Skip to main content
Log in

Observations of meteotsunami on the Louisiana shelf: a lone soliton with a soliton pack

Natural Hazards Aims and scope Submit manuscript

Abstract

The paper reports unique high-resolution observations of meteotsunami by a large array of oceanographic instruments deployed on the Atchafalaya Shelf (Louisiana, USA) in 2008 with the primary aim to study wave dissipation in muddy environments. The meteotsunami event on March 7, 2008, was caused by the passage of a cold front which was monitored by the NOAA NEXRAD radar. The observations of water surface elevations on the shelf show a highly detailed textbook picture of an undular bore (solibore) in the process of its disintegration into a train of solitons. The picture has a striking feature never reported before not only for the meteotsunamis but in other contexts of disintegration of a long-wave perturbation into a sequence of solitons as well—the persistent presence of a single soliton, well ahead of the solibore. Data analysis and simulations based on the celebrated variable-coefficient KdV (vKdV) equation first proposed by Ostrovsky and Pelinovsky (Izv Atmos Ocean Phys 11:37–41, 1975) explain the physics of this phenomenon and suggest that the formation of the lone soliton ahead of the solibore is very likely to be the result of the specific interplay of natural meteotsunami forcing and nearshore bathymetry. The analysis strongly suggests that the patterns of coexisting lone solitons and packets of cnoidal waves should be quite common for meteotsunamis. They were not observed before only because of the scarcity of high-resolution observations. The results highlight the effectiveness of the vKdV equation in providing understanding of the fundamental mechanisms of the complex natural phenomenon that would otherwise require computationally very expensive numerical models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Notes

  1. http://tidesandcurrents.noaa.gov/tsunami.

  2. http://volkov.oce.orst.edu/tides/.

  3. http://polaris.esr.org/ptm_index.html.

  4. http://www.ncdc.noaa.gov/.

  5. http://www.unidata.ucar.edu/downloads/netcdf/netcdf-java-4/index.jsp.

References

  • Bechle AJ, Kristovich DAR, Wu CH (2015) Meteotsunami occurrences and causes in Lake Michigan. J Geophys Res 120:8422–8438. doi:10.1002/2015JC011317

    Article  Google Scholar 

  • Benjamin SG, Weygandt SS, Brown JM, Hu M, Alexander CR, Smirnova TG, Olson JB, James EP, Dowell DC, Grell GA, Lin H, Peckham SE, Smith TL, Moninger WR, Kenyon JS, Manikin GS (2016) A North American hourly assimilation and model forecast cycle: the rapid refresh. Mon Weather Rev 144:1669–1694. doi:10.1175/MWR-D-15-0242.1

    Article  Google Scholar 

  • Bjørkavåg M, Kalisch H (2011) Wave breaking in Boussinesq models for undular bores. Phys Lett A 375(14):1570–1578. doi:10.1016/j.physleta.2011.02.060

    Article  Google Scholar 

  • Borrero JC, Lynett PJ, Kalligeris N (2015) Tsunami currents in ports. Phil Trans R Soc A 373:20140372. doi:10.1098/rsta.2014.0372

    Article  Google Scholar 

  • Caputo J-G, Stepanyants YA (2003) Bore formation, evolution and disintegration into solitons in shallow inhomogeneous channels. Nonlin Proc Geophys Eur Geosci Union 10(4/5):407–424

    Article  Google Scholar 

  • Chan I-C, Liu PL-F (2012) On the runup of long waves on a plane beach. J Geophys Res 117:C08006. doi:10.1029/2012JC007994

    Article  Google Scholar 

  • Chao YY (1970) The theory of wave refraction in shoaling water, including the effects of caustics and the spherical earth. New York, N.Y.: New York University, School of Engineering and Science, Department of Meteorology and Oceanography, http://catalog.hathitrust.org/Record/007254345

  • Chao YY (1972) Refraction of ocean surface waves on the continental shelf. Offshore Technol Conf. doi:10.4043/1616-MS

