Abstract

We apply the Lie-group formalism and the nonclassical method due to Bluman and Cole to deduce symmetries of the generalized Boussinesq equation, which has the classical Boussinesq equation as an special case. We study the class of functions f(u) for which this equation admit either the classical or the nonclassical method. The reductions obtained are derived. Some new exact solutions can be der...

[1] A time domain Boussinesq model for nearshore hydrodynamics is improved to obtain the conservation of vertical vorticity correct to second order and extended for use on an open coast using longshore periodic boundary conditions. The model is utilized to simulate surface waves and longshore currents under laboratory and field conditions. Satisfactory agreement is found between numerical resul...

settings for stabilization of nonlinear parabolic system with a Riccati-based strategy. Application to Navier-Stokes and Boussinesq equations with Neumann or Dirichlet control Mehdi Badra To cite this version: Mehdi Badra. Abstract settings for stabilization of nonlinear parabolic system with a Riccatibased strategy. Application to Navier-Stokes and Boussinesq equations with Neumann or Dirichle...

The general form of the cubic Boussinesq-type equation is considered. In special cases, this reduced to three different versions Boussinesq equations and also generalized modified equation. Using slowly varying envelope approximation perturbation reduction method transformed coupled nonlinear Schrodinger two-component solitary wave solution obtained. Explicit analytical expressions for shape pa...

The figures on the left show effect of Prandtl number (Pr) Rayleigh-B\'enard problem with Boussinesq conditions, for same Grashof ${10}^{9}$. Top: Pr = 12.73; bottom, ${10}^{\ensuremath{-}4}$. plot right shows that low molecular yields an inversely varying turbulent number; is, flow behaves effectively as a high fluid. data are non-Boussinesq conditions. qualitative is case well, but dependence...

This paper discusses flow control of fluids through porous media, specifically related to its application in petroleum science. The flow of fluids is described by the Boussinesq equation with mixed boundary conditions; a Neumann boundary condition describes no flow at the outer boundary of the porous media and a nonlinear boundary condition describes the interaction between the porous media and...

Many properties of emulsions arise from interfacial rheology, but a theoretical understanding of the effect of interfacial viscosities on droplet dynamics is lacking. Here we report such a theory, relating to isolated spherical drops in a Poiseuille flow. Stokes flow is assumed in the bulk phases, and a jump in hydrodynamic stress at the interface is balanced by Marangoni and surface viscous fo...