ESTONIAN ACADEMY
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eesti teaduste
akadeemia kirjastus
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Estonian Journal of Engineering

On the occurrence of non-reflecting cross-shore profiles along Estonian coasts of the Baltic Sea; pp. 110–123

Full article in PDF format | doi: 10.3176/eng.2013.2.02

Authors
Ira Didenkulova, Tarmo Soomere, Katri Pindsoo, Sten Suuroja

Abstract

Cross-shore beach profiles along Estonian coasts of the Baltic Sea are analysed from the viewpoint of the frequency of occurrence of convex sections that may support non-reflecting wave propagation and unexpectedly high run-up events. In total 194 beach profiles, measured in 2006–2011 at 16 locations, are examined by means of their approximation with the power function h(x) = Axb. About half of the profiles can be adequately approximated using a single power function. These profiles are almost all concave. The relevant exponents are clustered around b = 2/3 that is characteristic to the Dean’s Equilibrium Profile. The rest of the profiles can be divided into two sections, each of which is approximated by a power function. The underwater sections of such profiles predominantly match the Dean’s Equilibrium Profile. About 10% of the subaerial sections (about 7% of all examples) have the exponent close to b = 4/3, for which high run-up events are likely.


References

 1. Lay, Th., Kanamori, H., Ammon, Ch. J., Nettles, M., Ward, S. N., Aster, R. C., Beck, S. L., Bilek, S. L., Brudzinski, M. R., Butler, Rh. et al. The Great Sumatra-Andaman Earthquake of 26 December 2004. Science, 2005, 308, 1127–1133.
http://dx.doi.org/10.1126/science.1112250

 2. Mori, N., Takahashi, T., Yasuda, T. and Yanagisawa, H. Survey of 2011 Tohoku earthquake tsunami inundation and run-up. Geophys. Res. Lett., 2011, 38, L00G14.
http://dx.doi.org/10.1029/2011GL049210

 3. Kim, K. O., Lee, H. S., Yamashita, T. and Choi, B. H. Wave and storm surge simulations for Hurricane Katrina using coupled process based models. KSCE J. Civil Eng., 2008, 12, 1–8.
http://dx.doi.org/10.1007/s12205-008-8001-2

 4. Dube, S. K., Poulose, J. and Rao, A. D. Numerical simulation of storm surge associated with severe cyclonic storms in the Bay of Bengal during 2008–2011. Mausam, 2013, 64, 193–202.

 5. Orviku, K., Jaagus, J., Kont, A., Ratas, U. and Rivis, R. Increasing activity of coastal processes associated with climate change in Estonia. J. Coast. Res., 2003, 19, 364–375.

 6. Lehrman, J. B., Higgins, C. and Cox, D. Performance of highway bridge girder anchorages under simulated hurricane wave induced loads. J. Bridge Eng., 2012, 17, 259–271.
http://dx.doi.org/10.1061/(ASCE)BE.1943-5592.0000262

 7. Valdmann, A., Käärd, A., Kelpšaitė, L., Kurennoy, D. and Soomere, T. Marine coastal hazards for the eastern coasts of the Baltic Sea. Baltica, 2008, 21, 3–12.

 8. Carrier, G. F. and Greenspan, H. P. Water waves of finite amplitude on a sloping beach. J. Fluid Mech., 1958, 4, 97–109.
http://dx.doi.org/10.1017/S0022112058000331

 9. Kobayashi, N. and Wurjanto, A. Irregular wave setup and run-up on beaches. J. Waterw. Port Coast. Ocean Eng., 1992, 118, 368–386.
http://dx.doi.org/10.1061/(ASCE)0733-950X(1992)118:4(368)

10. Tadepalli, S. and Synolakis, C. E. The run-up of N-waves on sloping beaches. Proc. Roy. Soc. Math. Phys. Sci., 1994, 445, 99–112.
http://dx.doi.org/10.1098/rspa.1994.0050

11. Titov, V. V. and Synolakis, C. E. Extreme inundation flows during the Hokkaido-Nansei-Oki tsunami. Geophys. Res. Lett., 1997, 24, 1315–1318.
http://dx.doi.org/10.1029/97GL01128

12. Tadepalli, S. and Synolakis, C. E. Model for the leading waves of tsunamis. Phys. Rev. Lett., 1996, 77, 2141–2144.
http://dx.doi.org/10.1103/PhysRevLett.77.2141

13. Losada, I. J., Lara, J. L., Guanche, R. and Gonzalez-Ondina, J. M. Numerical analysis of wave overtopping of rubble mound breakwaters. Coast. Eng., 2008, 55, 47–62.
http://dx.doi.org/10.1016/j.coastaleng.2007.06.003

14. Dean, R. G. and Dalrymple, R. A. Coastal Processes with Engineering Applications. Cambridge University Press, Cambridge, 2002.

