= Adiabatic fluid perturbation
{title2=$\Delta s=0,\quad\Delta p=\gamma p\,\Delta\rho/\rho$}
An adiabatic fluid perturbation preserves the <specific entropy> of each displaced parcel. For a <perfect gas>, <mass conservation> gives $\Delta\rho=-\rho\nabla\cdot\boldsymbol\xi$ and the <adiabatic equation of state> gives $\Delta p=\gamma p\Delta\rho/\rho$. The corresponding <Eulerian perturbation of a fluid variable> is $\delta p=-\gamma p\nabla\cdot\boldsymbol\xi-\boldsymbol\xi\cdot\nabla p$. An isothermal equilibrium may still have adiabatic perturbations, because the thermodynamic constraint on displaced parcels differs from the equilibrium temperature profile.
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