混沌电对流的稀疏非线性模型
Sparse nonlinear models of chaotic electroconvection
摘要：
对流是一种基本的流体传输现象，其中流体的大规模运动例如由热梯度或电势驱动。对流模型的建立促进了混沌理论和多物理场系统降阶模型的发展;然而，这些模型仅限于相对简单的热对流现象。在这项工作中，我们开发了一个降阶模型的混沌电对流在高电瑞利数。该系统中的混沌与从Rayleigh-Benard对流获得的标准Lorenz模型有关，尽管我们的系统是由流体、电荷密度和电场之间更复杂的三向耦合驱动的。相干结构提取时间和空间分辨的电荷密度场通过适当的正交分解（POD）。一个非线性模型，然后开发这些相干结构的混沌时间演化的稀疏识别非线性动力学（SINDy）算法，约束，以保持在原始系统中观察到的对称性。由此产生的模型表现出主导的混沌动力学的原始高维系统，捕捉基本的非线性相互作用与一个简单的降阶模型。
英文摘要：
Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient or an electric potential. Modeling convection has given rise to the development of chaos theory and the reduced-order modeling of multiphysics systems; however, these models have been limited to relatively simple thermal convection phenomena. In this work, we develop a reduced-order model for chaotic electroconvection at high electric Rayleigh number. The chaos in this system is related to the standard Lorenz model obtained from Rayleigh-Benard convection, although our system is driven by a more complex three-way coupling between the fluid, the charge density, and the electric field. Coherent structures are extracted from temporally and spatially resolved charge density fields via proper orthogonal decomposition (POD). A nonlinear model is then developed for the chaotic time evolution of these coherent structures using the sparse identification of nonlinear dynamics (SINDy) algorithm, constrained to preserve the symmetries observed in the original system. The resulting model exhibits the dominant chaotic dynamics of the original high-dimensional system, capturing the essential nonlinear interactions with a simple reduced-order model.
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