown to excite a free double Kelvin wave (DKW). This new type of resonance only occurs for sufficiently large steps and disturbances with time scale greater than the inertial period. A storm crossing a step shelf can result in the excitation of an infinite set of edge waves, a single KW, a unique DKW and a first-mode continental shelf wave, depending on the topography and the disturbance time scale, translation speed and incident angle. The study of resonances and wave mode excitations generated by storms crossing a coast or a continental shelf may contribute to understanding how a particular combination of the storm characteristics can result in destructive coastal events with time scales encompassing the typical meteotsunami period band (tens of minutes) and storm surges with periods of several hours or days.

JFM classification

Geophysical and Geological Flows: Topographic effects Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 682 , 10 September 2011 , pp. 261 - 288
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Adams, J. K. & Buchwald, V. T. 1969 The generation of continental shelf waves. J. Fluid Mech. 35 (4), 815–826.Google Scholar
As-Salek, J. A. & Yasuda, T. 2001 Tide-surge interaction in the Meghna estuary: Most severe conditions. J. Phys. Oceanogr. 31 (10), 3059–3072.2.0.CO;2>CrossRefGoogle Scholar
Buchwald, V. T. & Adams, J. K. 1968 The propagation of continental shelf waves. Proc. R. Soc. Lond. A 305, 235–250.Google Scholar
Carton, J. A. 1984 Coastal circulation caused by an isolated storm. J. Phys. Oceanogr. 14 (1), 114–124.Google Scholar
Charnock, H. 1955 Wind stress on a water surface. Q. J. R. Meteorol. Soc. 81 (350), 639–640.CrossRefGoogle Scholar
Defant, A. 1961 Physical Oceanography. Pergamon.Google Scholar
Doodson, A. T. 1924 Meteorological perturbations of sea-level and tides. Geophys. J. Intl 1 (s4), 124–147.CrossRefGoogle Scholar
Ekman, V. W. 1905 On the influence of the Earth's rotation on ocean currents. Ark. Mat. Astron. Fys. 2 (11), 1–53.Google Scholar
Fandry, C., Leslie, L. & Steedman, R. 1984 Kelvin-type coastal surges generated by tropical cyclones. J. Phys. Oceanogr. 14 (3), 582–593.2.0.CO;2>CrossRefGoogle Scholar
Fritz, H. M., Blount, C., Sokoloski, R., Singleton, J., Fuggle, A., McAdoo, B. G., Moore, A., Grass, C. & Tate, B. 2007 Hurricane Katrina storm surge distribution and field observations on the Mississippi barrier islands. Estuar. Coast. Shelf Sci. 74 (1–2), 12–20.Google Scholar
Garratt, J. R. 1994 The Atmospheric Boundary Layer. Cambridge University Press.Google Scholar
Garrett, C. J. R. 1970 A theory of the Krakatoa tide gauge disturbances. Tellus 22 (1), 43–52.Google Scholar
Gill, A. E. 1982 Atmosphere–Ocean Dynamics. Academic Press.Google Scholar
Gill, A. E. & Schumann, E. H. 1974 The generation of long shelf waves by the wind. J. Phys. Oceanogr. 4 (1), 83–90.Google Scholar
Gordon, R. L. & Huthnance, J. M. 1987 Storm-driven continental shelf waves over the Scottish continental shelf. Cont. Shelf Res. 79 (9), 1015–1048.CrossRefGoogle Scholar
Goring, D. G. 2009 Meteotsunami resulting from the propagation of synoptic-scale weather systems. Phys. Chem. Earth 34 (17–18), 1009–1015.CrossRefGoogle Scholar
Greenspan, H. P. 1956 The generation of edge waves by moving pressure distributions. J. Fluid Mech. 1 (6), 574–592.Google Scholar
Grumm, R. H. 2010 The Devastating Western European Winter Storm, 27–28 February 2010. National Weather Service, NOAA, web-based interface available at: http://nws.met.psu.edu/severe/2010/28feb2010.pdf.Google Scholar
Holland, G. J. 1980 An analytic model of the wind and pressure profiles in hurricanes. Mon. Weath. Rev. 108 (8), 1212–1218.2.0.CO;2>CrossRefGoogle Scholar
