AI 中文总结
该研究针对地球物理流动的大涡模拟，开发改进型动态混合亚格子尺度模型，通过调节结构-功能平衡，在受迫二维和β平面湍流中实现了更优的能量传递平衡与模拟精度。
AI 中文摘要
地球物理湍流的大涡模拟（LES）所用的亚格子尺度（SGS）模型通常需要在耗散正则化与反向散射（即能量从未解析尺度向上解析尺度的传递）之间取得平衡。动态混合模型（DMMs）结合了功能涡粘性与结构闭合，其系数通过最小二乘估计得到，对Germano恒等式误差（GIE）而言是最优的。我们发现，经典DMM的最小二乘估计可能受结构分量主导，从而限制了功能分量的耗散正则化作用。为解决这一局限，我们开发了一种改进的基于Gram的框架，以构建全新的参数化族，包含完全耦合、顺序式及完全解耦的DMMs，具备可调节的结构-功能平衡。我们采用理想化受迫二维和β平面湍流框架，结合Leith模型与四阶非线性梯度模型，对所得闭合进行评估。先验结果显示，结构主导型模型与理想SGS强迫高度一致，且能准确重现局部SGS能量交换，包括反向散射。但在后验测试中，结构主导型模型呈现类噪声伪影，存在高波数谱偏差，表明净耗散不足。相比之下，顺序式DMM先确定功能分量，再由结构分量修正，既保留了大部分先验结构精度，又改善了后验涡度场、谱及域平均诊断结果。SGS能量与拟能传递的谱分析表明，该顺序式DMM在大于强迫尺度的尺度上允许反向散射，在更小尺度上增强耗散，从而提升了瞬时结构保真度与长期精度之间的平衡。
英文摘要
Subgrid-scale (SGS) models for large-eddy simulations (LES) of geophysical turbulence typically need to balance dissipative regularization with backscatter, the upscale transfer of energy from unresolved to resolved scales. Dynamic mixed models (DMMs) combine functional eddy viscosity and structural closures through dynamically estimated coefficients that are least-squares optimal with respect to the Germano identity error (GIE). We show that this classical DMM least-squares estimation can be dominated by the structural component, thereby limiting the functional component's dissipative regularizing role. To address this limitation, we develop a modified Gram-based framework to construct a novel parametric family of fully-coupled, sequential, and fully-decoupled DMMs with tunable structural-functional balance. We evaluate the resulting closures using an idealized forced two-dimensional and $β$-plane turbulence framework with the Leith model and the fourth-order nonlinear gradient model. A priori results show that structurally-dominated models achieve strong agreement with the ideal SGS forcing and accurately reproduce local SGS energy exchange, including backscatter. However, in a posteriori tests, structurally dominated models exhibit noise-like artifacts with high-wavenumber spectral deviations, indicating insufficient net dissipation. In contrast, the sequential DMM in which the functional component is determined first and then corrected by the structural component retains much of the a priori structural accuracy while improving the a posteriori vorticity fields, spectra, and domain-averaged diagnostics. Spectral SGS energy and enstrophy-transfer analyses show that this sequential DMM permits backscatter at scales larger than the forcing scale with enhanced dissipation at smaller scales, thereby improving the balance between instantaneous structural fidelity and long-term accuracy.
Comments26 pages, 11 figures, 5 tables
