Wave Motion Localization Effects in Elastic Waveguides

Dynamic effects characteristic of elastic bodies and associated with local disturbances in finite elastic bodies and inhomogeneous waveguides are analyzed and systematized. The physical causes of such disturbances are analyzed. It is shown that these disturbances are due to energy transfer from longitudinal to transverse waves and back, when they are reflected from the free surface of an elastic body __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 38–45, September 2005.     

The Patterns of Surface Capillary-gravity Short-crested Waves with Uniform Current Fields in Coastal Waters

A fully three-dimensional surface gravity-capillary short-crested wave system is studied as two progressive wave-trains of equal amplitude and frequency, which are collinear with uniform currents and doubly-periodic in the horizontal plane, are propagating at an angle to each other. The first- and second-order asymptotic analytical solutions of the short-crested wave system are obtained via a perturbation expansion in a small parameter associated with the wave steepness, therefore depicting a series of typical three-dimensional wave patterns involving currents, shallow and deep water, and surface capillary waves, and comparing them with each other.The project supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China (200428), the National Natural Science Foundation of China (10272072 and 50424913), the Shanghai Natural Science Foundation (05ZR14048), and the Shanghai Leading Academic Discipline Project (Y0103). The English text was polished by Yunming Chen.     

Instability of Buckley-Leverett flow in a heterogeneous medium

We study the simultaneous one-dimensional flow of water and oil in a heterogeneous medium modelled by the Buckley-Leverett equation. It is shown both by analytical solutions and by numerical experiments that this hyperbolic model is unstable in the following sense: Perturbations in physical parameters in a tiny region of the reservoir may lead to a totally different picture of the flow. This means that simulation results obtained by solving the hyperbolic Buckley-Leverett equation may be unreliable.Symbols and Notation f fractional flow function varying withs andx - value off outsideI - value off insideI - local approximation off around¯x - f ^–,f ⁺ values of - f _j ⁿ value off atS _j ⁿ andx _j - g acceleration due to gravity [ms^–2] - I interval containing a low permeable rock - k dimensionless absolute permeability - k ^* absolute permeability [m²] - k _c ^* characteristic absolute permeability [m²] - k _ro relative oil permeability - k _rw relative water permeability - L ^* characteristic length [m] - L ₁ the space of absolutely integrable functions - L the space of bounded functions - P _c dimensionless capillary pressure function - P _c ^* capillary pressure function [Pa] - P _c ^* characteristic pressure [Pa] - S similarity solution - S _j ⁿ numerical approximation tos(x_j, t_n) - S ₁, S₂,S ₃ constant values ofs - s water saturation - value ofs at - s ^L left state ofs (wrt. ) - s ^R right state ofs (wrt. ) - s s for a fixed value of in Section 3 - T value oft - t dimensionless time coordinate - t ^* time coordinate [s] - t _c ^* characteristic time [s] - t _n temporal grid point,t _n=n t - v ^* total filtration (Darcy) velocity [ms^–1] - W, , v dimensionless numbers defined by Equations (4), (5) and (6) - x dimensionless spatial coordinate [m] - x ^* spatial coordinate [m] - x _j spatial grid piont,x _j=j x - discontinuity curve in (x, t) space - right limiting value of¯x - left limiting value of¯x - angle between flow direction and horizontal direction - t temporal grid spacing - x spatial grid spacing - length ofI - parameter measuring the capillary effects - argument ofS - _o dimensionless dynamic oil viscosity - _w dimensionless dynamic water viscosity - _c ^* characteristic viscosity [kg m^–1s^–1] - _o ^* dynamic oil viscosity [kg m^–1s^–1] - _w ^* dynamic water viscosity [k gm^–1s^–1] - _o dimensionless density of oil - _w dimensionless density of water - _c ^* characteristic density [kgm^–3] - _o ^* density of oil [kgm^–3] - _w ^* density of water [kgm^–3] - porosity - dimensionless diffusion function varying withs andx - ^* dimensionless function varying with s andx ^* [kg^–1m³s] - _j ⁿ value of atS _j ⁿ andx _j This research has been supported by VISTA, a research cooperation between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap a.s. (Statoil).     

