法向电场下介质流体上的毛细管重力波奇异性

IF 1.9 4区 数学 Q1 MATHEMATICS, APPLIED
Tao Gao, Zhan Wang, Demetrios Papageorgiou
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引用次数: 0

摘要

SIAM 应用数学杂志》第 84 卷第 2 期第 523-542 页,2024 年 4 月。 摘要。正如 Papageorgiou [Annu. Rev. Fluid Mech., 51 (2019), pp. 155-187] 所总结的,强法向电场会导致流体力学系统中界面的不稳定性。在本研究中,研究了在垂直于未扰动自由表面的方向上施加电场时,有限深度介电流体上的电毛细重力波产生的奇异现象。在浅水中,对于线性不稳定体系中的小振幅周期性扰动,系统演化的结果是气液界面触及固体底部边界,导致破裂。针对长波极限推导出了一个准线性双曲模型,并用于研究触底奇点的形成。通过电化欧拉方程的时间共形映射,将理论预测与完全非线性计算进行了比较,结果显示两者吻合良好。另一方面,针对深水场景推导了一个非线性色散模型系统,该系统预测了炸裂奇点(即波幅在有限时间内趋于无穷大)。然而,当流体厚度显著增大时,人们可以从数值上显示出全欧拉方程中的自交非物理波结构或 2/3 幂尖顶奇点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Singularities of Capillary-Gravity Waves on Dielectric Fluid Under Normal Electric Fields
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 523-542, April 2024.
Abstract. As summarized by Papageorgiou [Annu. Rev. Fluid Mech., 51 (2019), pp. 155–187], a strong normal electric field can cause instability of the interface in a hydrodynamic system. In the present work, singularities arising in electrocapillary-gravity waves on a dielectric fluid of finite depth due to an electric field imposed in the direction perpendicular to the undisturbed free surface are investigated. In shallow water, for a small-amplitude periodic disturbance in the linearly unstable regime, the outcome of the system evolution is that the gas-liquid interface touches the solid bottom boundary, causing a rupture. A quasi-linear hyperbolic model is derived for the long-wave limit and used to study the formation of the touch-down singularity. The theoretical predictions are compared with the fully nonlinear computations by a time-dependent conformal mapping for the electrified Euler equations, showing good agreement. On the other hand, a nonlinear dispersive model system is derived for the deep-water scenario, which predicts the blowup singularity (i.e., the wave amplitude tends to infinity in a finite time). However, when the fluid thickness is significantly large, one can numerically show the self-intersection nonphysical wave structure or 2/3 power cusp singularity in the full Euler equations.
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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
期刊介绍: SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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