Propagation of wave packets in the boundary layer on a curved surface

The development of wave packets excited in a boundary layer by means of a local deformation of the surface in the longitudinal-transverse interaction regime is considered. A solution of the linearized system of equations of interaction theory is constructed using a Laplace transformation with respect to time and a Fourier transformation with respect to the space variables. Two problems are separately examined. In the first, the disturbances are induced by a surface deformation sinusoidal in the transverse direction. It is shown that the center of the wave packet with the greatest oscillation amplitude moves in a direction opposite to that of the flow in the boundary layer. At the same time the wave packet expands, so that in the course of time any fixed point will enter the region of growing oscillations. In the second problem the source of the disturbances is isolated. In this case the wave packet acquires a horseshoe shape. Expanding, it carries the disturbances away from the source in all directions, including upstream relative to the flow in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 59–68, March–April, 1990.     

Self-similar solutions describing the propagation of solitary waves above underwater ridges and troughs

The nonlinear ray method [1] is used to investigate the propagation of solitary waves over an uneven bottom. In the process of nonlinear evolution of the wave front, singular points develop in it; these are treated in the given model as discontinuities [2, 3]. In contrast to earlier studies, it is not assumed here that the intensity of the discontinuity is weak. Boundary conditions at the discontinuities are introduced on the basis of the results of Miles and Bakholdin [4–6], and this makes it possible to take into account the energy loss at a discontinuity and the effects of wave reflection and construct a number of new self-similar solutions for the propagation of a wave above a ridge and trough. The main attention is devoted to considering how the type of solution depends on the parameters of the wave and the relief. For certain values of the parameters, the self-similar solution of the encounter of a homogeneous wave with a ridge is not unique. The reason for this is the singularity of the relief at the end of the ridge. A numerical investigation has therefore also been made of the encounter of a wave with a ridge having a smooth relief at its end. For an under-water trough and a ridge—trough system, self-similar solutions with complete or partial reflection or transmission of the wave energy into the trough are found. A reflected wave can also arise from an encounter with a ridge.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 137–144, September–October, 1985.I thank A. G. Kulikovskii and A. A. Barmin for their interest in the work and for valuable comments made as the paper was being prepared for press.     

Reflection of surface waves by a vertical step at the bottom of a basin

A study is made of the propagation of surface waves in a basin with a vertical step in the bottom. The problem is solved by fitting solutions on the horizontal boundary that continues the bottom of the shallow-water region of the basin; the factorization method is used. It is shown that the reflection of the waves depends on the wavelength of the incident waves and the difference between the two depths in the basin.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 181–185, January–February, 1984.     

Flow in a stratum in the case of pumping from an imperfect well near a basin

A study is made of the three-dimensional stationary problem of the flow of ground water to a well of the type of a point sink in a stratum of unbounded thickness in one direction. The stratum is bounded at the top by the bottom of the basin and a stratum of impermeable ground. The problem is investigated in the framework of potential flow theory based on Darcy's law [1, 2], and the solution is obtained in the form of quadratures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 161–164, September–October, 1980.     

Construction and Analysis of an Analytical Solution for the Surface Rayleigh Wave within the Framework of the Cosserat Continuum

The problem of propagation of an acoustic surface Rayleigh wave in an infinite half-space is considered within the framework of the asymmetric theory of elasticity (Cosserat medium). It is assumed that material deformation is described not only by the displacement vector but also by an independent rotation vector. A global analytical solution of the problem in displacements is obtained. A comparative analysis of the solution obtained and the corresponding solution for the classical elastic medium is performed. Macroparameters characterizing the difference of the stress-strain state from that predicted by the classical theory of elasticity are introduced.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 116–124, July– August, 2005.     

Well production indicators in a deformable reservoir interacting with rocks

Steady-state flow towards a well through a thin porous deformable two-layer reservoir with allowance for deformation of the surrounding rocks is investigated. The permeability of the reservoir is considered to be a function of the displacements of its top and bottom. The effect of deformation on the well production indicators is studied. The results obtained agree qualitatively with the data of full-scale experiments. Earlier, in [1–5], in considering the self-consistent processes of flow through porous media and their deformation attention was concentrated on the analysis of the stress-strain state of the rocks and reservoir and on unsteady problems within the framework of the nonlocally elastic flow regime.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 86–93, January–February, 1995.     