Huthnance, J. M. 1975 On trapped waves over a continental shelf. J. Fluid Mech. 69 (4), 689–704.CrossRefGoogle Scholar
Irish, J. L., Resio, D. T. & Ratcliff, J. J. 2008 The influence of storm size on hurricane surge. J. Phys. Oceanogr. 38, 2003–2013.Google Scholar
Jarosz, E., Mitchell, D. A., Wang, D. W. & Teague, W. J. 2007 Bottom-up determination of air–sea momentum exchange under a major tropical cyclone. Science 315 (5819), 1707.Google Scholar
Johns, B. & Lighthill, J. 1993 Modelling of storm surges in the bay of bengal. In Tropical Cyclone Disasters (ed. Lighthill, J., Zheng, Z., Holland, G. J. & Emanuel, K.), pp. 410–422. Peking University Press.Google Scholar
Kajiura, K. 1962 A note on the generation of boundary waves of Kelvin type. J. Oceanogr. Soc. Japan 18, 49–58.CrossRefGoogle Scholar
Ke, Z. & Yankovsky, A. 2011 Relative role of subinertial and superinertial modes in the coastal long wave response forced by the landfall of a tropical cyclone. Cont. Shelf Res. 31, 929–938.CrossRefGoogle Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
Large, W. G. & Pond, S. 1981 Open ocean momentum flux measurements in moderate to strong winds. J. Phys. Oceanogr. 11 (3), 324–336.Google Scholar
Larsen, J. C. 1969 Long waves along a single-step topography in a semi-infinite uniformly rotating ocean. J. Mar. Res 27 (1), 1–6.Google Scholar
LeBlond, P. H. & Mysak, L. A. 1978 Waves in the Ocean. Elsevier.Google Scholar
Lighthill, J. 1998 Fluid mechanics of tropical cyclones. Theor. Comp. Fluid Dyn. 10 (1), 3–21.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1968 a On the trapping of waves along a discontinuity of depth in a rotating ocean. J. Fluid Mech. 31 (3), 417–434.Google Scholar
Longuet-Higgins, M. S. 1968 b Double Kelvin waves with continuous depth profiles. J. Fluid Mech. 34 (1), 49–80.CrossRefGoogle Scholar
Makin, V. K. 2005 A note on the drag of the sea surface at hurricane winds. Boundary-Layer Meteorol. 115 (1), 169–176.CrossRefGoogle Scholar
Mercer, D., Sheng, J., Greatbatch, R. J. & Bobanovic, J. 2002 Barotropic waves generated by storms moving rapidly over shallow water. J. Geophys. Res. 107, 3152–3168.Google Scholar
Monserrat, S., Ibbetson, A. & Thorpe, A. J. 1991 Atmospheric gravity waves and the Rissaga phenomenon. Q. J. R. Meteorol. Soc. 117, 553–570.Google Scholar
Monserrat, S., Vilibić, I. & Rabinovich, A. B. 2006 Meteotsunamis: atmospherically induced destructive ocean waves in the tsunami frequency band. Nat. Hazards Earth Syst. Sci. 6, 1035–1051.CrossRefGoogle Scholar
Moon, I. J., Ginis, I. & Hara, T. 2004 Effect of surface waves on air–sea momentum exchange. Part II. Behavior of drag coefficient under tropical cyclones. J. Atmos. Sci. 61, 2334–2348.2.0.CO;2>CrossRefGoogle Scholar
Munk, W., Snodgrass, F. & Wimbush, M. 1970 Tides off-shore: Transition from California coastal to deep-sea waters. Geophys. Fluid Dyn. 1 (1), 161–235.CrossRefGoogle Scholar
Mysak, L. A. 1967 a On the theory of continental shelf waves. J. Mar. Res. 25, 205–227.Google Scholar
Mysak, L. A. 1967 b On the very low frequency spectrum of the sea level on a continental shelf. J. Geophys. Res. 72 (12), 3043–3047.Google Scholar
Mysak, L. A. 1969 On the generation of double Kelvin waves. J. Fluid Mech. 37 (3), 417–434.Google Scholar
Mysak, L. A. 1980 Recent advances in shelf wave dynamics. Rev. Geophys. 18 (1), 211–241.Google Scholar
Nomitsu, T. 1935 A theory of tsunamis and seiches produced by wind and barometric gradient. Mem. Coll. Sci. Imp. Univ. Kyoto A 18 (4), 201–214.Google Scholar
Powell, M. D. 1980 Evaluations of diagnostic marine boundary-layer models applied to hurricanes. Mon. Weath. Rev. 108 (6), 757–766.Google Scholar
