Dissipative Boussinesq equations

Dissipative Boussinesq equations

The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated nu...

Dissipative Boussinesq system of equations in the Bénard-Marangoni phenomenon.

By using the long-wave approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a BénardMarangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it can be interpreted as a dissipative generalization of the usual Boussinesq system of equations. As a particular case, a strictly dissipative version of the Boussines...

Derivation of dissipative Boussinesq equations using the Dirichlet-to-Neumann operator approach

The water wave theory traditionally assumes the fluid to be perfect, thus neglecting all effects of the viscosity. However, the explanation of several experimental data sets requires the explicit inclusion of dissipative effects. In order to meet these practical problems, the theory of visco-potential flows has been developed (see P.-F. Liu & A. Orfila [42] and D. Dutykh & F. Dias [25]). Then, ...

The 2D Incompressible Boussinesq Equations

Long-time Asymptotic Behavior of Two-dimensional Dissipative Boussinesq Systems

In this article, we consider the two-dimensional dissipative Boussinesq systems which model surface waves in three space dimensions. The long time asymptotics of the solutions for a large class of such systems are obtained rigorously for small initial data.