Abstract
In the framework of the nonlinear long wave theory, the evolution of a single wave propagating in the bays with U-shaped cross-section is studied. A good conformity was found between the numerical and analytical estimates of the wave height variation along the bay axis. It is shown that the influence of the shape of the bay cross-section on the wave field is manifested in the sea level rise with the approach to the bay periphery. Estimates of vertical run-up and drainage depth of the shore at the bay top with different cross-sectional shape were obtained. It is found that in bays with a triangular cross-sectional shape there are the greatest run-up height and the greatest drainage depths from the shore. The distance traveled by the wave from the bay entrance to the point of wave breaking is the largest for the bay with cross-sectional shape is approximate to rectangular.
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References
Bazykina AYu, Dotsenko SF (2015) Nonlinear effects at propagation of long surface waves in the channels with a variable cross-section. Phys Oceanogr 4:3–13
Bazykina AY, Dotsenko SF (2016) Vliyanie nelineynosti I donnogo treniya na dlinnye volny v kanalah peremennogo poperechnogo secheniya [Influence of non-linearity and bottom friction on long waves in channels of variable cross-section]. Processy v Geosredah 2:97–103 (in Russian)
Didenkulov OI, Didenkulova II, Pelinovsky EN, Kurkin AA (2015) Influence of the shape of the bay cross section on wave run-up 2015. Izv AN Fiz Atmosfery i Okeana 51(6):741–747
Didenkulova I (2013) Tsunami runup in narrow bays: the case of Samoa 2009 tsunami. Nat Hazards 65(3):1629–1636
Didenkulova II, Pelinovsky DE, Tyugin DY et al (2012) Begushchie dlinnye volny v vodnyh pryamougolnyh kanalah peremennogo secheniya [The running long waves in the water rectangular channels of variable section]. Vestn MGOU 5:89–93 (in Russian)
Didenkulova I, Pelinovsky E (2011a) Runup of tsunami waves in U-shaped bays. Pure Appl Geophys 168:1239–1249
Didenkulova I, Pelinovsky E (2011b) Nonlinear wave evolution and runup in an in-clined channel of a parabolic cross-section. Phys Fluids 23(8):086602
Friedrichs CT, Aubrey DG (1994) Tidal propagation in strongly convergent channels. J Geoph Res 99(C2):3321–3336
Garayshin VV, Harris MW, Nicolsky DJ, Pelinovsky EN, Rybkin AV (2016) An analytical and numerical study of long waves run-up in U-shaped and V-shaped bays. Appl Math Comput 279:187–197
Kowalik Z (2001) Basic relations between tsunamis calculations and their physics. Sci Tsun Hazar 19(2):99–115
Kowalik Z, Murty TS (1993) Numerical simulation of two-dimensional tsunami runup. Mar Geodesy 16:87–100
Levin BV, Nosov MA (2016) Physics of tsunamis. Springer, p 388
Rybkin A, Pelinovsky E, Didenkulova I (2014) Nonlinear wave run-up in bays of arbi-trary cross-section: generalization of the Carrier-Greenspan approach. J Fluid Mech 748:416–432
Sielecki A, Wurtele M (1970) The numerical integration of the non-linear shallow-water equations with sloping boundaries. J Comp Phys 6:219–236
Voltcinger NE, Pyaskovsky RV (1968) The main oceanological problems of the shal-low water theory, L. Gidrometeoizdat 300
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Belokon, A.Y., Fomin, V.V. (2022). Propagation of a Single Long Wave in the Bays with U-Shaped Cross-Section Form. In: Chaplina, T. (eds) Processes in GeoMedia—Volume IV. Springer Geology. Springer, Cham. https://doi.org/10.1007/978-3-030-76328-2_15
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DOI: https://doi.org/10.1007/978-3-030-76328-2_15
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