### Abstract

Elliptic mild slope equation based models are widely used to compute wavefields in regions of complex, arbitrarily varying topography and geometry. They are used in applications involving wave reflection, diffraction, refraction, nearshore breaking and frictional dissipation. However, these are based on linear wave theory; therefore, nonlinear interactions among frequency components are ignored. In this study, a modified form of the nonlinear elliptic mild-slope equation is used to numerically model the nonlinear wave transformation. The Alternating Direction Implicit (ADI) scheme is employed to solve the equation with appropriate boundary conditions. The nonlinear energy transfer among frequency components, are modeled in the presence of wave reflection, diffraction, refraction, etc. In addition, transformation of wave spectra is studied by incorporating the effects of wave breaking. The computations are compared with the laboratory data and other results. Overall the model performs reasonably well and has improved applicability in comparison to the mild slope models based on parabolic approximation.

Original language | English |
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Title of host publication | Proceedings of the 23rd International Offshore and Polar Engineering Conference, ISOPE 2013 |

Pages | 1061-1067 |

Number of pages | 7 |

Publication status | Published - 2013 |

Externally published | Yes |

Event | 23rd International Offshore and Polar Engineering Conference, ISOPE 2013 - Anchorage, AK, United States Duration: 30 Jun 2013 → 5 Jul 2013 |

### Other

Other | 23rd International Offshore and Polar Engineering Conference, ISOPE 2013 |
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Country | United States |

City | Anchorage, AK |

Period | 30/6/13 → 5/7/13 |

### Fingerprint

### Keywords

- Coasts and harbors
- Mild-slope equation
- Multiple-scale analysis
- Wave-wave interactions

### ASJC Scopus subject areas

- Energy Engineering and Power Technology
- Ocean Engineering
- Mechanical Engineering

### Cite this

*Proceedings of the 23rd International Offshore and Polar Engineering Conference, ISOPE 2013*(pp. 1061-1067)

**Numerical modeling of nonlinear wave transformation using elliptic mild slope equation.** / Sharma, Abhishek; Panchang, Vijay; Kaihatu, James M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 23rd International Offshore and Polar Engineering Conference, ISOPE 2013.*pp. 1061-1067, 23rd International Offshore and Polar Engineering Conference, ISOPE 2013, Anchorage, AK, United States, 30/6/13.

}

TY - GEN

T1 - Numerical modeling of nonlinear wave transformation using elliptic mild slope equation

AU - Sharma, Abhishek

AU - Panchang, Vijay

AU - Kaihatu, James M.

PY - 2013

Y1 - 2013

N2 - Elliptic mild slope equation based models are widely used to compute wavefields in regions of complex, arbitrarily varying topography and geometry. They are used in applications involving wave reflection, diffraction, refraction, nearshore breaking and frictional dissipation. However, these are based on linear wave theory; therefore, nonlinear interactions among frequency components are ignored. In this study, a modified form of the nonlinear elliptic mild-slope equation is used to numerically model the nonlinear wave transformation. The Alternating Direction Implicit (ADI) scheme is employed to solve the equation with appropriate boundary conditions. The nonlinear energy transfer among frequency components, are modeled in the presence of wave reflection, diffraction, refraction, etc. In addition, transformation of wave spectra is studied by incorporating the effects of wave breaking. The computations are compared with the laboratory data and other results. Overall the model performs reasonably well and has improved applicability in comparison to the mild slope models based on parabolic approximation.

AB - Elliptic mild slope equation based models are widely used to compute wavefields in regions of complex, arbitrarily varying topography and geometry. They are used in applications involving wave reflection, diffraction, refraction, nearshore breaking and frictional dissipation. However, these are based on linear wave theory; therefore, nonlinear interactions among frequency components are ignored. In this study, a modified form of the nonlinear elliptic mild-slope equation is used to numerically model the nonlinear wave transformation. The Alternating Direction Implicit (ADI) scheme is employed to solve the equation with appropriate boundary conditions. The nonlinear energy transfer among frequency components, are modeled in the presence of wave reflection, diffraction, refraction, etc. In addition, transformation of wave spectra is studied by incorporating the effects of wave breaking. The computations are compared with the laboratory data and other results. Overall the model performs reasonably well and has improved applicability in comparison to the mild slope models based on parabolic approximation.

KW - Coasts and harbors

KW - Mild-slope equation

KW - Multiple-scale analysis

KW - Wave-wave interactions

UR - http://www.scopus.com/inward/record.url?scp=84883730743&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883730743&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84883730743

SN - 9781880653999

SP - 1061

EP - 1067

BT - Proceedings of the 23rd International Offshore and Polar Engineering Conference, ISOPE 2013

ER -