| Title |
Derivation of Extended Mild-Slope Equation Using Euler-Lagrange Equation |
| Keywords |
wave transformation equation;extended mild-slope equation;higher-order bottom variation;Euler-Lagrange equation;파랑변형식;확장형 완경사방정식;고차의 수심변화;Euler-Lagrange 식 |
| Abstract |
In this study, we derive the extended mild-slope equation in terms of the velocity potential using the Euler-Lagrange equation. First, we follow Kim and Bai (2004) who derive the complementary mild-slope equation in terms of the stream function using the Euler-Lagrange equation and we compare their equation to the existing extended mild-slope equations of the velocity potential. Second, we derive the extended mild-slope equation in terms of the velocity potential using the Euler-Lagrange equation. In the developed equation, the higher-order bottom variation terms are newly developed and found to be the same as those of Massel (1993) and Chamberlain and Porter (1995). The present study makes wide the area of coastal engineering by developing the extended mild-slope equation with a way which has never been used before. |