Behavior of a floating elastic plate during vibrations of a bottom segment

The Wiener-Hopf technique is used to obtain an analytical solution for the problem of vibrations of a floating semi-infinite elastic plate due to earthquake-induced vibrations of a bottom segment. An explicit solution is obtained ignoring the inertial term. The surface-wave amplitudes and ice-plate deflection are studied numerically as functions of the frequency and position of the vibrating bottom segment, ice thickness, and fluid depth.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 98–108, March–April, 2005.     

Stability and Instability of Fourth-Order Solitary Waves

We study ground-state traveling wave solutions of a fourth-order wave equation. We find conditions on the speed of the waves which imply stability and instability of the solitary waves. The analysis depends on the variational characterization of the ground states rather than information about the linearized operator.     

Instability of a Collision Surface During High-Velocity Impact

The physical mechanisms of development of hydrodynamic instability during high-velocity impact are analyzed analytically and using numerical simulation. A new mechanism of development of instability based on the assumption of the existence of initial perturbations on the surfaces of the colliding plates is proposed. The progressive displacement of the maximum of the specific surface mixed mass from the shortwave to the longwave spectrum range and the self-similarity of the variation of the interface are established.     

Incremental Magnetoelastic Deformations,with Application to Surface Instability

In this paper the equations governing the deformations of infinitesimal (incremental) disturbances superimposed on finite static deformation fields involving magnetic and elastic interactions are presented. The coupling between the equations of mechanical equilibrium and Maxwell’s equations complicates the incremental formulation and particular attention is therefore paid to the derivation of the incremental equations, of the tensors of magnetoelastic moduli and of the incremental boundary conditions at a magnetoelastic/vacuum interface. The problem of surface stability for a solid half-space under plane strain with a magnetic field normal to its surface is used to illustrate the general results. The analysis involved leads to the simultaneous resolution of a bicubic and vanishing of a 7×7 determinant. In order to provide specific demonstration of the effect of the magnetic field, the material model is specialized to that of a “magnetoelastic Mooney–Rivlin solid”. Depending on the magnitudes of the magnetic field and the magnetoelastic coupling parameters, this shows that the half-space may become either more stable or less stable than in the absence of a magnetic field.      

Vibrations of a Floating Elastic Plate Due to Periodic Displacements of a Bottom Segment

The problem of the behavior of a floating elastic thin plate under periodic vibrations of a bottom segment is solved using a numerical procedure based on the Wiener-Hopf technique. The effects of the vibration frequency, the position of the vibrating bottom segment, and the fluid depth on the vibration frequencies of the fluid and plate are studied numerically.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 166–179, September–October, 2005.     

Experimental Investigation of Thermocapillary Convection Induced by a Local Temperature Inhomogeneity near the Liquid Surface. 1. Solid Source of Heat

The structure and stability of a thermocapillary flow from a concentrated source of heat located near the free surface of the liquid filling a deep reservoir are experimentally studied. For a certain power of the heat source, oscillatory instability leading to formation of surface waves is observed. Possible mechanisms of the observed instability are discussed.     

流体动力润滑油膜破裂的热力学失稳机理

分析了流体动力学润滑过程中的热量传递及对润滑剂流变特性的影响,得出了流体动力润滑油膜发生热力学失稳的条件,建立了描述润滑剂温度非牛顿效应的本构方程数值计算结果表明,由于温度的影响,流体动力润滑油膜存在最大承载能力;在临界状态,微小的扰动将会引起油膜失稳而丧失承载能力。初步揭示了流体动力学力润滑膜破失效的内在力学机制。     

高Bond数下黏性液滴的Rayleigh-Taylor不稳定性

给出了高Bond数下黏性液滴表面Rayleigh-Taylor线性不稳定性的分析解，这种不稳定性对于超音速气流作用下液滴破碎的早期阶段起着至关重要的作用．基于稳定性分析的结果，导出了用于估算稳定液滴的最大直径及液滴无量纲初始破碎时间的计算式，这些计算式与相关文献给出的实验和分析结果比较显示了良好的一致．     

Nonlinear Viscous Flows with a Free Surface

An asymptotic solution of the problem of time evolution of a periodic wave on the surface of a viscous, infinitely deep fluid in the approximation quadratic in the wave amplitude is proposed.     

