Hydrodynamic instability is one of the primary sources of degrading the fusion yields in inertial confinement fusion (ICF) experiments. The presence of non-uniformities during the hot spot formation leads to dominant experimental signatures of implosion asymmetries. The physical mechanism of how hydrodynamic instabilities manifest themselves in experimental observable plays an important role to interpret three-dimensional (3-D) effects on ICF experimental data.

In the first part of the thesis, we describe the development of a 3-D radiation-hydrodynamic Eulerian spherical moving-mesh parallel code DEC3D to model the deceleration-phase Rayleigh-Taylor instability. The new code implements advanced modern numerical methods including the high-resolution shock-capturing technique the piecewise parabolic method for hydrodynamics, the macro-zoning technique to treat small time-step problems of the spherical mesh, and the integration of HYPRE to solve the implicit multi-group radiation diffusion. A single-mode and multi-mode simulation database was established to study the relations between 3-D hydrodynamic effects and implosion asymmetries.

In the second part of the thesis, two comprehensive physical models were developed: to explain the effects of the residual kinetic energy on the degradation of fusion yields and hot-spot pressures, and the property of larger hot-spot volumes for low modes, and to explain the effects of 3-D hot-spot flow asymmetries on the variations of ion-temperature measurements. An analytical method of velocity variance decomposition was developed to infer the minimum ion temperatures and explain the physical mechanism of larger apparent ion temperatures than the true thermal ion temperatures.