Premium
Disintegration of Cnoidal Waves over Smooth Topography
Author(s) -
Ag Yehuda,
Pelinovsky Efim,
Sheremet Alexandru
Publication year - 1998
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00085
Subject(s) - cnoidal wave , nonlinear system , harmonics , harmonic , korteweg–de vries equation , physics , classical mechanics , stokes wave , mathematical analysis , mathematics , mechanics , optics , wave propagation , breaking wave , acoustics , quantum mechanics , voltage
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 cnoidal 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 depth, a simple analytical model based on a two‐harmonic representation of the cnoidal wave demonstrates the main features of the process of disintegration of the cnoidal structure of the nonlinear wave. Numerical simulations of the interaction of several harmonics confirm the analytical conclusions.