Simple Form:

This approximation is used to treat a compressible fluid as an incompressible one provided two conditions are met.

• density variations over some scale in the fluid are small (meaning usually less than 20%)
• the flow has a low mach number (usually less than 0.3)

Under these conditions the buoyancy termm in the equation of motion is what matters the most.

For the case of temperature this looks like:



Which means the boussinesq appromation requires:





Complex Form: