Steady Wind-Generated Gravity-Capillary Waves on Viscous Liquid Film Flows

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-03-21 DOI:10.1137/23m1586318

Y. Meng, D. T. Papageorgiou, J.-M. Vanden-Broeck

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Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 477-496, April 2024.
Abstract. Steady gravity-capillary periodic waves on the surface of a thin viscous liquid film supported by an air stream on an inclined wall are investigated. Based on lubrication approximation and thin air-foil theory, this problem is reduced to an integro-differential equation. The small-amplitude analysis is carried out to obtain two analytical solutions up to the second order. Numerical computation shows there exist two distinct primary bifurcation branches starting from infinitesimal waves, which approach solitary wave configuration in the long-wave limit when the values of physical parameters are above certain thresholds. New families of solutions manifest themselves either as secondary bifurcation occurring on primary branches or as isolated solution branches. The limiting configurations of the primary solution branches with the increase of two parameters are studied in two different cases, where one and two limiting configurations are obtained, respectively. For the latter case, the approximation of the configurations is given.

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粘性液体薄膜流上由风产生的稳定重力-毛细管波

SIAM 应用数学杂志》第 84 卷第 2 期第 477-496 页，2024 年 4 月。摘要。研究了倾斜壁上由气流支撑的薄粘性液膜表面上的稳定重力-毛细周期波。基于润滑近似和薄气膜理论，将该问题简化为积分微分方程。通过小振幅分析，得到了直到二阶的两个解析解。数值计算表明，存在两个不同的主要分岔分支，它们从无穷小波开始，当物理参数值超过一定临界值时，在长波极限接近孤波构型。新的解系要么表现为发生在主分支上的次级分岔，要么表现为孤立的解分支。我们在两种不同的情况下研究了随着两个参数的增加主解分支的极限构型，分别获得了一个和两个极限构型。对于后一种情况，给出了构型的近似值。

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

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.