Analysis of a Simplified Model of Rigid Structure Floating in a Viscous Fluid

Journal of Nonlinear Science - We study the interaction of surface water waves with a floating solid constraint to move only in the vertical direction. The first novelty we bring in is that we...     

在粘性流体中船行波的速度场

从Navier-Stokes方程出发,导得了水上运动物体船行波的波高和水平速度二重积分的表达式.其次采用Lighthill两步法将上述的积分表达式化为代数表达式.与海水作为理想流体所得的结果相比,消除或减弱了原有的奇性,提高了船行波的数字资料的精度.     

The Rolling Motion of A Viscous Fluid On and Off a Rigid Surface

An analytical solution is obtained for the local flow field near a point of steady attachment to or detachment from a rigid boundary. The possible free surface shapes depend on the capillary number.     

Nonuniqueness of a Solution to the Problem on Motion of a Rigid Body in a Viscous Incompressible Fluid

This paper is devoted to the problem on motion of a rigid body in a viscous incompressible fluid. It is proved that there exist at least two weak solutions of this problem if collisions of the body with the boundary of the flow domain are allowed. These solutions have different behavior of the body after the collision. Namely, for the first solution, the body goes away from the boundary after the collision. In the second solution, the body and the boundary remain in contact. Bibliography 15 titles.To Vsevolod Alekseevich Solonnikov on the occasion of his jubilee__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 306, 2003, pp. 199–209.     

Small Motions and Normal Oscillations of a Double Pendulum with Cavities Containing a Viscous Incompressible Liquid

The linear hydrodynamic problem involving the small motions and normal oscillations of a double pendulum with cavities completely filled with a liquid is examined. The problem is solved using the methods of functional analysis. An existence theorem is formulated for the solutions to the Cauchy problem and the properties of the normal oscillations are described.     

Frequencies of Free Acoustic Oscillations in a Fluid Separating Rigid and Elastic Tube Walls of Finite Length

A solution of the problem of determining the frequencies and mode shapes of free nonsymmetric oscillations in an annular volume filled with an ideal compressible fluid is constructed. The inner tube and the end plane walls are ideally rigid. A thin elastic shell with edges clamped to the end walls is located on the outer tube boundary. A phenomenon of a decrease in the fundamental frequency as the thickness of a fluid layer adjacent to the elastic wall decreases is confirmed. Bibliography: 8 titles.     

About the Decay of Vorticity in a Two-dimensional Incompressible Viscous Fluid

The main purpose of this article is to investigate the behavior of the vorticity in a two dimensional incompressible viscous medium. We give bounds for the maximal amount of vorticity which can be concentrated in a domain of a given size. In order to obtain bounds we compare the vorticity equation to the heat equation in ²     

On the Wetting of a Surface by a Very Viscous Fluid

The movement of a small viscous droplet on a flat surface is considered in self-spreading, in roundup, and as a result of an adhesion gradient. Edge conditions based on the dynamic contact angle are discussed within the context of lubrication theory. Tangential slip at the contact line is shown to be small compared to the normal velocity. The shapes of the droplet and its contact line are calculated, and nonlinear and inertial effects assessed.     

Torsional Oscillations of a Rigid Convex Inclusion Embedded in an Elastic Solid

The problem discussed in this paper concerns a rigid axi-symmetricbody of convex form embedded in an infinite isotropic elasticsolid. When the inclusion is set in motion by an impulsive torqueapplied about the axis of symmetry it executes a damped torsionaloscillation and generates a shear pulse in the surrounding elasticmaterial. A representation of the elastic wave field in theform of a progressing wave expansion is shown to lead to anintegral equation of Volterra type for the angular motion ofthe inclusion. The exact solution obtained by Chadwick &Trowbridge (1967) for the case of a spherical inclusion is thenre-derived and used in developing an approximate method of solutionof the more general problem described above. Detailed resultsare worked out for spheroidal inclusions of oblate and prolateforms and numerical results are presented and discussed.     

固壁近旁Stokes流中粘性液滴的运动和变形

发展了一种模拟固壁近旁轴对称Stokes流中粘性液滴的运动和变形及直接计算固壁上应力的边界积分方法．用此方法对不同的液滴-固壁初始相对间距、粘度比、表面张力和浮力联合参数以及环境流动参数情况进行了数值实验．数值结果显示,由于环境流动和浮力的作用,随着时间的推进,液滴在轴向压缩,在径向拉伸．当环境流动的作用弱于浮力作用时,随着时间的推移,液滴上升并向上弯,固壁上由液滴运动所引起的应力不断减小．当环境流动的作用强于浮力作用时,随着时间的推移,液滴变得越来越扁．在这种情形,当大初始间距时,壁面上的应力随液滴的演变而增大;当小初始间距时,由环境流动、浮力及壁面对流动的较强作用的联合影响,此应力随液滴的演变而减小．由于液滴运动所引起的壁面应力的有效作用仅限于对称轴附近的一个小范围内,且此范围随液滴与固壁的初始间距增大而增大．应力的大小随初始间距增大而大为减小．表面张力对液滴变形有阻止作用．液滴粘性会减小液滴的变形和位置迁移．     

Estimate of the Generalized Energy in a Free-Boundary Problem for a Viscous Incompressible Fluid

We introduce and estimate the generalized energy in the problem on evolution of an isolated fluid mass bounded by a free surface under the surface tension force. Bibliography: 9 titles.     

弱粘性流体中垂直激励表面波的阻尼效应

在竖直振动的圆柱形容器中,将Navier-Stokes方程线性化,利用两时间尺度奇异摄动展开法研究了弱粘性流体的单一自由面驻波运动．整个流场被分为外部势流区和内部边界层区两部分,对两部分区域分别求解,得到包含阻尼项和外驱动影响的线性振幅方程．利用稳定性分析,得到形成稳定表面波的条件,给出了临界曲线．此外,还获得了阻尼系数的解析表达式．最后,将线性阻尼加到理想流体条件下所得到的色散关系中对其进行修正,理论结果证明修正后的驱动频率更加接近实验的结果．通过计算发现,当驱动的频率较低时,流体的粘性对表面波模式选择有重要影响,而表面张力的影响不明显;但当驱动频率较高时,流体的表面张力起主要作用,而流体的粘性影响甚小．     

Estimates for the Resolvent of the Operator Appearing in the Study of Equilibrium Figures of a Rotating Viscous Incompressible Fluid

An estimate in the -norm is obtained for a solution to a linear problem with parameter connected with the evolution problem for an isolated liquid mass. Bibliography: 7 titles.     

Homogenization of the Equations of Filtration of a Viscous Fluid in Two Porous Media

A homogenized model of filtration of a viscous fluid in two domains with common boundary is deduced on the basis of the method of two-scale convergence. The domains represent an elastic medium with perforated pores. The fluid, filling the pores, is the same in both domains, and the properties of the solid skeleton are distinct.     

Weak Solutions for the Motion of a Self-propelled Deformable Structure in a Viscous Incompressible Fluid

We consider the three-dimensional motion of a self-propelled deformable structure into a viscous incompressible fluid. The deformation of the solid is given whereas its position is unknown. Such a system could model the propulsion of fish-like swimmers. The equations of motion of the fluid are the Navier-Stokes equations and the equations for the structure are deduced from Newton’s laws. The corresponding system is a free boundary problem and the main result of the paper is the existence of weak solutions for this problem.