= Anelastic approximation
{title2=$\nabla\cdot(\rho_0\mathbf u)=0$}
An anelastic model filters acoustic density fluctuations while retaining a prescribed stratified reference <mass density>. For $\rho_0\propto e^{-z/H}$, continuity is $u_x+v_y+w_z-w/H=0$. Momentum and buoyancy conventions must be consistent: with reduced pressure $\Phi=p'/\rho_0$, a pressure acceleration $-\nabla\Phi$ contains a vertical density-gradient term that is absent from $-\rho_0^{-1}\nabla p'$. The two expressions cannot be interchanged when deriving waves in a stratified atmosphere.
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