水平电场下界面波的Hamilton原理与多尺度建模  

Interfacial electrohydrodynamic waves under horizontal electric fields: Hamilton’s principle and multi-scale modeling

作　　者：王展 WANG Zhan(Chinese Academy of Sciences,Beijing 100190,China;School of Engineering Science,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院力学研究所,北京100190 [2]中国科学院大学工程科学学院,北京100049

出　　处：《力学进展》2022年第3期719-729,共11页Advances in Mechanics

基　　金：中国科学院B类战略先导(XDB22040203);中国科学院青年交叉团队项目的资助。

摘　　要：本文研究水平电场下两层电介质流体间界面波动的多尺度建模.首先对此系统的Hamilton原理给出详细证明;然后基于Hamilton结构和Dirichlet–Neumann算子的解析性质,将Hamilton量中的动能与电势能展开成收敛级数形式并确定截断阶数,最后通过计算截断后近似总能量的变分导数得到约化模型.上述过程对该问题给出了一套建立多尺度非线性模型的系统方法.文章再以“上层深水、下层浅水”为例详细阐述了多尺度建模的全过程,并利用修正的Petviashvili迭代方法计算了新模型中的非线性相干结构.本文所发展的渐近分析技巧不同于之前的工作,其优点在于所导出的约化模型自然保留能量守恒的性质;同时,本文亦将原有结果推广至三维情形.This paper is concerned with the multi-scale modeling of interfacial waves between two dielectric fluids under a horizontal electric field. First, we give a detailed proof of the Hamilton principle for this system. Next, based on the Hamiltonian structure and the analytical property of the Dirichlet-Neumann operator, the kinetic energy and electric potential energy in the Hamiltonian are expanded into the form of convergent series, and the order of truncation is determined. Finally, the reduced model is obtained by calculating the variational derivatives of the approximate total energy after truncation. The above process provides a systematic method for establishing nonlinear multi-scale models. Taking the case of “deep upper layer and shallow lower layer” as an example, we describe the whole modeling process in detail. Furthermore, the nonlinear coherent structure in the newly proposed model is computed using the modified Petviashvili iterative method. The asymptotic technique developed in this paper differs from previous work. Its advantage is that the derived reduced models naturally retain the energy conservation property;at the same time, this paper also extends the previous results to the three-dimensional situation.

关 键 词：哈密顿 界面波 电流体力学 多尺度建模 

分 类 号：O353[理学—流体力学] O361[理学—力学]