Stability of the boundary layer above the surface of a wave travelling over a plate

The two-dimensional problem of the stability of the flow of an incompressible fluid over a rigid surface perturbed by a wave travelling in the propagation direction of the flow is discussed in the linear approximation. The problem is solved in the coordinate system at rest with respect to the travelling wave. The parameters of this wave are not eigenvalues of the corresponding linear problem of the stability. The solution is sought in the form of a series in powers of the wave amplitude with an accuracy out to the quadratic term inclusively. Calculations are made of the dependence of the neutral stability curve on the amplitude, wavelength, and phase velocity.Translated from Zhurnal Prikladnoi Mekhaniki Tekhnicheskoi Fiziki, No. 5, pp. 49–52, September–October, 1979.     

Wave propagation and resonance phenomena in inhomogeneous media

The waveguide and resonance properties of inhomogeneous penetrable one–dimensional–periodical structures that consist of two different media are studied within the framework of a one–dimensional approximation. The pass and stop bands are determined. A dispersion relation for all the waveguide modes is obtained. Explicit expressions for low waveguide frequencies and corresponding phase velocities of waveguide modes for mono– and polydisperse media are found. The influence of the polydispersity of the sizes of heterogeneities on the low frequencies of a pass band is considered. A pass band in the range of low frequencies is detected. It is shown that the polydispersity does not affect the waveguide properties of a medium at low frequencies of the first pass band. The resonance phenomena in periodical media and structures are investigated. The resonance phenomena are shown to occur for an unlimited discrete set of frequencies if the group velocity of the waveguide mode for them is zero; in this case, the growth of the oscillation amplitude is localized in the neighborhood of a source (localization of the resonance). A synchrophasotron resonance at which the infinite chain of oscillation sources has the oscillations phase of a corresponding traveling wave from the pass band is detected.     

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.     

Reflection of a Dam–Break Wave at a Vertical Wall. Numerical Modeling and Experiment

Results of the experimental study and numerical modeling of the reflection of a dam–break wave at the vertical end wall of a channel are given. A wave forms with distance from a partition creating the initial level difference of the liquid. It is shown that a numerical calculation based on the Zheleznyak—Pelinovskii nonlinear dispersion model satisfactorily describes the height of the splash–up, the amplitude of reflected waves, and the wave velocity in front of the wall for smooth and dam–break waves. It is also shown that, for smooth and weakly breaking (without significant entrainment of air) incoming waves, the experimental values of the height of the splash–up at the wall agree well with relevant experimental and calculated data for solitary waves.     

Formation and Amplification of Shock Waves in a Bubble “Cord”

The structure and dynamics of the wave field generated by a bubble system in the form of an axial bubble cylinder (cord) excited by a plane shock wave propagating along the axis in an axisymmetric shock tube are numerically examined. It is shown that consecutive excitation of oscillations of the bubble zone results in formation of a quasi-steady shock wave in the cord and in the ambient liquid. Results of the numerical analysis of the maximum amplitude of the resulting wave as a function of problems parameters are described.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 46–52, September–October, 2005.     

Evolution of a long wave in shallow water

Asymptotic expressions are obtained for the amplitude of a nonlinear long wave propagating in shallow water of variable (smoothly varying) depth.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 186–188, September–October, 1987.The authors are grateful to S. L. Lopatnikov for discussing their results.     

Destabilisation of flows with free surface by high-frequency waves

When wave packets of small but finite amplitude propagate in liquids and gases average fields (average flows, average displacements of the interfaces between different liquids, etc.) arise because of the nonlinearity of the media [l, 2], their amplitude being proportional to the square of the wave amplitude. The present paper is an investigation of such fields that arise when a packet of surface waves propagates on a horizontally inhomogeneous flow. It is shown that the average flows induced by the waves can strongly destabilize or stabilize the main flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 162–163, May–June, 1983.     

Propagation of surface gravity waves in a layer of electrically conducting liquid

The wave motion of a weakly conducting incompressible liquid in a transverse magnetic field is investigated within the framework of the nonlinear theory of magnetohydrodynamics. The influence of MHD interaction effects on harmonic perturbations of infinitesimal amplitude is analyzed and a long-wave equation of the Kortewegde Vries-Burgers type describing the evolution of weakly nonlinear perturbations of the free surface is derived. It is shown that the influence of the electrical conductivity leads to a change in both the dissipative and the dispersive properties of the system.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 173–175, July–August, 1989.     

