The Boussinesq approximation is a simplification used in fluid dynamics to analyze the behavior of fluid flow, especially in cases where the density differences within the fluid are small compared to the ambient density. It’s named after the French mathematician Joseph Boussinesq. The Boussinesq approximation equation is:

Where:

• $\rho$ is the density of the fluid,
• $\rho 0$ is the reference density,
• $\alpha$ is the coefficient of thermal expansion,
• $T$ is the temperature of the fluid, and
• T0​ is the reference temperature.