Bousinesq approximation

We then go on to consider three examples of instabilities that arise because of buoyancy and Marangoni effects in a nonisothermal system. This is preceded by a brief discussion of the Bousinesq approximation of the Navier Stokes and thermal energy equations. 

Here, D is the species diffusivity. In deriving the Bousinesq approximation of the Navier-Stokes equations, we must remember that the material properties now depend both on the temperature and the solute concentration, e.g.,... 

We assume that the fluid still satisfies the Bousinesq approximation in that all properties are fixed except for the density, which decreases linearly with increase of the temperature. 

Buoyancy forces due to fluid density variations are accounted for by the linear Bousinesq approximation. 

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See also in sourсe #XX -- [ , ]

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