论文标题
Kolmogorov流：最小的低维模型中的线性稳定性和能量转移
Kolmogorov flow: Linear Stability and Energy Transfers in a minimal low-dimensional model
论文作者
论文摘要
在本文中，我们通过采用盖勒金截断和craya herring基础来得出一个四模型，以用于速度场的分解。之后，我们对模型进行分叉分析。尽管我们的低维模型的模式少于过去模型，但它捕获了Kolmogorov流的主要分叉的基本特征。例如，它重现了超临界干草叉分叉和过去的流动结构的临界雷诺数。我们还展示了从中间尺度到大尺度的能量传输。我们对kolmogorov流进行直接的数值模拟，并表明我们的模型预测与数值模拟非常匹配。
In this paper, we derive a four-mode model for the Kolmogorov flow by employing Galerkin truncation and Craya-Herring basis for the decomposition of velocity field. After this, we perform a bifurcation analysis of the model. Though our low-dimensional model has fewer modes than the past models, it captures the essential features of the primary bifurcation of the Kolmogorov flow. For example, it reproduces the critical Reynolds number for the supercritical pitchfork bifurcation and the flow structures of the past works. We also demonstrate energy transfers from intermediate scales to large scales. We perform direct numerical simulations of the Kolmogorov flow and show that our model predictions match with the numerical simulations very well.
