Bulk hydrodynamic stability and turbulent saturation in compressing hot spots

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.