STEADY STATE SOLUTIONS OF THE FORCED KORTEWEG-DE VRIES EQUATION OVER COSINUSOIDAL TOPOGRAPHIES WITH TWO SPATIAL WAVENUMBERS

• Main Author: Theodore Adriano, Farrell
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/76177
• Institution: Institut Teknologi Bandung

In this thesis, the free surface flow over a spatially wavy bottom is analysed using the stationary fKdV (forced Korteweg-De Vries) equation. In particular, perturbations to the uniform, solitary, and cnoidal solutions due to a bottom sinusoidal topography with 2 spatial wavenumbers are studied using the fKdV equation. By asymptotic analysis, it is shown that there are several types of near solitary solutions which depends on the amplitudes and the wavenumbers of the topography. Furthermore, several types of resonances may occur in the near cnoidal solution due to the interaction between the 2 topography’s wavenumbers. This analysis is shown to be consistent with the numerical results. The solution structure to these perturbations is also analyzed by calculating the bifurcation diagrams using pseudo arclength numerical continuation.