An analytical and numerical study of long wave run-up in U-shaped and V-shaped bays

Garayshin, V.V.; Harris, Matthew W.; Nicolsky, D.J.; Pelinovsky, Efim N.; Rybkin, A.V.

doi:10.1016/j.amc.2016.01.005

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i

An analytical and numerical study of long wave run-up in U-shaped and V-shaped bays

2016
By Garayshin, V.V. ; Harris, Matthew W. ; Nicolsky, D.J. ; ...
Source: Applied Mathematics and Computation, 279: 187-197

[PDF-565.84 KB]

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Journal Title:

Applied Mathematics and Computation
Personal Author:

Garayshin, V.V. ; Harris, Matthew W. ; Nicolsky, D.J. ; Pelinovsky, Efim N. ; Rybkin, A.V.

Garayshin, V.V. ; Harris, Matthew W. ; Nicolsky, D.J. ; Pelinovsky, Efim N. ; Rybkin, A.V. Less -
NOAA Program & Office:

OAR (Oceanic and Atmospheric Research) ; CIFAR (Cooperative Institute for Alaska Research)

OAR (Oceanic and Atmospheric Research) ; CIFAR (Cooperative Institute for Alaska Research) Less -
Description:

By assuming the flow is uniform along the narrow long bays, the 2-D nonlinear shallow-water equations are reduced to a linear semi-axis variable-coefficient 1-D wave equation via the generalized Carrier–Greenspan transformation. The run-up of long waves in constantly sloping U-shaped and V-shaped bays is studied both analytically and numerically within the framework of the 1-D nonlinear shallow-water theory. An analytic solution, in the form of a double integral, to the resulting linear wave equation is obtained by utilizing the Hankel transform, and consequently the solution to the tsunami run-up problem is developed by applying the inverse generalized Carrier–Greenspan transform. The presented solution is a generalization of the solutions found by Carrier et al. (2003) and Didenkulova and Pelinovsky (2011) for the case of a plane beach and a parabolic bay, respectively. The shoreline dynamics in U-shaped and V-shaped bays are computed via a double integral through standard integration techniques.
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Bays Waves
Source:

Applied Mathematics and Computation, 279: 187-197
DOI:

https://doi.org/10.1016/j.amc.2016.01.005
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Journal Article
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Grant no. NA08OAR4320751
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urn:sha256:99553cc87a23d9bd0cc0c6bf405397fb8ea087d23778e40d9f6249d58c6f8ac0
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An analytical and numerical study of long wave run-up in U-shaped and V-shaped bays

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