Dinamika Gelombang Cnoidal di Atas Dasar Tak Rata Menggunakan Persamaan Gelombang Dua Arah Boussinesq

Warsoma Djohan ( Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, ITB)

Jurnal Matematika & Sains
Vol 2, No 2 (1997)

Waves over uneven bottom which are running in two directions are governed by Boussinesq equations. When the bottom is flat, the Boussinesq equations have a periodic travelling wave solution, i.e. a solution which is running undisturbed in shape and velocity. This travelling wave is called a cnoidal wave. In this research the distortion of a cnoidal wave due to decreasing depth will be studied numerically. A cnoidal wave is initially running above flat bottom, then the depth decreases and flat again with depth h1 (< h0). First, a cnoidal wave is constructed as solution of the constrained critical point problem, i.e. finding the extremism of energy with constraints momentum and mass. Then the Boussinesq equations are discritized using the direct Fourier truncation method. Numerical simulation shows that the cnoidal wave constructed above is indeed a travelling wave solution. By choosing h1 to be the eigendepth of the two-soliton solution of KdV according to the inverse scattering theory, numerical simulations show the splitting process of an initial cnoidal wave into two waves.