Boussinesq approximation (buoyancy)

The Boussinesq approximation (after Joseph Boussinesq ) is a simplification of the hydrodynamic Navier -Stokes equations. They modeled gravity variations flows where density variations can be neglected ( unless they are multiplied by the gravitational acceleration, see below) and not show up to large temperature gradients.

Boussinesqe currents are relatively common in nature (for example, fronts, ocean currents and katabatic winds ), industry ( dispersion dense gases ) and houses ( Natural ventilation, central heating).

The approximation is very accurate for many such currents and simplifies the mathematics and physics of the problem significantly. The advantage is that there is a problem with multiple streams only a density must be taken into account, because the difference of the densities neglected, and the ratio of the densities is approximated by one.

A dimensional analysis shows that under these circumstances, the gravity should be received only as a reduced gravity g ':

.

Here, it is immaterial in the denominator, which is selected of the two densities, since they are almost identical.