Nonlinear interfacial progressive waves near a boundary in a Boussinesq fluid

A Boussinesq system for two-way propagation of interfacial waves

The theory of internal waves between two layers of immiscible fluids is important both for its applications in oceanography and engineering, and as a source of interesting mathematical model equations that exhibit nonlinearity and dispersion. A Boussinesq system for two-way propagation of interfacial waves in a rigid lid configuration is derived. In most cases, the nonlinearity is quadratic. Ho...

On Nonlinear Water Waves in a Channel

A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves

Fully nonlinear extensions of Boussinesq equations are derived to simulate surface wave propagation in coastal regions. By using the velocity at a certain depth as a dependent variable (Nwogu 1993), the resulting equations have significantly improved linear dispersion properties in intermediate water depths when compared to standard Boussinesq approximations. Since no assumption of small nonlin...

Higher-order nonlinear evolution equation for interfacial waves in a two-layer fluid system.

An alternative type of nonlinear evolution equation is derived that describes interfacial waves in a two-layer fiuid system. The equation presented here is a higher-order version of the Benjamin-Ono (BO) equation. A solitary-wave solution of the equation is obtained by means of a singular perturbation method. The characteristics of the solution are discussed in comparison with those for a highe...

A fully nonlinear Boussinesq model for surface waves

A Boussinesq-type model is derived which is accurate to O(kh) 4 and which retains the full representation of the fluid kinematics in nonlinear surface boundary condition terms, by not assuming weak nonlinearity. The model is derived for a horizontal bottom , and is based explicitly on a fourth-order polynomial representation of the vertical dependence of the velocity potential. In order to achi...