Three-wave resonance interaction of disturbances in a boundary layer

The three-frequency resonance of Tolman-Schlichting waves, one of which propagates along the stream while the other two propagate at adjacent angles to it, is investigated as a function of the spectrum and initial intensity in incompressible flows of the boundary-layer type within the framework of a weakly nonlinear theory. In the parallel-flow approximation such an interaction leads to the formation of unstable self-oscillations. The spatial evolution of the associated disturbances is studied with allowance for the self-similar deformation of the velocity profile of the main flow. It is shown that such development can lead to a sharp amplification of the oscillations, primarily of those propagating at an angle to the flow. The role of the effects under consideration in the transitional process and the connection with experimental data are discussed. As experiments [1, 2] show, in the process of a transition from a laminar boundary layer to a turbulent region, well described by the linear theory of hydrodynamic stability, there first comes a section of the excitation of harmonics of a Tolman-Schlichting wave, the appearance of three-dimensional structures, and a rapid growth in the intensity of low-frequency oscillations. There is no doubt that in this section the phenomena are dependent on the nonlinear character of the development with disturbances. The resonance interaction of wave triads can play an important role in this. For small enough amplitudes such an interaction is described by a first-order theory [3, 4], and in the general case the nonlinear effects associated with them should occur sooner than others. The importance of resonance triads for the explanation of the development of three-dimensional structures in a layer and the generation of intense pulsations has already been emphasized in [5, 6]. The clarification of the properties of the evolution of resonantly interacting disturbances therefore is important for an understanding of this transitional process.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 78–84, September–October, 1978.The authors thank V. Ya. Levchenko for a discussion of the work.     

Experimental and theoretical/numerical investigations of thin films bonding strength

A laser spallation facility has been developed to measure the strength of planar interfaces between a substrate and a thin coating. This quantity is a central requirement in contemporary thin film and protective coatings technology and its successful measurement should improve the scientific/technological potential for the design of advanced composites, protective coatings of composites that operate in hostile environments, and in joining of dissimilar materials. The technique involves impinging a laser pulse of ultra short duration on the rear surface of the substrate, which is coated by a thin layer of energy absorbing metal such as Sn and Pb. The explosive evaporation of the metallic layer, confined between a fused quartz crystal and the substrate, induces a compressive shock wave, which propagates through the substrate toward the material interface. Upon reflection from the free surface of the coating, the pressure pulse is converted into a tensile wave which, under certain conditions, can lead to spallation at the interface. It is shown by mathematical simulation that atomic bond rupture is the mechanism of separation in this experiment. Since the interaction of laser energy with matter is a complicated, highly non-linear process, our investigations, at first, were based on measurement of the pressure pulse generated by the threshold flux level that leads to spallation, by using a micro-electronics device with a piezo-electric crystal, and on computation of the tensile stress experienced at the material interface, by numerical simulation of the induced stress wave propagation. Several substrate/coating (ceramic/ceramic and ceramic/metal) systems have been investigated such as, 1–15 μm SiC by CVD, 1–4 μm TiC and TiN by PVD coatings on sapphire substrates, as well as 1–2 μm Au, Sn and Ag coatings by sputtering on sapphire, fused quartz and glass substrates. For identically prepared specimens, the measured threshold energy levels are reproducible, thus leading to reproducible bond strength values, while the spall size, as expected, is dependent on the laser pulse energy level. Finally, the bond strength values obtained are in very good agreement with similar data derived by direct experimental techniques based on Laser-Doppler-Interferometry.     

Two-dimensional problem for internal waves generated by moving singular sources

When bodies move in a liquid with inhomogeneous density in a gravitational field waves are excited even at low velocities and in the absence of boundaries. They are the so-called internal waves (buoyancy waves), which play an important part in geophysical processes in the ocean and the atmosphere [1–4]. A method based on the replacement of the bodies by systems of point sources is now commonly used to calculate the fields of internal waves generated by moving bodies. However, even so the problems of the generation of waves by a point source and dipole are usually solved approximately or numerically [5–11]. In the present paper, we obtain exact results on the spectral distribution of the emitted waves and the total radiation energy per unit time for some of the simplest sources in the two-dimensional case for an incompressible fluid with exponential density stratification. The wave resistance is obtained simply by dividing the energy loss per unit time by the velocity of the source. In the final section, some results for the three-dimensional case are briefly formulated for comparison.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 77–83, March–April, 1981.     

