论文标题
图书馆驱动的惯性波和球形壳中的平均纬向流
Libration-driven inertial waves and mean zonal flows in spherical shells
论文作者
论文摘要
由于引力与轨道伴侣的重力相互作用，我们的太阳系中的几个行星体经历了强迫库，从而导致其金属液态核心或地下海洋的复杂流体运动。在这项研究中，我们在数值上研究了纵向图的球形壳中的流动。当库频率小于旋转频率的两倍，并且库幅度很小时，我们将重点放在几个剪切层的Ekman数字依赖性上。时间相关的流动主要由由于Ekman泵送奇异性而激发的临界纬度的惯性波，形成了锥形剪切层。特别是，以前的理论研究提出了从内部边界的临界纬度产生的锥形剪切层的不同尺度。我们的数值结果有利于速度振幅缩放$ \ MATHRM {o}（\ VAREPSILON E^{1/12}）$由LeDizès\＆Le Le Bars（2017）预测到缩放$ \ Mathrm {O}（O}（O}（\ Varepsilon E^{1/6}），在我们的计算中，不够小，无法固定这个缩放。边界层中的非线性相互作用驱动带有几个地质剪切的平均层状流动。 Our numerical results show that geostrophic shears associated with the critical latitudes at the inner and outer boundaries exhibit the same scalings, i.e. an amplitude of $\mathrm{O}(\varepsilon^2 E^{-1/10})$ over a width of $\mathrm{O}(E^{1/5})$.除了与临界纬度相关的地质剪切外，我们的数值结果表明，惯性波的反射可以诱导地质剪切，幅度为$ \ mathrm {o}（\ varepsilon^2 e^2 e^{ - 1/6}）$，而不是$ \ mathrm mathrm mathrm {o^o^a^o^of $ \ mathrm {^o}（
Several planetary bodies in our solar system undergo a forced libration owing to gravitational interactions with their orbital companions, leading to complex fluid motions in their metallic liquid cores or subsurface oceans. In this study, we numerically investigate flows in longitudinally librating spherical shells. We focus on the Ekman number dependencies of several shear layers when the libration frequency is less than twice of the rotation frequency and the libration amplitude is small. Time-dependent flows mainly consist of inertial waves excited at the critical latitudes due to the Ekman pumping singularities, forming conical shear layers. In particular, previous theoretical studies have proposed different scalings for the conical shear layers spawned from the critical latitudes at the inner boundary. Our numerical results favor the velocity amplitude scaling $\mathrm{O}(\varepsilon E^{1/12})$ predicted by Le Dizès \& Le Bars (2017) over the scaling $\mathrm{O}(\varepsilon E^{1/6})$ initially proposed by Kerswell (1995), though the Ekman numbers in our calculations are not sufficiently small to pin down this scaling. Non-linear interactions in the boundary layers drive a mean zonal flow with several geostrophic shears. Our numerical results show that geostrophic shears associated with the critical latitudes at the inner and outer boundaries exhibit the same scalings, i.e. an amplitude of $\mathrm{O}(\varepsilon^2 E^{-1/10})$ over a width of $\mathrm{O}(E^{1/5})$. Apart from the geostrophic shear associated with the critical latitude, our numerical results show that the reflection of inertial waves can induce a geostrophic shear with an amplitude of $\mathrm{O}(\varepsilon^2 E^{-1/6})$ over a width of $\mathrm{O}(E^{1/3})$.