Action of a Periodic Load on an Elastic Floating Plate

The problem of the behavior of an elastic floating plate in the form of a strip under the action of a periodic surface load is solved using the Wiener-Hopf technique. The shortwave approximation is found in explicit form. The effect of the frequency and nature of the acting load on the vibration amplitudes of the fluid and the plate is investigated numerically. It is found that for certain loads no waves propagate in the fluid and the vibrations of the plate are localized in the neighborhood of the acting load. Conditions under which local vibration can be realized are found.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 132–146.Original Russian Text Copyright © 2005 by Tkacheva.     

Strain Relaxation in an Alloy Film with a Rough Free Surface

We study strain relief by surface roughness and composition variation in a stressed alloy film. Instead of using common perturbation techniques, we derive a rigorous relaxation formula based on the energy approach in the case of slightly undulating surface and fluctuating composition. We do not require any a priori assumption of elastic isotropy or identical material properties between film and substrate in deriving our result. We show that the change of elastic energy is negative, giving rise to energy relief due to the presence of free surface. We apply our result to the study of compositional and morphological instabilities of a stressed thin layer with a free surface. The critical wave number of instability is determined by the competition between the destabilizing influence of elastic strain energy and the stabilizing influence of chemical and surface energies.     

薄膜沿加热平板下落的稳定性分布

本文分析了薄膜沿加热平板下落的稳定性。在时间模式下，发现流动的不稳定性是由表面波不稳定和加毛细不稳定构成的，同时当流体的热扩散越大以及界面热量损失越小时，热毛细不稳定越剧烈，在时空模式下，流动随着Marangoni数的增大。流动有可能从对流不稳定过渡到绝对不稳定，这一结论尚待实验验证。     

Nonlinear Effects of the Stress Driven Rearrangement Instability of Solid Free Surfaces

The roughness of the free surface of a non-hydrostatically stressed solid has been expanded in Fourier series and the influence of the first three harmonics of this development has been investigated by means of a static variational calculation of the elastic and surface energies. The deformation of the bumps and grooves of the roughness has been determined and the optimal shape of the free surface has been characterized. Mathematics Subject Classifications (2000) 82B24, 73C05, 73C02, 73V25, 73B30, 73S10.     

Instability theory of shock wave in a shock tube

The instability theory of shock wave in a shock tube including the effects of tube wall and contact surface is studied. The experimental data of unstable shock wave coincide with one of instability criteria derived in the present paper.     

Divergent Instability Domains of a Fluid-Conveying Cantilevered Pipe with a Combined Support

The divergent instability of a fluid-conveying pipe is analyzed numerically. The pipe is modeled by a cantilevered beam restrained at the left end and supported by a special device (a rotational elastic restraint plus a Q-apparatus) at the right end. Divergent instability domains of the pipe are obtained by varying the rotational elastic constant of the right restraint     

Instability of a horizontal plane-channel flow of a dilute suspension

The stability of a horizontal plane-channel flow of a dilute suspension is studied theoretically. It is shown that the mechanism of action of the sedimenting particles on the flow stability parameters is equivalent to the effect of a distributed flow stratification and is attributable to the vertical nonuniformity of the body force induced by the excess weight of the sedimenting particles. A strong dependence of the disturbance growth rate on the location of the interface between the suspension and the pure liquid is detected.     

Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers

The Kelvin–Helmholtz instability is believed to be the dominant instability mechanism for free shear flows at large Reynolds numbers. At small Reynolds numbers, a new instability mode is identified when the temporal instability of parallel viscous two fluid mixing layers is extended to current-fluid mud systems by considering a composite error function velocity profile. The new mode is caused by the large viscosity difference between the two fluids. This interfacial mode exists when the fluid mud boundary layer is sufficiently thin. Its performance is different from that of the Kelvin–Helmholtz mode. This mode has not yet been reported for interface instability problems with large viscosity contrasts.These results are essential for further stability analysis of flows relevant to the breaking up of this type of interface.