Features of the Interaction of Simple Waves Propagating In A Composite

Longitudinal plane simple waves having initial profiles in the form of the Chebyshov–Hermite function and propagating in a solid two-phase mixture are studied. The interaction between two simple waves, generation of the third wave because of this interaction, and the conditions for its occurrence are successively stated. The case where the third wave is not generated is analyzed numerically for the first time     

Effect of the parameters of an electron beam on the process of accumulation of hot electrons in a mirror trap

A study is made of the mechanism of generation and accumulation of hot electrons during the interaction of an electron beam with a cold plasma in a mirror machine. The energy density distribution of the hot component of the plasma (nT) along the radius of the system, the time dependence of the diamagnetism, and the escape of fast electrons from the beam region into the loss cone are measured. It is established that there is a considerable difference in the processes of accumulation of hot electrons depending on whether the beam current or beam energy is varied. It is concluded that under the conditions of these experiments the hot component of the plasma is formed from the beam electrons.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 49–54, July–August, 1974.The authors are grateful to L. I. Rudakov for valuable remarks.     

宽幅钢箱梁环焊缝焊接顺序优化研究

基于热弹塑性有限元法,采用ANSYS软件建立了网格疏密过渡的单箱五室钢箱梁壳单元模型;结合高效的分段移动热源,实现了对大型复杂长焊缝结构焊接全过程的数值模拟,并定性对比了宽幅钢箱梁在不同的环焊缝焊接顺序下顶板和底板的变形情况.分析结果表明:腹板焊缝的焊接顺序对竖向最大变形值(绝对值)的影响不大,其值主要取决于顶板和底板...     

Nonlinear wave motions of a liquid in a vibrating axisymmetric cavity

The problem of the nonlinear wave deformation of the free surface of a liquid due to the translational motions of the containing vessel is examined. Bogolyubov's averaging method is used to investigate the characteristics of the wave motions of the liquid in the resonance zones in the case of a cylindrical vessel. Relations are obtained characterizing the variation of the amplitude of the circular wave with the frequencies of the external perturbations in the steady-state wave process; the conditions of occurrence and stability of such processes are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 120–125, May–June, 1989.     

Effect of cooling rate on fracture behavior of polypropylene

The purpose of this work is to investigate the influence of morphology, induced by cooling rate during molding, on the time–temperature dependence of fracture behavior of polypropylene (PP). Fractures tests were performed over a range of loading rates from 0.2 mm/min to 2.5 m/s, using the single edge notched bending specimen. The results show that the transition temperature from brittle to ductile behavior increases with decreasing cooling rate. However, at very low loading speed (0.2 mm/min), an opposite effect is observed, the brittle–ductile transition temperature diminishes with lower cooling rate. At low test speeds, the fracture performance is reduced with a decreasing cooling rate. Conversely, under impact, the fracture toughness of PP is enhanced with a decrease in cooling rate. This is explained by the mechanism of blunting of the crack tip due to adiabatic heating under high loading rates. The blunting effect results in a more significant plastic deformation of the crystalline region that requires a higher energy. The brittle–ductile transition was characterized by an energy activation process expressed by the Arrhenius equation. Decreasing the cooling rate results in a decrease of both the pre-exponential factor and the energy barrier controlling the time–temperature dependence of fracture behavior. The reduction of the pre-exponential factor corresponds to a more ordered morphology due to a reduction in the entropy and is consistent with a higher crystallinity. The reduction of activation energy with higher crystalline level suggests that the brittle–ductile transition also involves the primary relaxation process that is known to occur mostly in an amorphous structure. A higher crystallinity would restrain the primary relaxation processes and the brittle–ductile transition becomes more dependent on the secondary movements of the chain segments. The results demonstrate that the relationship between deformation rate, temperature, and mechanical performance of PP is not only controlled by molecular relaxation processes, but also strongly dependent on its morphology.     

SPH evaluation of the hydrodynamic consequences induced by reef degradation

An apparent increase in the frequency and intensity of natural disturbances and anthropogenic activities accelerates the global degradation of coral reefs. The emergency planning for coastal erosion and flooding along the low-lying coasts fronted by coral reefs underscores the need to predict and evaluate reasonably the hydrodynamic consequences of reef degradation. Here the ability of the well validated Smoothed Particle Hydrodynamics (SPH) porous model is enhanced by integrating a momentum source wave maker for wave groups generation in water of arbitrary depth. Validated results show the SPH model can predict properly the propagation and transformation of wave groups over the complex coral reef. The model is finally adopted to predict the hydrodynamic consequences induced by reef degradation both under the reef resonance and off-resonance conditions. This work provides a general framework for understanding the effects of reef degradation on the spatial distributions of wave setup, wave-induced current and low frequency wave energy over the reef-flat under the action of bichromatic wave groups with different frequency differences.     