15. Monserrat, S., Vilibic, I. and Rabinovich, A. B. Meteotsunamis: atmospherically induced destructive ocean waves in the tsunami frequency band. Nat. Hazards Earth Syst. Sci., 2006, 6, 1035–1051.
http://dx.doi.org/10.5194/nhess-6-1035-2006

16. Rabinovich, A. B. and Monserrat, S. Meteorological tsunamis near the Balearic and Kuril Islands: Descriptive and statistical analysis. Nat. Hazards, 1996, 13, 55–90.
http://dx.doi.org/10.1007/BF00156506

17. Kharif, C. and Pelinovsky, E. Physical mechanisms of the rogue wave phenomenon. Eur. J. Mech. B Fluids, 2003, 22, 603–634.
http://dx.doi.org/10.1016/j.euromechflu.2003.09.002

18. Didenkulova, I. I., Slunyaev, A. V., Pelinovsky, E. N. and Kharif, Ch. Freak waves in 2005. Nat. Hazards Earth Syst. Sci., 2006, 6, 1007–1015.
http://dx.doi.org/10.5194/nhess-6-1007-2006

19. Nikolkina, I. and Didenkulova, I. Rogue waves in 2006–2010. Nat. Hazards Earth Syst. Sci., 2011, 11, 2913–2924.
http://dx.doi.org/10.5194/nhess-11-2913-2011

20. Levin, B. and Nosov, M. Physics of Tsunamis. Springer, Berlin, 2008.

21. Didenkulova, I. I., Zahibo, N., Kurkin, A. A., Levin, B. V., Pelinovsky, E. N. and Soomere, T. Runup of nonlinearly deformed waves on a coast. Dokl. Earth Sci., 2006, 411, 1241–1243.
http://dx.doi.org/10.1134/S1028334X06080186

22. Didenkulova, I. and Pelinovsky, E. Non-dispersive traveling waves in inclined shallow water channels. Phys. Lett. A, 2009, 373, 3883–3887.
http://dx.doi.org/10.1016/j.physleta.2009.08.051

23. Didenkulova, I. and Pelinovsky, E. Runup of tsunami waves in U-shaped bays. Pure Appl. Geophys., 2011, 168, 1239–1249.
http://dx.doi.org/10.1007/s00024-010-0232-8

24. Fritz, H. M., Kongko, W., Moore, A., McAdoo, B., Goff, J., Harbitz, C., Uslu, B., Kallige­ris, N., Suteja, D., Kalsum, K. et al. Extreme runup from the 17 July 2006 Java tsunami. Geophys. Res. Lett., 2007, 34, L12602.
http://dx.doi.org/10.1029/2007GL029404

25. Okal, E. A., Fritz, H. M., Synolakis, C. E., Borrero, J. C., Weiss, R., Lynett, P. J., Titov, V. V., Foteinis, S., Jaffe, B. E., Liu, P. L.-F. and Chan, I.-Ch. Field survey of the Samoa tsunami of 29 September 2009. Seismol. Res. Lett., 2010, 81, 577–591.
http://dx.doi.org/10.1785/gssrl.81.4.577

26. Clements, D. L. and Rogers, C. Analytic solution of the linearized shallow-water wave equations for certain continuous depth variations. J. Aust. Math. Soc., B, 1975, 19, 81–94.

27. Didenkulova, I. and Pelinovsky, E. Traveling water waves along a quartic bottom profile. Proc. Estonian Acad. Sci., 2010, 59, 166–171.
http://dx.doi.org/10.3176/proc.2010.2.16

28. Didenkulova, I., Pelinovsky, E. and Soomere, T. Long surface wave dynamics along a convex bottom. J. Geophys. Res., 2009, 114, C07006.
http://dx.doi.org/10.1029/2008JC005027

29. Didenkulova, I. I. and Pelinovsky, E. N. Reflection of a long wave from an underwater slope. Oceanology, 2011, 51, 568–573.
http://dx.doi.org/10.1134/S0001437011040060

30. Didenkulova, I. and Soomere, T. Formation of two-section cross-shore profile under joint influence of random short waves and groups of long waves. Marine Geol., 2011, 289, 29–33.
http://dx.doi.org/10.1016/j.margeo.2011.09.011

31. Dean, R. G. Equilibrium beach profiles: characteristics and applications. J. Coast. Res., 1991, 7, 53–84.

32. Yeh, H., Liu, P. L.-F. and Synolakis, C. (eds). Long-Wave Runup Models. World Scientific, 1996.

33. Liu, P. L.-F., Yeh, H. and Synolakis, C. (eds). Advances in Coastal and Ocean Engineering: Advanced Numerical Models for Simulating Tsunami Waves and Runup. World Scientific, 2008.
http://dx.doi.org/10.1142/9789812790910

34. Bruun, P. Coast Erosion and the Development of Beach Profiles. Beach Erosion Board Technical Memorandum No. 44, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS, 1954.

35. Dean, R. G. Equilibrium Beach Profiles: U.S. Atlantic and Gulf Coasts. Ocean Eng. Rep. 12, Dep. of Civil Eng., University of Delavare, Newark, 1977.