Powell, M. D., Vickery, P. J. & Reinhold, T. A. 2003 Reduced drag coefficient for high wind speeds in tropical cyclones. Nature 422 (6929), 279–283.CrossRefGoogle ScholarPubMed
Proudman, J. 1953 Dynamical Oceanography. Wiley.Google Scholar
Rabinovich, A. B. & Monserrat, S. 1996 Meteorological tsunamis near the Balearic and Kuril Islands: Descriptive and statistical analysis. Natural Hazards 13 (1), 55–90.CrossRefGoogle Scholar
Rego, J. L. & Li, C. 2009 On the importance of the forward speed of hurricanes in storm surge forecasting: A numerical study. Geophys. Res. Lett. 36 (7), L07609.Google Scholar
Robinson, A. R. 1964 Continental shelf waves and the response of sea level to weather systems. J. Geophys. Res. 69 (2), 367–368.Google Scholar
Signorini, S. R., Wei, J. S. & Miller, C. D. 1992 Hurricane-induced surge and currents on the Texas–Louisiana shelf. J. Geophys. Res. 97 (C2), 2229–2242.Google Scholar
Simpson, R. H. 1974 The hurricane disaster potential scale. Weatherwise 27 (8), 169–186.Google Scholar
Smith, S. D. & Banke, E. G. 1975 Variation of the sea surface drag coefficient with wind speed. Q. J. R. Meteorol. Soc. 101 (429), 665–673.CrossRefGoogle Scholar
Snodgrass, F. E., Munk, W. H. & Miller, G. R. 1962 Long-period waves over California's continental borderland. Part I. Background spectra. J. Mar. Res. 20, 3–30.Google Scholar
Tang, C. L., Gui, Q. & DeTracey, B. M. 1998 Barotropic response of the Labrador/Newfoundland Shelf to a moving storm. J. Phys. Oceanogr. 28 (6), 1152–1172.2.0.CO;2>CrossRefGoogle Scholar
Teague, W. J., Jarosz, E., Wang, D. W. & Mitchell, D. A. 2007 Observed oceanic response over the upper continental slope and outer shelf during Hurricane Ivan. J. Phys. Oceanogr. 37 (9), 2181–2206.Google Scholar
Thiebaut, S. & Vennell, R. 2010 Observation of a fast continental shelf wave generated by a storm impacting Newfoundland using wavelet and cross wavelet analyses. J. Phys. Oceanogr. 40 (2), 417–428.CrossRefGoogle Scholar
Thomson, R. E. 1970 On the generation of Kelvin-type waves by atmospheric disturbances. J. Fluid Mech. 42 (4), 657–670.Google Scholar
Vallis, G. K. 2006 Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge University Press.Google Scholar
Vennell, R. 2007 Long barotropic waves generated by a storm crossing topography. J. Phys. Oceanogr. 37 (12), 2809–2823.CrossRefGoogle Scholar
Vennell, R. 2010 Resonance and trapping of topographic transient ocean waves generated by a moving atmospheric disturbance. J. Fluid Mech. 650, 427–442.Google Scholar
Vickery, P. J. & Wadhera, D. 2009 Statistical models of Holland pressure profile parameter and radius to maximum winds of hurricanes from flight-level pressure and H*wind data. J. Appl. Meteorol. Climatol. 47 (10), 2497–2517.Google Scholar
Vilibić, I., Monserrat, S., Rabinovich, A. & Mihanović, H. 2008 Numerical modelling of the destructive meteotsunami of 15 June, 2006 on the coast of the Balearic Islands. Pure Appl. Geophys. 165 (11), 2169–2195.CrossRefGoogle Scholar
Weisberg, R. H. & Zheng, L. 2006 Hurricane storm surge simulations for Tampa Bay. Estuar. Coasts 29 (6), 899–913.CrossRefGoogle Scholar
Wu, J. 1982 Wind-stress coefficients over sea surface from breeze to hurricane. J. Geophys. Res. 87 (C12), 9704–9706.Google Scholar
Xie, L., Pietrafesa, L. J. & Zhang, C. 1999 Subinertial response of the Gulf Stream system to Hurricane Fran of 1996. Geophys. Res. Lett. 26 (23), 3457–3460.Google Scholar
Yankovsky, A. E. 2008 Long-wave response of the West Florida Shelf to the landfall of Hurricane Wilma, October 2005. J. Coast. Res. 24 (4C), 33–39.CrossRefGoogle Scholar
Yankovsky, A. E. 2009 Large-scale edge waves generated by hurricane landfall. J. Geophys. Res. 114, C03014.Google Scholar