<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The paper deals with interactions between water waves propagating in fluid of constant depth. In formulation of this problem, a nonlinear character of these interactions is taken into account. In particular, in order to simplify a solution to nonlinear boundary conditions at the free surface, a system of material coordinates is employed as independent variables in the description of the phenomenon. The main attention is focused on the transient solutions corresponding to fluid motion starting from rest. With respect to the initial value problem considered, we confine our attention to a finite fluid domain. For a finite elapse of time, measured from the starting point, the solution in a finite fluid area mimics a solution within an infinite domain, inherent for wave propagation problems. Because of the complicated structure of equations describing nonlinear waves, an approximate formulation is considered, which is based on a power series expansion of dependent variables with respect to a small parameter. Such a solution is assumed to be accurate in describing the main features of the phenomenon. Numerical experiments are conducted to illustrate the approximate formulation developed in this paper.</p></abstract>

The paper deals with interactions between water waves propagating in fluid of constant depth. In formulation of this problem, a nonlinear character of these interactions is taken into account. In particular, in order to simplify a solution to nonlinear boundary conditions at the free surface, a system of material coordinates is employed as independent variables in the description of the phenomenon. The main attention is focused on the transient solutions corresponding to fluid motion starting from rest. With respect to the initial value problem considered, we confine our attention to a finite fluid domain. For a finite elapse of time, measured from the starting point, the solution in a finite fluid area mimics a solution within an infinite domain, inherent for wave propagation problems. Because of the complicated structure of equations describing nonlinear waves, an approximate formulation is considered, which is based on a power series expansion of dependent variables with respect to a small parameter. Such a solution is assumed to be accurate in describing the main features of the phenomenon. Numerical experiments are conducted to illustrate the approximate formulation developed in this paper.

Nonlinear Interactions between Gravity Waves in Water of Constant Depth

Institute of Hydro-Engineering, Polish Academy of Sciences, ul. Kościerska 7, 80-328 Gdańsk, Poland

Archives of Hydro-Engineering and Environmental Mechanics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Nonlinear Interactions between Gravity Waves in Water of Constant Depth"}

The paper deals with interactions between water waves propagating in fluid of constant depth. In formulation of this problem, a nonlinear character of these...

Nonlinear Interactions between Gravity Waves in Water of Constant Depth

Published Online: Dec 01, 2015

Page range: 3 - 25

Received: Feb 09, 2015

Accepted: Mar 19, 2015

DOI: https://doi.org/10.1515/heem-2015-0016

Keywords
nonlinear water wave, wave interaction, material variables, potential solution

© 2015 Kazimierz Szmidt et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Nonlinear Interactions between Gravity Waves in Water of Constant Depth

Published Online: Dec 01, 2015

Page range: 3 - 25

Received: Feb 09, 2015

Accepted: Mar 19, 2015

DOI: https://doi.org/10.1515/heem-2015-0016

Keywordsnonlinear water wave, wave interaction, material variables, potential solution

© 2015 Kazimierz Szmidt et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
nonlinear water wave, wave interaction, material variables, potential solution