Boussinesq equations
= Boussinesq equations
{c}
The inviscid Boussinesq equations for velocity $\mathbf u$, buoyancy $b$, and reference density $\rho_0$ are
$$
\frac{D\mathbf u}{Dt}
=-\rho_0^{-1}\nabla p+b\widehat{\mathbf z},
\qquad
\nabla\cdot\mathbf u=0,
$$
together with an advection or advection–diffusion equation for $b$.