Numerical Schemes for Stochastic Backscatter in the Inverse Cascade of Quasigeostrophic Turbulence
Numerical Schemes for Stochastic Backscatter in the Inverse Cascade of Quasigeostrophic Turbulence
复制标题
准地转湍流逆级联中随机后向散射的数值方案
DOI：
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发表时间：
2015
影响因子：
1.6
通讯作者：
A. Majda
中科院分区：
文献类型：
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作者：
I. Grooms;Yoonsang Lee;A. Majda
后向散射是湍流中能量从小尺度向大尺度传递的过程，在地球物理湍流的逆能量级联中至关重要，其中能量的净传递是从小尺度向大尺度的。在欠分辨模拟中建模后向散射的一种方法是添加随机强迫项。本研究，设置在理想化的上下文中的两层准地转湍流的逆级联，集中在空间和时间相关性的重要性，在数值随机后向散射计划时，使用低阶有限差分空间离散。最小随机后向散射方案被开发为随机超参数化的简化版本[Grooms和Majda，J. Comput.物理、271，（2014），pp. 78- 98]。这种简化的方案允许详细的数值分析的空间和时间的相关结构的建模后向散射。它的基本属性包括一个本地制定服从有限差分码和非周期域，可调的空间和时间相关性的实施。实验表明，该计划在理想的上下文中的均匀两层准地转湍流的随机后向散射是平滑的粗网格尺度时，使用低阶有限差分格式在反级联制度的需要。相反，时间相关的反向散射是不太重要的实现现实的能量谱。预计这里研究的简化后向散射方案的空间和时间相关性将为更现实的模型中随机后向散射方案的发展提供信息。
Backscatter is the process of energy transfer from small to large scales in turbulence; it is crucially important in the inverse energy cascades of geophysical turbulence, where the net transfer of energy is from small to large scales. One approach to modeling backscatter in underresolved simulations is to add a stochastic forcing term. This study, set in the idealized context of the inverse cascade of two-layer quasigeostrophic turbulence, focuses on the importance of spatial and temporal correlation in numerical stochastic backscatter schemes when used with low-order finite-difference spatial discretizations. A minimal stochastic backscatter scheme is developed as a stripped-down version of stochastic superparameterization [Grooms and Majda, J. Comput. Phys., 271, (2014), pp. 78--98]. This simplified scheme allows detailed numerical analysis of the spatial and temporal correlation structure of the modeled backscatter. Its essential properties include a local formulation amenable to implementation in finite difference codes and nonperiodic domains, and tunable spatial and temporal correlations. Experiments with this scheme in the idealized context of homogeneous two-layer quasigeostrophic turbulence demonstrate the need for stochastic backscatter to be smooth at the coarse grid scale when used with low-order finite-difference schemes in an inverse-cascade regime. In contrast, temporal correlation of the backscatter is much less important for achieving realistic energy spectra. It is expected that the spatial and temporal correlation properties of the simplified backscatter schemes examined here will inform the development of stochastic backscatter schemes in more realistic models.