Linearized Boussinesq equations
= Linearized Boussinesq equations
{c}
The linearized Boussinesq equations describe small velocity, pressure, and buoyancy perturbations about a motionless, stably stratified reference state. With <kinematic viscosity> $\nu$, <mass diffusivity> $\kappa$, and <buoyancy frequency> $N$, they are
$$
(\partial_t-\nu\nabla^2)\mathbf u=-\frac1{\rho_0}\nabla p+b\mathbf e_z,
\qquad
(\partial_t-\kappa\nabla^2)b=-N^2w,
\qquad
\nabla\mathbin\cdot\mathbf u=0.
$$