  For hot spots compressed at constant velocity, we give a hydrodynamic
stability criterion that describes the expected energy behavior of non-radial
hydrodynamic motion for different classes of trajectories (in $\rho R$ --- $T$
space). For a given compression velocity, this criterion depends on $\rho R$,
$T$, and $\mathrm{d}T/\mathrm{d}(\rho R)$ (the trajectory slope), and applies
point-wise, so that the expected behavior can be determined instantaneously
along the trajectory. Among the classes of trajectories are those where the
hydromotion is guaranteed to decrease, and those where the hydromotion is
bounded by a saturated value. We calculate this saturated value, and find the
compression velocities for which hydromotion may be a substantial fraction of
hot-spot energy at burn time. The Lindl "attractor" trajectory (Lindl, 1995) is
shown to experience non-radial hydrodynamic energy that grows towards this
saturated state. Comparing the saturation value to available detailed 3D
simulation results, we find that the fluctuating velocities in these
simulations reach substantial fractions of the saturated value.
