Motivated by the desire to understand the rich dynamics of precessionally driven flow in a liquid planetary core, we investigate, through numerical simulations, the precessing fluid motion in a ro- taring cylindrical ...Motivated by the desire to understand the rich dynamics of precessionally driven flow in a liquid planetary core, we investigate, through numerical simulations, the precessing fluid motion in a ro- taring cylindrical annulus, which simultaneously possesses slow precession. The same problem has been studied extensively in cylinders, where the precessing flow is characterized by three key parameters： the Ekman number E, the Poincar6 number Po and the radius-height aspect ratio F. While in an annulus, there is another parameter, the inner-radius-height aspect ratio T, 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 be- tween the boundary effects and the inertial modes can trigger more turbulence, introducing a transitional regime of rich dynamics to disordered flow. The inertial mode u111, followed by u113 or u112, always dominates the precessing flow when 0.001 ≤Po ≤ 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 a laminar to disordered flow.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11673052 and 41661164034)the Pilot Project of the Chinese Academy of Sciences(No.XDB18010203)
文摘Motivated by the desire to understand the rich dynamics of precessionally driven flow in a liquid planetary core, we investigate, through numerical simulations, the precessing fluid motion in a ro- taring cylindrical annulus, which simultaneously possesses slow precession. The same problem has been studied extensively in cylinders, where the precessing flow is characterized by three key parameters： the Ekman number E, the Poincar6 number Po and the radius-height aspect ratio F. While in an annulus, there is another parameter, the inner-radius-height aspect ratio T, 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 be- tween the boundary effects and the inertial modes can trigger more turbulence, introducing a transitional regime of rich dynamics to disordered flow. The inertial mode u111, followed by u113 or u112, always dominates the precessing flow when 0.001 ≤Po ≤ 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 a laminar to disordered flow.
