Our aim is to study the effect of a continuous prescribed density variation on the propagation of ocean waves. More precisely, we derive KdV-type shallow water model equations for unidirectional flows along the Equator from the full governing equations by taking into account a prescribed but arbitrary depth-dependent density distribution. In contrast to the case of constant density, we obtain for each fixed water depth a different model equation for the horizontal component of the velocity field. We derive explicit formulas for traveling wave solutions of these model equations and perform a detailed analysis of the effect of a given density distribution on the depth-structure of the corresponding traveling waves.
|Number of pages||13|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|Publication status||Published - 2019|
- Continuous density stratification
- Equatorial shallow water equations
- Explicit traveling wave solutions