Investigation of wave fields in a fluid layer and elastic half-space excited by a near-bottom source of vibrations

Questions of a study of acoustic and seismic wave propagation in the ocean and the underlying medium, associated with problems of marine hydrolocation (sonar) and the investigation of tsunami wave predecessors caused by underwater volcanic eruptions are of great interest at this time. The simplest model, a point source of vibrations located in a fluid layer at a certain range from the bottom, is used to describe the mentioned wave processes. Wave fields in a fluid and elastic base are investigated in this paper, analytical formulas are obtained, and results of a numerical analysis are presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 49–51, July–August, 1984.     

Generation of Nonlinear Waves on a Viscoelastic Coating in a Turbulent Boundary Layer

Self–induced excitation of periodic nonlinear waves on a viscoelastic coating interacting with a turbulent boundary layer of an incompressible flow is studied. The response of the flow to multiwave excitation of the coating surface is determined in the approximation of small slopes. A system of equations is obtained for complex amplitudes of multiple harmonics of a slow (divergent) wave resulting from the development of hydroelastic instability on a coating with large losses. It is shown that three–wave resonant relations between the harmonics lead to the development of explosive instability, which is stabilized due to the deformation of the mean (Sover the wave period) shear flow in the boundary layer. Conditions of soft and hard excitation of divergent waves are determined. Based on the calculations performed, qualitative features of excitation of divergent waves in known experiments are explained.     

Re-examined principles of thrust generation by a track on soft ground

Dr. Bekker’s first book Theory of land locomotion offers in fact two different concepts of thrust generation on soft ground with respect to the slip: (a) as the push of grousers causing horizontal soil “distortion” and (b) as the shear force in the failure plane linked with the shear deformation. Bekker preferred the second concept and backed it up by the unique shear-ring measuring technique. To clear up the matter, the author decided to re-examine the thrust generation by a track plate experimentally in field conditions. The tests have shown that the initial stage of thrust generation in compressible ground is always horizontal soil compression by grousers, which divides the soil under a track into separate blocks initially at rest. This compression increases at least to the transition point, when a block is sheared off simultaneously at the bottom and in both lateral planes and starts sliding along the channel formed by the preceding grouser. The analysis of these measurements enabled to define the compressive displacement of the face of the soil block (travel of the grouser) appurtenant to the mentioned transition point, useful to define the thrust–slip curve. The case may also be described by the conventional shear stress–shear displacement relationship, imagined to take place in the bottom failure plane, however, namely the “shear displacement” is rather an unusual quantity.     

Generation of a magnetic field in the shear deformation region of a conducting material upon high–velocity penetration

It is shown that when a high–velocity impactor penetrates into a conducting target with a transverse magnetic field, conditions for considerable field amplification are produced in the shear deformation region on the lateral surface of the impactor. Field generation in a conducting medium deformed in shear is considered within the framework of a plane one–dimensional problem of magnetohydrodynamics. The results obtained indicate that along the boundary of the cavity produced by the impactor in the target with a magnetic field, a thin layer with a very high field intensity (about 100 T) is formed. The possibility of explosion of this layer due to the magnetic pressure acting in it is analyzed.     

Shock–Free Breakup of Droplets. Temporal Characteristics

In the present paper, we consider the shock–free breakup of droplets in their encounter with a layer (sheet) of a moving gas in the absence of pressure perturbations when the droplets are affected by a short U–shaped pulse of aerodynamic forces. Under a high pressure of the ambient gas medium p₀ = 20—80 bar, the droplets (ethanol or liquid oxygen) have a chance to break up after stay in a thing (2—5 mm thick) gas layer (jet) moving with a velocity of 1—10 m/sec. A distinctive feature of the process is that the characteristic time of droplet deformation and the period of natural oscillations coincide with the residence time for the droplets in the region of their interaction with the gas stream. Empirical formulas are proposed for determination of the total breakup time and the duration of the droplet disintegration stage in shock–free breakup.