QG和漂移turbulence中的三重级联行为和纬向喷流的产生
Triple cascade behaviour in QG and drift turbulence and generation of zonal jets
摘要：
本文在CHM模型下研究了准地转湍流和等离子体漂移湍流。我们从理论上和数值模拟上重点关注{ \em纬向涡度}的守恒及其在纬向急流形成中的作用。在\cite{perm,BNZ_invariant}中首次对大尺度湍流和各向异性湍流这两种特殊情况下的平流层不变量进行了预测。论文\cite{perm,BNZ_invariant}还预测，三个不变量，能量，拟能和zonostrophy，将各向异性级联到不相交的部门在$k$ -空间，使能量级联被“推”到大尺度的纬向尺度。在本文中，我们考虑的尺度远小于Rossby变形半径和推广的Fjørtoft参数的\cite{perm,BNZ_invariant}找到在这种情况下的三个级联的方向。我们第一次用数值方法证明了CHM模式的纬向涡度是很好的守恒的，并且证明了如果非线性足够弱，能量、涡度拟能和纬向涡度级联可以用Fjørtoft参数来描述。此外，数值计算中我们观察到，臭氧层在后期的保守性令人惊讶地好，即使初始非线性很强，三级级联的图片是相当准确的。
英文摘要：
We study quasi-geostrophic turbulence and plasma drift turbulence within the Charney-Hasegawa-Mima (CHM) model. We focus, theoretically and using numerical simulations, on conservation of {\em zonostrophy} and on its role in the formation of the zonal jets. The zonostrophy invariant was first predicted in \cite{perm,BNZ_invariant} in two special cases -- large-scale turbulence and anisotropic turbulence. Papers \cite{perm,BNZ_invariant} also predicted that the three invariants, energy, enstrophy and zonostrophy, will cascade anisotropically into non-intersecting sectors in the $k$-space, so that the energy cascade is "pushed" into the large-scale zonal scales. In the present paper, we consider the scales much less than the Rossby deformation radius and generalise the Fjørtoft argument of \cite{perm,BNZ_invariant} to find the directions of the three cascades in this case. For the first time, we demonstrate numerically that zonostrophy is well conserved by the CHM model, and that the energy, enstrophy and zonostrophy cascade as prescribed by the Fjørtoft argument if the nonlinearity is sufficiently weak. Moreover, numerically we observe that zonostrophy is conserved surprisingly well at late times and the triple-cascade picture is rather accurate even if the initial nonlinearity is strong.
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