Precession Effects on Liquid Planetary Core

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.