Implementation of the LANS-α turbulence model in a primitive equation ocean model
Implementation of the LANS-α turbulence model in a primitive equation ocean model
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LANS-α 湍流模型在原始方程海洋模型中的实现
DOI：
10.1016/j.jcp.2008.02.018
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
B. Wingate
中科院分区：
文献类型：
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作者：
M. Hecht;Darryl D. Holm;M. Petersen;B. Wingate
本文介绍了原始方程海洋模型中拉格朗日平均纳维-斯托克斯-α (LANS-α) 湍流模型的首次数值实现和测试。我们使用的海洋模型是洛斯阿拉莫斯平行海洋计划（POP）；我们将 POP 和 LANS-α 的实现称为 POP-α。提出了 POP-α 的两个版本：完整的 POP-α 算法源自 LANS-α 原方程，但需要嵌套迭代，这使得实际模拟速度太慢；提出了一种简化的POP-α算法，该算法没有嵌套迭代，并且比完整算法快两到三倍。简化算法并不是从 LANS-α 模型方程的正式推导得出的。尽管如此，根据全局平均温度和动能、温度和速度场快照以及温度方差来判断，简化算法的模拟几乎与完整算法相同。两种 POP-α 算法都可以比标准 POP 更长的时间步长稳定运行。在理想化的测试问题中对完整和简化的 POP-α 算法的实现进行了比较，该问题捕获了南极绕极流的某些方面，斜压不稳定是该问题的突出问题。两种 POP-α 算法都会生成类似于标准 POP 的更高分辨率模拟的统计数据。线性稳定性分析表明，完整的 POP-α 算法和简化的 POP-α 算法都受益于 LANS-α 方程考虑小尺度对大尺度影响的方式。两种算法（1）都是稳定的； (2) 有效罗斯贝变形半径大于未建模方程的变形半径； (3) 在高波数下，相对于未建模的波，降低建模的罗斯贝波和重力波的传播速度。
This paper presents the first numerical implementation and tests of the Lagrangian-averaged Navier–Stokes-alpha (LANS-α) turbulence model in a primitive equation ocean model. The ocean model with which we work is the Los Alamos Parallel Ocean Program (POP); we refer to POP and our implementation of LANS-α as POP-α. Two versions of POP-α are presented: the full POP-α algorithm is derived from the LANS-α primitive equations, but requires a nested iteration that makes it too slow for practical simulations; a reduced POP-α algorithm is proposed, which lacks the nested iteration and is two to three times faster than the full algorithm. The reduced algorithm does not follow from a formal derivation of the LANS-α model equations. Despite this, simulations of the reduced algorithm are nearly identical to the full algorithm, as judged by globally averaged temperature and kinetic energy, snapshots of temperature and velocity fields, and temperature variance. Both POP-α algorithms can run stably with longer timesteps than standard POP. Comparison of implementations of full and reduced POP-α algorithms are made within an idealized test problem that captures some aspects of the Antarctic Circumpolar Current, a problem in which baroclinic instability is prominent. Both POP-α algorithms produce statistics that resemble higher-resolution simulations of standard POP. A linear stability analysis shows that both the full and reduced POP-α algorithms benefit from the way the LANS-α equations take into account the effects of the small scales on the large. Both algorithms (1) are stable; (2) have an effective Rossby deformation radius that is larger than the deformation radius of the unmodeled equations; and (3) reduce the propagation speeds of the modeled Rossby and gravity waves relative to the unmodeled waves at high wave numbers.