  • Choi BH, Pelinovsky E, Kim KO, Lee JS (2003) Simulation of the trans-oceanic tsunami propagation due to the 1883 Krakatau volcanic eruption. Nat Hazards Earth Syst Sci 3:321–332

    Article  Google Scholar 

  • Churchill DD, Houston SH, Bond NA (1995) The Daytona Beach Wave of 3–4 July 1992: a shallow-water gravity wave forced by a propagating squall line. Bul Am Met Soc 76(1):21–32

    Article  Google Scholar 

  • Engelstad AT, Janssen THC, van Herbers G, Vledder S, Elgar B, Raubenheimer L Trainor, Garcia-Garcia A (2013) Wave evolution across the Louisiana shelf. Cont Shelf Res 52:190–202

    Article  Google Scholar 

  • Egbert GD, Erofeeva SY (2002) Efficient inverse modeling of barotropic ocean tides. J Atmos Ocean Technol 19:183–204. doi:10.1175/1520-0426(2002)019<0183:EIMOBO>2.0.CO;2

    Article  Google Scholar 

  • El GA, Grimshaw RHJ, Smyth NF (2009) Transcritical shallow-water flow past topography: finite-amplitude theory. J Fluid Mech 640:187–214. doi:10.1017/S0022112009991315

    Article  Google Scholar 

  • El GA, Grimshaw RHJ, Tiong WK (2012) Transformation of a shoaling undular bore. J Fluid Mech 709:371–395. doi:10.1017/jfm.2012.338

    Article  Google Scholar 

  • Engelbrecht JK, Fridman VE, Pelinovsky EN (1988) Nonlinear evolution equations. Longman/Wiley, New York

    Google Scholar 

  • Ewing M, Press F, Donn WJ (1954) An explanation of the Lake Michigan wave of 26 June 1954. Science 120:684–686

    Article  Google Scholar 

  • Greenspan HP (1956) The generation of edge waves by moving pressure disturbances. J Fluid Mech 1:574–592

    Article  Google Scholar 

  • Grimshaw R (2007) Solitary waves propagating over variable topography. In: Kundu A (ed) Tsunami and nonlinear waves. Springer, Berlin, pp 49–62

    Google Scholar 

  • Griswold GM (1963) Numerical calculation of wave refraction. J Geophys Res 68(6):1715–1723. doi:10.1029/JZ068i006p01715

    Article  Google Scholar 

  • Grue J, Pelinovsky EN, Fructus D, Talipova T, Kharif C (2008) Formation of undular bores and solitary waves in the Strait of Malacca caused by the 26 December 2004 Indian Ocean tsunami. J Geophys Res 113(C05008):2007J. doi:10.1029/C004343

    Google Scholar 

  • Hardy JW, Hsu SA (1997) A climatology of winter cyclogenesis intensity in the northwest Gulf of Mexico. Natl Weather Dig 22:3–7

    Google Scholar 

  • Hibiya T, Kajiura K (1982) Origin of “Abiki” phenomenon (kind of seiches) in Nagasaki Bay. J Oceanogr Soc Jpn 38:172–182

    Article  Google Scholar 

  • Holden H, Karlsen KH, Lie K-A, Risebro NH (2010) Splitting methods for partial differential equations with rough solutions, analysis and matlab programs, ems series of lectures in mathematics, A, Ranicki edn. University of Edinburgh, UK

    Book  Google Scholar 

  • Holloway PE, Pelinovsky E, Talipova TG, Barnes B (1997) A non-linear model of internal tide transformation on the Australian north west shelf. J Phys Oceanogr 27:871–896

    Article  Google Scholar 

  • Holloway PE, Pelinovsky E, Talipova TG (1999) A generalized Korteweg-de Vries model of internal tide transformation in the coastal zone. J Geophys Res 104:18 333–18 350

