# Boussinesq approximation

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## Boussinesq approximation

[′bü·si′nesk ə‚präk·sə′mā·shən]
(fluid mechanics)
The assumption (frequently used in the theory of convection) that the fluid is incompressible except insofar as the thermal expansion produces a buoyancy, represented by a term g α T, where g is the acceleration of gravity, α is the coefficient of thermal expansion, and T is the perturbation temperature.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Internal waves are generated through the interaction between the tidal flow and the topography in a nonuniform fluid layer by solving the Navier-Stokes equation in Boussinesq approximation. Basically the mathematical representation of the internal waves of the ocean is a system of nonlinear partial differential equations (PDEs) .
As it can be seen, the behavior of these simulation results seems to be quite reasonable, thus confirming, qualitatively, the validity of the proposed numerical method, in particular, the concentration of the hot air in the upper part of the nacelle which is due to the decrease in its density, thus confirming the suitability of the adopted Boussinesq approximation.
In this paper, we consider the dynamical models of the ocean or the atmosphere which arise from the density dependent incompressible Navier-Stokes equations by using the so-called Boussinesq approximation .
As explained in detail in , the Boussinesq approximation is valid only when both [alpha] and [beta] are small and have the same order of magnitude.
During hydrogen dispersion, the discrepancy in concentration is one of the main drive forces of flow motion, which give us the basic idea to use an analogue of Boussinesq approximation in thermal convection problems.
Making use of the Boussinesq approximation, the equations that we consider in the present paper are as follows:
According to the Boussinesq approximation these equations get the following expressions (M.E.Eglit et al, 1996)
Variations of all fluid properties other than the variations of density except in so far as they give rise to a body force, are ignored completely (Boussinesq approximation).
In the Eulerian frame, two second-order models have been proposed: an algebraic model, in the spirit of single phase flow, and a Reynolds stress differential model, in which only the equations for the three particle fluctuating velocity correlations [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (i = 1, 2, 3) had to be solved, while the calculation of the shear stresses relied on a Boussinesq approximation which has been justified theoretically and numerically.
Boussinesq approximation is used in oceanography and then [rho] can be take as a constant.
Keywords and Phrases: Free convective flow, radiation, buoyancy, boussinesq approximation, corrugated channel, and incompressible viscous fluid.

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