= Lagrangian fluid displacement
{c}
{title2=$\boldsymbol\xi$}
The Lagrangian fluid displacement $\boldsymbol\xi$ compares neighbouring fluid trajectories. Linear <velocity> <perturbations> about a steady flow $\mathbf U$ obey $\delta\mathbf u=(\partial_t+\mathbf U\cdot\nabla)\boldsymbol\xi-(\boldsymbol\xi\cdot\nabla)\mathbf U$. For a background scalar $f_0$, its material <perturbation> is $\Delta f=\delta f+\boldsymbol\xi\cdot\nabla f_0$. In an axisymmetric <normal mode> about cylindrical rotation, the radial and vertical <velocities> are $-i\omega\xi_r$ and $-i\omega\xi_z$. The displacement of a <free surface> is needed to impose the <Lagrangian pressure perturbation> condition.
// Target: astrophysics.bigb
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