On some nonlinear wave diffraction and refraction solutions in shallow water

TY - GEN

T1 - On some nonlinear wave diffraction and refraction solutions in shallow water

AU - Hayatdavoodi, Masoud

AU - Ertekin, R. Cengiz

PY - 2022/6/5

Y1 - 2022/6/5

N2 - Diffraction and refraction of nonlinear shallow water waves due to uneven bathymetry is studied numerically in two and three dimensions. The numerical tank consists of a wavemaker at the upwave side of the domain, the submerged obstacles in the middle of the domain, and a numerical wave absorber on the downwave of the domain. The numerical wavemaker is capable of generating solitary and cnoidal waves as solutions of the Green-Naghdi (GN) equations. The nonlinear wave refraction and diffraction is studied by use of the Level I GN equations. The system of equations are solved numerically in time domain by use of a second-order finite difference approach, and in a boundary-fitted coordinate system. Various forms of three-dimensional bathymetry with large slopes, including flat and curved ramps from deep to shallow regions are considered. Results include solitary and cnoidal wave surface elevation and particle velocities and are compared with the existing solutions where possible. Overall very good agreement is observed. Discussion is provided on the nonlinearity and dispersion effects on the wave diffraction and refraction, as well as on the performance of the GN equations in solving these problems.

AB - Diffraction and refraction of nonlinear shallow water waves due to uneven bathymetry is studied numerically in two and three dimensions. The numerical tank consists of a wavemaker at the upwave side of the domain, the submerged obstacles in the middle of the domain, and a numerical wave absorber on the downwave of the domain. The numerical wavemaker is capable of generating solitary and cnoidal waves as solutions of the Green-Naghdi (GN) equations. The nonlinear wave refraction and diffraction is studied by use of the Level I GN equations. The system of equations are solved numerically in time domain by use of a second-order finite difference approach, and in a boundary-fitted coordinate system. Various forms of three-dimensional bathymetry with large slopes, including flat and curved ramps from deep to shallow regions are considered. Results include solitary and cnoidal wave surface elevation and particle velocities and are compared with the existing solutions where possible. Overall very good agreement is observed. Discussion is provided on the nonlinearity and dispersion effects on the wave diffraction and refraction, as well as on the performance of the GN equations in solving these problems.

KW - Green-Naghdi equations

KW - Nonlinear waves

KW - soliton fission

KW - wave refraction and diffraction

UR - https://event.asme.org/OMAE

UR - https://www.scopus.com/pages/publications/85140789238

U2 - 10.1115/OMAE2022-79413

DO - 10.1115/OMAE2022-79413

M3 - Conference contribution

SN - 9780791885895

BT - Proceedings of the ASME 2022 41st International Conference on Ocean, Offshore and Arctic Engineering (OMAE2022)

PB - American Society of Mechanical Engineers

CY - Germany

T2 - ASME 2022 41st International Conference on Ocean, Offshore and Arctic Engineering (OMAE 2022)

Y2 - 5 June 2022 through 10 June 2022

ER -