http://arxiv.org/abs/1712.02127
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.
M. Liu and L. Li
Thu, 7 Dec 17
72/72
Comments: 14 pages, 4 figures, 2 tables