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## Long wave run-up in asymmetric bays and in fjords with two separate heads

Modeling of tsunamis in glacial fjords prompts us to evaluate applicability of the crosssectionally

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