It is typical for low-resolution simulations of the ocean to miss not only small- but also large-scale patterns of the flow dynamics compared with their high-resolution analogues. It is usually attributed to the inability of coarse-grid models to properly reproduce the effects of the unresolved small-scale dynamics on the resolved large scales. In part, the reason for that is that coarse-grid models fail to at least keep the coarse-grid solution within the region of phase space occupied by the true solution (the high-resolution solution projected onto the coarse grid). In this paper we offer a solution to this problem by computing the image point in the phase space restricted to the region of the true flow dynamics. The proposed method shows encouraging results for both low- and high-dimensional phase spaces, it takes a near-zero effort to implement into existing numerical codes and has ample room for further improvements.

与高分辨率模拟物相比，低分辨率海洋模拟不仅会漏掉流动动力学的小规模模式，而且还会错过大范围的流动动力学模式。通常将其归因于粗网格模型无法适当地重现未解析的小规模动力学对已分解的大尺度的影响。部分原因是，粗网格模型无法将粗网格解决方案至少保持在真实解所占据的相空间区域内（将高分辨率解决方案投影到粗网格上）。在本文中，我们通过计算限制在真实流动动力学区域内的相空间中的图像点，为该问题提供了解决方案。所提出的方法对于低维和高维相空间都显示出令人鼓舞的结果，