DISINTEGRATION OF CNOIDAL WAVES OVER SMOOTH TOPOGRAPHY

The transformation of cnoidal waves in a basin with smooth topography is studied in the frame of the variable-coefficient Korteweg-de Vries equation and the generalized Zakharov's system. It is shown that the c noidal structure of the propagating nonlinear wave is destroyed if the topography contains a periodic component with a characteristic scale close to the nonlinearity length. Focusing on waves in intermediate de pth, a simple analytical model based on a two-harmonic representation of the cnoidal wave demonstrates the main features of the process of d isintegration of the cnoidal structure of the nonlinear wave. Numerica l simulations of the interaction of several harmonics confirm the anal ytical conclusions.