A Generalization of Lorenz’s Model for the Predictability of Flows with Many Scales of Motion
A Generalization of Lorenz’s Model for the Predictability of Flows with Many Scales of Motion
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DOI：
10.1175/2007jas2449.1
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发表时间：
2008-03
影响因子：
3.1
通讯作者：
R. Rotunno;C. Snyder
中科院分区：
文献类型：
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作者：
R. Rotunno;C. Snyder
在一篇开创性的论文中，e·n·洛伦兹提出，具有许多运动尺度的流动，其中较小尺度的误差会扩散到较大尺度，并且误差加倍时间随着尺度的减小而减少，这些流动具有有限范围的可预测性。虽然洛伦兹有限可预测性理论被广泛理解和接受，但该理论所依据的模型却不那么为人所理解和接受。对该模式的主要反对意见是，它基于二维涡度方程（2DV），同时强调使用大气天气尺度上具有“5/3”能谱的基本湍流的结果，而不是使用理论和观测上更一致的“3”能谱的结果。目前的工作推广了洛伦兹模型，使其可以应用于表面准地转方程（sqg），这些方程在数学上与2DV非常相似，但已知具有从大尺度强迫降尺度的5/3动能谱。这个广义洛伦兹模型在这里被应用于2DV（3谱）和SQG（5/3谱），分别产生了无限和有限可预测性的流的例子。对这两种模型进行比较分析，可以识别出具有有限可预测性的多尺度流的独特属性。
In a seminal paper, E. N. Lorenz proposed that flows with many scales of motion in which smaller-scale error spreads to larger scales and in which the error-doubling time decreases with decreasing scale have a finite range of predictability. Although the Lorenz theory of limited predictability is widely understood and accepted, the model upon which the theory is based is less so. The primary objection to the model is that it is based on the two-dimensional vorticity equation (2DV) while simultaneously emphasizing results using a basic turbulent flow with a “5/3” energy spectrum in the atmospheric synoptic scale instead of those using a more theoretically and observationally consistent “3” spectrum. The present work generalizes the Lorenz model so that it may apply to the surface quasigeostrophic equations (SQGs), which are mathematically very similar to 2DV but are known to have a 5/3 kinetic energy spectrum downscale from a large-scale forcing. This generalized Lorenz model is applied here to both 2DV (with a 3 spectrum) and SQG (with a 5/3 spectrum), producing examples of flows with unlimited and limited predictability, respectively. Comparative analysis of the two models allows for the identification of the distinctive attributes of a many-scaled flow with limited predictability.