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...

We discuss turbulent dynamics and mixing of a variable-density flow subject to a uniformacceleration field. The flow resulting from initial misalignments of pressure and density gradients is investigated for small to large density ratios, with evidence that the smalldensity ratio flow is described by the Boussinesq approximation. A new shear-layer growth rate is reported. Spectra collapse when ...

In this paper we consider the solution of the enhanced Boussinesq equations of Madsen and Sørensen (Coast.Eng. 18, 1992) by means of residual based discretizations. In particular, we investigate the applicability of upwind and stabilized variants of the Residual Distribution and Galerkin finite element schemes for the simulation of wave propagation and transformation over complex bathymetries. ...

The Oberbeck–Boussinesq approximation is the most commonly employed theoretical scheme for study of natural or mixed convection flows. However, misunderstanding this approximated framework a possibility that may cause emergence paradoxes or, at least, incorrect conclusions. In paper, basic features are briefly recalled and three simple examples where be misused provided. Such misuses lead to er...

In the present paper we complement the work in [2] with presenting the analytical framework for general optimal boundary control problems of the Boussinesq approximation. We prove existence of optimal controls, use results of [6] to prove existence and uniqueness of solutions to state and the adjoint system, and derive first order necessary as well as second order sufficient optimality conditions.

This paper presents the Dual Scattering Channel (DSC) numerical solution of the Navier-Stokes equations for viscous quasi-incompressible flow in the Oberbeck-Boussinesq approximation. The implementation in hexahedral non-orthogonal mesh is outlined. A numerical example illustrates the approach. MSC-classes: 65C20, 65M06, 76D05 Westerham, March 31, 2006

Abstract We consider a general compressible viscous and heat conducting fluid confined between two parallel plates heated from the bottom. The time evolution of is described by Navier–Stokes–Fourier system considered in regime low Mach Froude numbers suitably interrelated. Surprisingly differently to case Neumann boundary conditions for temperature, asymptotic limit identified as Oberbeck–Bouss...

This paper presents the Dual Scattering Channel (DSC) numerical solution of the Navier-Stokes equations for viscous quasi-incompressible flow in the Oberbeck-Boussinesq approximation. The implementation in hexahedral non-orthogonal mesh is outlined. A numerical example illustrates the approach. MSC-classes: 65C20, 65M06, 76D05 Westerham on October 05, 2005