Two-dimensional turbulence on a sphere
Two-dimensional turbulence on a sphere
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球体上的二维湍流
DOI：
10.1017/jfm.2021.1130
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发表时间：
2022
影响因子：
3.7
通讯作者：
A. Nordmark
中科院分区：
文献类型：
--
作者：
E. Lindborg;A. Nordmark
摘要 继 Fjørtoft（Tellus，第 5 卷，1953 年，第 225-230 页）之后，我们对球体上的非发散流进行了光谱分析。结果表明，球谐能谱在球谐系统极轴旋转的情况下保持不变，并认为各向同性的约束不会简化分析，而只能排除低阶模态。推导了谱能量方程，结果表明粘性项的形式与以前的研究中给出的形式略有不同。 Fjørtoft（Tellus，第 5 卷，1953 年，第 225-230 页）在能量传递仅限于三种模式的情况下导出的涉及三元模态内能量传递的关系是在一般条件下导出的。这些关系表明，三元组中有两种类型的相互作用。第一种类型是中间模式充当其他两种模式的源，第二种类型是中间模式充当接收器。 Gkioulekas & Tung (J. Fluid Mech., vol. 576, 2007, pp. 173–189) 在窄带强迫和平稳性假设下在傅里叶空间中导出的指示级联方向的不等式在球谐空间中在第一类相互作用占主导地位的假设下导出。根据推导的方程讨论了 Kraichnan 的双级联理论（Phys. Fluids，第 10 卷，1967 年，第 1417-1423 页），并假设在有限尺度分离的流动中，两个级联可能在很大程度上由相同的三元相互作用产生。最后，我们得出结论，球面几何是通过模拟探索二维湍流的最佳试验场。
Abstract Following Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) we undertake a spectral analysis of a non-divergent flow on a sphere. It is shown that the spherical harmonic energy spectrum is invariant under rotations of the polar axis of the spherical harmonic system and argued that a constraint of isotropy would not simplify the analysis but only exclude low-order modes. The spectral energy equation is derived and it is shown that the viscous term has a slightly different form than given in previous studies. The relations involving energy transfer within a triad of modes, which Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) derived under the condition that energy transfer is restricted to three modes, are derived under general conditions. These relations show that there are two types of interaction within a triad. The first type is where the middle mode acts as a source for the two other modes and the second type is where it acts as a sink. The inequality indicating cascade directions which was derived by Gkioulekas & Tung (J. Fluid Mech., vol. 576, 2007, pp. 173–189) in Fourier space under the assumptions of narrow band forcing and stationarity is derived in spherical harmonic space under the assumption of dominance of first type interactions. The double cascade theory of Kraichnan (Phys. Fluids, vol. 10, 1967, pp. 1417–1423) is discussed in the light of the derived equations and it is hypothesised that in flows with limited scale separation the two cascades may, to a large extent, be produced by the same triad interactions. Finally, we conclude that the spherical geometry is the optimal test ground for exploration of two-dimensional turbulence by means of simulations.
影响因子：
3.7
作者：
Burgess B
通讯作者：
Burgess B