    Article  Google Scholar 

  • Horvath K, and Vilibić I (2014) Atmospheric mesoscale conditions during the Boothbay meteotsunami: a numerical sensitivity study using a high-resolution mesoscale model, in, Meteorological Tsunamis: The U.S. Coast and other coastal regions, Vilibić et al. eds. Nat Haz (74):55–74

  • Jaramillo S, Sheremet A, Allison M, Reed A, Holland KT (2009) Wave-mud interactions over the muddy Atchafalaya subaqueous clinoform, Louisiana, USA: wave-driven sediment transport. J Geophys Res 114(C04002):2008J. doi:10.1029/C004821

    Google Scholar 

  • Johnson RS (2008) On the development of a solitary wave moving over an uneven bottom. Math Proce Camb Philos Soc 73(01):183. doi:10.1017/S0305004100047605

    Article  Google Scholar 

  • Kamchatnov M, Kuo Y-H, Lin T-C, Horng T-L, Gou S-C, Clift R, Grimshaw RHJ (2012) Undular bore theory for the Gardner equation. Phys Rev E 86(3):036605. doi:10.1103/PhysRevE.86.036605

    Article  Google Scholar 

  • Kharif C, Pelinovsky E, Slunyaev A (2009) Rogue waves in the ocean. Advances in geophysical and environmental mechanics and mathematics. Springer, Berlin

    Google Scholar 

  • Liu PL-F, Park YS, Cowen EA (2007) Boundary layer flow and bed shear stress under a solitary wave. J Fluid Mech 574:449–463. doi:10.1017/S0022112006004253

    Article  Google Scholar 

  • Lynett PJ, Borrero J, Son S, Wilson R, Miller K (2014) Assessment of the tsunami-induced current hazard. Geophys Res Lett 41(2048–2055):2013G. doi:10.1002/L058680

    Google Scholar 

  • Madsen PA, Fuhrman DR, Schaffer HA (2008) On the solitary wave paradigm for tsunamis. J Geophys Res 113:C12012. doi:10.1029/2008JC004932

    Article  Google Scholar 

  • Mercer D, Sheng J, Greatbatch RJ, Bobanović J (2002) Barotropic waves generated by storms moving rapidly over shallow water. J Geophys Res 107(C10):3152. doi:10.1029/2001JC001140

    Article  Google Scholar 

  • Monserrat S, Vilibić I, Rabinovich AB (2006) Meteotsunamis: atmospherically induced destructive ocean waves in the tsunami frequency band. Nat Hazards Earth Syst Sci 6:1035–1051

    Article  Google Scholar 

  • Osborne AR (1995) The inverse scattering transform: tools for the nonlinear Fourier analysis and filtering of ocean surface waves. Chaos Solitons Fractals 5:2623–2637

    Article  Google Scholar 

  • Ostrovsky LA, Pelinovsky EN (1975) Refraction of nonlinear ocean waves in a beach zone. Izv Atmos Ocean Phys 11:37–41

    Google Scholar 

  • Ostrovsky LA, Shrira VI (1976) Instability and self-refraction of solitons Sov. Phys JETP 44:738–743

    Google Scholar 

  • Paxton CH, Sobien DA (1998) Resonant Interaction between an atmospheric gravity wave and shallow water wave along Florida’s West Coast. Bul Am Met Soc 79(12):2727–2732

    Article  Google Scholar 

  • Pelinovsky EN, Stepanyants YA, Talipova TG (1993) Nonlinear dispersion model of sea waves in the coastal zone. J Korean Soc Coast Ocean Eng 5:307–317

    Google Scholar 

  • Pelinovsky EN, Choi BH, Talipova T, Woo SB, Kim DC (2010) Solitary wave transformation on the underwater step: asymptotic theory and numerical experiments. Appl Math Comp 217:1704–1718

    Article  Google Scholar 

  • Proudman J (1929) The effects on the sea of changes in atmospheric pressure. Geophys Suppl Mon Not R Astr Soc 2(4):197–209

