Alexei Rybkin

Research Field

Abstract We present an exact analytical solution of the nonlinear shallow water theory for wave run-up in inclined channels of arbitrary cross-section, which generalizes previous studies on wave run-up for a plane beach and channels of parabolic cross-section. The solution is found using a hodograph-type transform, which extends the well-known Carrier–Greenspan transform for wave run-up on a plane beach. As a result, the nonlinear shallow water equations are reduced to a single one-dimensional linear wave equation for an auxiliary function and all physical variables can be expressed in terms of this function by purely algebraic formulas. In the special case of a U-shaped channel this equation coincides with a spherically symmetric wave equation in space, whose dimension is defined by the channel cross-section and can be fractional. As an example, the run-up of a sinusoidal wave on a beach is considered for channels of several different cross-sections and the influence of the cross-section on wave run-up characteristics is studied.

Hodograph

Section (typography)

10.1017/jfm.2014.197

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Citations (63)

Inverse problem for the nonlinear long wave runup on a plane sloping beach

Applied Mathematics Letters (2023)

Alexei Rybkin Efim Pelinovsky Noah Palmer

Kondratiev wave

10.1016/j.aml.2023.108786

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Citations (2)

Long Wave Runup in Asymmetric Bays and in Fjords With Two Separate Heads

Journal of Geophysical Research Oceans (2018)

Amir Raz Dmitry Nicolsky Alexei Rybkin Efim Pelinovsky

Abstract 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.

Fjord

10.1002/2017jc013100

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Citations (11)

Run-Up of Long Waves in Piecewise Sloping U-Shaped Bays

Pure and Applied Geophysics (2017)

Dalton Anderson M. W. Harris Harrison Hartle Dmitry Nicolsky Efim Pelinovsky

Shallow water equations

10.1007/s00024-017-1476-3

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Citations (17)

Robust Computations of Runup in Inclined U- and V-Shaped Bays