压缩贝塔效应：行星中纬向风的来源？
The compressional beta effect: a source of zonal winds in planets?
摘要：
像木星和土星这样的巨大行星在其表面上具有强烈的纬向风模式。虽然在过去的几十年里，已经提出了几种不同的机制来驱动这些喷流，但纬向风的起源仍然不清楚。在这里，我们探讨了行星旋转与对流流体的压缩和膨胀的相互作用可以通过压缩莱茵型机制驱动多个深纬向喷流的可能性，正如Ingersoll和Pollard（1982）最初提出的那样。在一定的限制，这种深层机制被证明是数学上类似于经典的莱茵河机制可能在云的水平。预计射流将出现在压缩莱茵长度$l_R = (2 Ω\langle H_ρ^{-1} \rangle v_{jet}^{-1} )^{-1/2}$上，其中$Ω$是角速度，$\langle H_ρ^{-1} \rangle$是平均逆密度标度高度，$v_{jet}$是典型的射流速度。使用滞弹性近似的二维数值模拟表明，这种机制鲁棒地产生预测宽度的射流，并且它通常在比$O(l_R)$更深的系统中占主导地位。观察到潜在的涡阶梯自发形成，通常伴随着不稳定分层浮力阶梯。该机制仅在大旋转速率下运行，超过了球壳深对流三维模拟中通常达到的旋转速率。应用于木星和土星，压缩莱茵尺度合理地符合现有的观测。有趣的是，即使是弱的垂直密度变化，如那些在地球核心可以引起大量的射流，导致根本不同的流动结构比预测的Boussinesq模型通常在这种情况下使用。
英文摘要：
Giant planets like Jupiter and Saturn feature strong zonal wind patterns on their surfaces. Although several different mechanisms that may drive these jets have been proposed over the last decades, the origin of the zonal winds is still unclear. Here, we explore the possibility that the interplay of planetary rotation with the compression and expansion of the convecting fluid can drive multiple deep zonal jets by a compressional Rhines-type mechanism, as originally proposed by Ingersoll and Pollard (1982). In a certain limit, this deep mechanism is shown to be mathematically analogous to the classical Rhines mechanism possibly operating at cloud level. Jets are predicted to occur on a compressional Rhines length $l_R = (2 Ω\langle H_ρ^{-1} \rangle v_{jet}^{-1} )^{-1/2}$, where $Ω$ is the angular velocity, $\langle H_ρ^{-1} \rangle$ is the mean inverse density scale height and $v_{jet}$ is the typical jet velocity. Two-dimensional numerical simulations using the anelastic approximation reveal that this mechanism robustly generates jets of the predicted width, and that it typically dominates the dynamics in systems deeper than $O(l_R)$. Potential vorticity staircases are observed to form spontaneously and are typically accompanied by unstably stratified buoyancy staircases. The mechanism only operates at large rotation rates, exceeding those typically reached in three-dimensional simulations of deep convection in spherical shells. Applied to Jupiter and Saturn, the compressional Rhines scaling reasonably fits the available observations. Interestingly, even weak vertical density variations such as those in the Earth core can give rise to a large number of jets, leading to fundamentally different flow structures than predicted by the Boussinesq models typically used in this context.
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