    Article  Google Scholar 

  • Rabinovich AB, Monserrat S (1996) Meteorological tsunamis near the Balearic and Kuril Islands: descriptive and statistical analysis. Nat Hazards Earth Syst Sci 13(1):55–90

    Google Scholar 

  • Rabinovich AB, Monserrat S (1998) Generation of meteorological tsunamis (large amplitude seiches) near the Balearic and Kuril Islands. Nat Hazards Earth Syst Sci 18(1):27–55

    Google Scholar 

  • Rabinovich AB (2009) Seiches and harbor oscillations. In: Kim YC (ed) Handbook of coastal and ocean engineering. World Scientific Publ, Singapore, pp 193–236

    Chapter  Google Scholar 

  • Ruppert JH Jr, Bosart LF (2014) A case study of the interaction of a mesoscale gravity wave with a mesoscale convective system. Mon Weather Rev 142:1403–1429. doi:10.1175/MWR-D-13-00274.1

    Article  Google Scholar 

  • Safak I, Sheremet A, Allison MA, Hsu T-J (2010) Bottom turbulence on the muddy atchafalaya shelf, Louisiana, USA. J Geophys Res 115(C12019):2010. doi:10.1029/2010JC006157

    Google Scholar 

  • Sahin C, Safak I, Sheremet A, Mehta AJ (2012) Observations on cohesive bed reworking by waves: Atchafalaya Shelf, Louisiana. J Geophys Res 117:C09025. doi:10.1029/2011JC007821

    Article  Google Scholar 

  • Šepić J, Vilibić I, Strelec Mahović N (2012) Northern Adriatic meteorological tsunamis: observations, link to the atmosphere, and predictability. J Geophys Res 117:C02002. doi:10.1029/2011JC007608

    Google Scholar 

  • Šepić J, Vilibić I, Rabinovich AB, and Monserrat S (2015) Widespread tsunami-like waves of 23-27 June in the Mediterranean and Black Seas generated by high-altitude atmospheric forcing, Sci. Rep. 5, Article No. 11682, doi:10.1038/srep11682

  • Sergeeva A, Pelinovsky E, Talipova TG (2011) Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework. Nat Hazards Earth Syst Sci 11(2):323–330. doi:10.5194/nhess-11-323-2011

    Article  Google Scholar 

  • Tian M, Sheremet A, Kaihatu JM, Ma G (2015) On the Shoaling of solitary waves in the presence of short random waves. J Phys Oceanogr 45:792–806

    Article  Google Scholar 

  • Thompson PG, Mitchum C Vonesch, Li J (2013) Variability of winter storminess in the eastern united states during the twentieth century from tide gauges. J Climate 26:9713–9726

    Article  Google Scholar 

  • Vilibić I, Monserrat S, Rabinovich AB (2014) Meteorological Tsunamis: the U.S. East Coast and Other Coastal Regions. Nat Hazards Earth Syst Sci 74(1)

  • Whitham GB (1973) Linear and nonlinear waves. A Wiley Series of Texts, Monographs and Tracts, Pure and Applied Mathematics

Download references

Acknowledgments

This research was supported by Office of Naval Research Grants N00014-13-1-0620 and NSF Grant CMMI-1208147 “Interaction of Tsunamis with Short Waves and Bottom Sediment - Numerical and Physical Modeling.” The experimental work was funded by Office of Naval Research Grants N00014-10-1-0363, N00014-10-1-0805, and N00014-11-1-0269. The authors are grateful for the thoughtful advice and suggestions provided by two anonymous referees.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alex Sheremet.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sheremet, A., Gravois, U. & Shrira, V. Observations of meteotsunami on the Louisiana shelf: a lone soliton with a soliton pack. Nat Hazards 84 (Suppl 2), 471–492 (2016). https://doi.org/10.1007/s11069-016-2446-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11069-016-2446-2

Keywords

Navigation