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Long Wave Runup in Asymmetric Bays and in Fjords With Two Separate Heads
Author(s) -
Raz Amir,
Nicolsky Dmitry,
Rybkin Alexei,
Pelinovsky Efim
Publication year - 2018
Publication title -
journal of geophysical research: oceans
Language(s) - English
Resource type - Journals
eISSN - 2169-9291
pISSN - 2169-9275
DOI - 10.1002/2017jc013100
Subject(s) - fjord , nonlinear system , geology , cross section (physics) , waves and shallow water , shore , transformation (genetics) , plane (geometry) , mechanics , geometry , physics , oceanography , mathematics , biochemistry , chemistry , quantum mechanics , gene
Modeling of tsunamis in glacial fjords prompts us to evaluate applicability of the cross‐sectionally averaged nonlinear shallow water equations to model propagation and runup of long waves in asymmetrical bays and also in fjords with two heads. We utilize the Tuck‐Hwang transformation, initially introduced for the plane beaches and currently generalized for bays with arbitrary cross section, to transform the nonlinear governing equations into a linear equation. The solution of the linearized equation describing the runup at the shore line is computed by taking into account the incident wave at the toe of the last sloping segment. We verify our predictions against direct numerical simulation of the 2‐D shallow water equations and show that our solution is valid both for bays with an asymmetric L‐shaped cross section, and for fjords with two heads—bays with a W‐shaped cross section.