A Boussinesq system for two-way propagation of interfacial waves

Hai Yen Nguyen (1) , Frédéric Dias (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

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. However, when the square of the depth ratio is close to the density ratio, the coefficients of the quadratic nonlinearities become small and cubic nonlinearities must be considered. The propagation as well as the collision of solitary waves and/or fronts is studied numerically.

Mots clés: Boussinesq system; solitary waves

Domaines: Mécanique des fluides [physics.class-ph]

Hai Yen Nguyen, Frédéric Dias. A Boussinesq system for two-way propagation of interfacial waves. 2007. ⟨hal-00171606⟩