# Boussinesq approximation

From AMS Glossary

## Boussinesq approximation

An approximation to the dynamical equations of motion whereby density is assumed to be constant except in the buoyancy term, -

*g*ρ′, of the vertical velocity equation, where*g*is the gravitational acceleration and ρ′ is the density deviation.The approximation is reasonable if the vertical extent of the dynamics being considered is much smaller than the density scale height—the height over which the density changes by a factor

*e*. It is generally applicable to most oceanographic circumstances. If a system does not satisfy the Boussinesq approximation it is said to be non-Boussinesq.