36. Steetzel, H. J. Cross-shore Transport During Storm Surges. Delft Hydraulics, Delft, The Netherlands, Publ. No. 476, 1993.

37. Kit, E. and Pelinovsky, E. Dynamical models for cross-shore transport and equilibrium bottom profiles. J. Waterw. Port Coast. Ocean Eng., 1998, 124, 138–146.
http://dx.doi.org/10.1061/(ASCE)0733-950X(1998)124:3(138)

38. Didenkulova, I., Pelinovsky, E., Soomere, T. and Parnell, K. E. Beach profile change caused by vessel wakes and wind waves in Tallinn Bay, the Baltic Sea. J. Coast. Res., 2011, Special Issue 64, 60–64.

39. Romańczyk, W., Boczar-Karakiewicz, B. and Bona, J. L. Extended equilibrium beach profiles. Coast. Eng., 2005, 52, 727–744.
http://dx.doi.org/10.1016/j.coastaleng.2005.05.002

40. Are, F. and Reimnitz, E. The A and m coefficients in the Bruun/Dean Equilibrium Profile equation seen from the Arctic. J. Coast. Res., 2008, 24, 243–249.
http://dx.doi.org/10.2112/05-0572.1

41. Kobayashi, N. Analytical solution for dune erosion by storms. J. Waterw. Port Coast. Ocean Eng., 1987, 113, 401–418.
http://dx.doi.org/10.1061/(ASCE)0733-950X(1987)113:4(401)

42. Dai, Z.-J., Du, J.-Z., Li, C.-C. and Chen, Z.-S. The configuration of equilibrium beach profile in South China. Geomorphology, 2007, 86, 441–454.
http://dx.doi.org/10.1016/j.geomorph.2006.09.016

43. Inman, D. L., Elwany, M. H. S. and Jenkins, S. A. Shore-rise and bar-berm profiles on ocean beaches. J. Geophys. Res., 1993, 98, 18181–18199.
http://dx.doi.org/10.1029/93JC00996

44. Bernabeu, A. M., Medina, R. and Vidal, C. A morphological model of the beach profile integrating wave and tidal influence. Marine Geol., 2003, 197, 95–116.
http://dx.doi.org/10.1016/S0025-3227(03)00087-2

45. Wright, L. D. and Short, A. D. 1984. Morphodynamic variability of surf zones and beaches: A synthesis. Marine Geol., 1984, 56, 93–118.
http://dx.doi.org/10.1016/0025-3227(84)90008-2

46. Orviku, K. Estonian Coasts. Eesti NSV TA Geoloogia Instituut, Tallinn, 1974 (in Russian).

47. Orviku, K. and Granö, O. Contemporary coasts. In Geology of the Gulf of Finland (Raukas, A. and Hyvärinen, H., eds), 219–238. Valgus, Tallinn (in Russian).

48. Suuroja, S., Karimov, M., Talpas, A. and Suuroja, K. Mererannikute seire. Aruanne riikliku keskkonnaseire alamprogrammi “Mererannikute seire” täitmisest 2006. aastal. Tallinn, 2007.

49. Suuroja, S., Talpas, A. and Suuroja, K. Eesti Riikliku Keskkonnaseire mererannikute seire allprogrammi 2007. a aastaaruanne. Tallinn, 2008.

50. Suuroja, S., Talpas, A. and Suuroja, K. Eesti Riikliku Keskkonnaseire mererannikute seire allprogrammi 2008. a aastaaruanne. Tallinn, 2009.

51. Suuroja, S., Talpas, A. and Suuroja, K. Eesti Riikliku Keskkonnaseire mererannikute seire allprogrammi 2009. a aastaaruanne. Tallinn, 2010.

52. Suuroja, S., Talpas, A. and Suuroja, K. Eesti Riikliku Keskkonnaseire mererannikute seire allprogrammi 2010. a aastaaruanne. Tallinn, 2011.

53. Soomere, T. and Räämet, A. Spatial patterns of the wave climate in the Baltic Proper and the Gulf of Finland. Oceanologia, 2011, 53(1-TI), 335–371.
http://dx.doi.org/10.5697/oc.53-1-TI.335

54. Didenkulova, I., Nikolkina, I., Pelinovsky, E. and Zahibo, N. Tsunami waves generated by submarine landslides of variable volume: analytical solutions for a basin of variable depth. Nat. Hazards Earth Syst. Sci., 2010, 10, 2407–2419.
http://dx.doi.org/10.5194/nhess-10-2407-2010

55. Kask, A., Soomere, T., Healy, T. R. and Delpeche, N. Rapid estimates of sediment loss for “almost equilibrium” beaches. J. Coast. Res., 2009, 25, Special Issue 56, 971–975.

56. Kartau, K., Soomere, T. and Tõnisson, H. Quantification of sediment loss from semi-sheltered beaches: a case study for Valgerand Beach, Pärnu Bay, the Baltic Sea. J. Coast. Res., 2011, Special Issue 64, 100–104.


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