土星北极喷流形成和平衡的基于统计状态动力学的理论
Statistical state dynamics based theory for the formation and equilibration of Saturn's north polar jet
摘要：
在大气湍流中，具有大部分流动动能的相干射流是常见的。在气态行星中，这些喷流由小尺度对流激发的非相干湍流维持。大尺度相干波有时会与喷流共存，一个突出的例子是土星的六边形北极喷流（NPJ）。形成和维持这种动荡状态的机制仍然难以捉摸。湍流的相干行星尺度分量产生，并通过与非相干小尺度湍流分量的相互作用来维持。通过采用统计状态动力学（SSD）模型，获得了理论上的理解射流/波/湍流共存制度的动力学。在这里，一个二阶封闭实现的两层β-平面SSD是用来开发一个理论，占的结构和动力学的NPJ。在弱喷流阻尼极限的SSD平衡的渐近分析预测与NPJ观测一致的通用喷流结构。这个渐近理论还预测了突出射流扰动的波数（6）。用该模型对射流/波/湍流区动力学进行的分析表明，射流的形成受$β$的有效值控制;获得了与观测相符的该参数的所需值。由于这是一个强大的预测，它被视为一个间接的观察，深极向倾斜的稳定层下面的NPJ。所需的斜率是从NPJ结构的观测中获得的，维持射流所需的小尺度湍流激发也是如此。观测到的喷流结构，然后预测的理论是波六扰动。这种波，这是确定与平衡射流的最不稳定的模式，被证明是主要负责与所观察到的结构和振幅的射流平衡。
英文摘要：
Coherent jets with most of the kinetic energy of the flow are common in atmospheric turbulence. In the gaseous planets these jets are maintained by incoherent turbulence excited by small-scale convection. Large-scale coherent waves are sometimes observed to coexist with the jets; a prominent example is Saturn's hexagonal North polar jet (NPJ). The mechanism responsible for forming and maintaining such a turbulent state remains elusive. The coherent planetary-scale component of the turbulence arises and is maintained by interaction with the incoherent small-scale turbulence component. Theoretical understanding of the dynamics of the jet/wave/turbulence coexistence regime is gained by employing a statistical state dynamics (SSD) model. Here, a second-order closure implementation of a two-layer beta-plane SSD is used to develop a theory that accounts for the structure and dynamics of the NPJ. Asymptotic analysis of the SSD equilibrium in the weak jet damping limit predicts a universal jet structure in agreement with NPJ observations. This asymptotic theory also predicts the wavenumber (six) of the prominent jet perturbation. Analysis with this model of the jet/wave/turbulence regime dynamics reveals that jet formation is controlled by the effective value of $β$; the required value of this parameter for correspondence with observation is obtained. As this is a robust prediction it is taken as an indirect observation of a deep poleward sloping stable layer beneath the NPJ. The slope required is obtained from observations of NPJ structure as is the small-scale turbulence excitation required to maintain the jet. The observed jet structure is then predicted by the theory as is the wave-six disturbance. This wave, which is identified with the least stable mode of the equilibrated jet, is shown to be primarily responsible for equilibrating the jet with the observed structure and amplitude.
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