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In fluid dynamics, the Boussinesq approximation , named for Joseph Valentin Boussinesq] is used in the field of buoyancy-driven flow. It ignores density differences except where they appear in terms multiplied by g, the acceleration due to gravity. The essence of the Boussinesq approximation is that the difference in inertia is negligible but gravity is sufficiently strong to make the specific weight appreciably different between the two fluids. Sound waves are impossible/neglected when the Boussinesq approximation is used since sound waves move via density variations.
Boussinesq flows are common in nature , industry , and the built environment. The approximation is extremely accurate for many such flows, and makes the mathematics and physics simpler.