  Motivated by the desire to understand the rich dynamics of precessionally
driven flow in the liquid planetary core, we investigate, through numerical
simulations, the precessing fluid motion in a rotating cylindrical annulus
which possesses slow precession simultaneously. The same problem has been
studied extensively in cylinders where the precessing flow is characterized by
three key parameters: the Ekman number $E$, the Poincar$\acute{\mathrm e}$
number $Po$ and the radius-height aspect ratio $\Gamma$. While in an annulus,
there is another parameter, the inner-radius-height aspect ratio $\Upsilon$,
which also plays an important role in controlling the structure and evolution
of the flow. By decomposing the nonlinear solution into a set of inertial
modes, we demonstrate the properties of both weakly and moderately precessing
flows. It is found that, when the precessional force is weak, the flow is
stable with a constant amplitude of kinetic energy. As the precessional force
increases, our simulation suggests that the nonlinear interaction between the
boundary effects and the inertial modes can trigger more turbulence,
introducing a transitional regime of rich dynamics to disordered flow. The
inertial mode $\bm u_{111}$, followed by $\bm u_{113}$ or $\bm u_{112}$, always
dominates the precessing flow when $0.001\leq Po\leq 0.05$, ranging from weak
to moderate precession. Moreover, the precessing flow in an annulus shows more
stability than in a cylinder which is likely to be caused by the effect of the
inner boundary that restricts the growth of resonant and non-resonant inertial
modes. Furthermore, the mechanism of triadic resonance is not found in the
transitional regime from the laminar to disordered flow.