Reflection of a sound wave by an evaporating surface

The reflection of a sound wave traveling through saturated vapor by the flat surface of the condensed phase is considered. It is shown that the intensity of the reflected wave is less than in the absence of evaporation and depends nonmonotonically on the angle of incidence, the position of the minimum being determined by the coefficient of condensation and independent of the viscous and heat conducting properties of the gas. The effect can be used to measure the condensation coefficient. The structure of the layers that arise near the surface is considered. A new type of acoustic flow with a velocity of the order of the amplitude of the speed of sound is found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. A, 149–156, July–August, 1988.     

Experimental investigation of nonaxisymmetric inertia waves in a rotating fluid

The properties of nonaxisymmetric waves in a fluid rotating as a rigid body in a cylindrical vessel has been studied experimentally. The method of resonance generation of the required mode is used, as this does not lead to restructuring of the basic flow. It is shown that resonance generation of the natural mode is an essentially unsteady process, whose initial stage conforms closely to the linear theory. It is established that after reaching a critical amplitude the wave ceases to grow and its original structure decays nonlinearly.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 176–180, January–February, 1987.     

Numerical simulation of the nonuniform breakup of capillary jets

The problem of the evolution of the surface of a jet up to the stage at which it breaks up into droplets is solved numerically for two initial wave disturbances. The wave number of one of these coincides with the wave number of the disturbance that grows most strongly according to the linear theory, while the wave number of the other is varied. The effect of the wave numbers and the amplitude ratio of the initial disturbances on the breakup time and the appearance of nonuniformity is investigated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 12–17, March–April, 1993.     

Wave motions in viscoelastic tubes. Forced oscillations

A characteristic of small blood and lymphatic vessels is the capacity of the wall to change its rheological properties and lumen by active contraction of the annular muscle cells contained in it [1–3]. A model of flow in the vessels taking this feature into account has been proposed in [4, 5], where a linear stability analysis is also given. A consequence of wall activity is the existence of auto-oscillatory flow conditions [6–8], which have also been discovered in the numerical solutions of the corresponding problems [9, 10]. Up to the present time flows have only been studied under steady conditions at the ends of the vessel and in the environment. The wall of an actual blood vessel is subject to various actions, frequently of a periodic nature: pressure pulsations at entry and rhythmically changing external forces applied from the surrounding tissues. Data exist on the sensitivity of vessels to transient actions [11–13], in particular on the relationship of their hydraulic resistance to frequency and amplitude of the action. There has been frequent discussion of the hypothesis that bv contraction of muscles in its walls or by external compression the vessel can act as a valveless pump [14, 15]. Within the framework of the quasione-dimensional approximation given below [4] the movement of liquid along a viscoelastic tube in the presence of small amplitude periodic external actions has been studied. A general solution of the problem has been constructed and concrete examples are given illustrating the features of forced wave motions in a tube having passive and active properties.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 4, pp. 94–99, July–August, 1984.     

Growth of artificially induced disturbances in a supersonic boundary layer

This work proposes a method of inducing artificial disturbances of adjustable amplitude in a supersonic boundary layer. Using the proposed method, an experimental study is made of the development of a three-dimensional wave packet of low intensity at a frequency of 20 kHz in the boundary layer of a flat plate at Mach number M = 2.0. The Fourier components of the wave packet are determined. The data obtained are compared with the results of calculating the linear stability of the supersonic boundary layer in a plane-parallel flow approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 37–43, September–October, 1984.     

Standing vortex waves in deep water

Standing vibrations of the free surface of an infinitely deep fluid exist in the presence of a weak (of the order of the wave amplitude) shear flow. As a result of the interaction with the flow the waves acquire a vorticity proportional to the cube of their amplitude.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 158–161, May–June, 1996.     

Diffraction of acoustic waves on the leading edge of a flat plate in a supersonic flow

A scheme is proposed for calculating the intensity of the acoustic wave field generated by diffraction of a beam of acoustic waves on a sharp leading edge of a flat plate in a supersonic flow. This wave field is shown to be a functional of the mass-flow amplitude distribution in the acoustic field at the level of the plate surface upstream of the latter. This distribution can be found on the basis of measurements. The discontinuity of the normal-to-plate component of the velocity perturbation on the plate edge plays an important role in determining mass-flow fluctuations along the plate. At large distances from the leading edge of the plate, where the diffraction wave on the boundary-layer edge degenerates into longitudinal acoustic waves, the amplitude of mass-flow fluctuations decreases with increasing distance from the leading edge and depends on wave orientation.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 64–70, March–April, 2005.     

Internal waves in a two-layer electrically conducting fluid in the presence of a magnetic field

The propagation of linear and nonlinear internal waves along the interface between two weakly conducting media differing in density and electrical conductivity is investigated and the influence of MHD interaction effects on their characteristics is analyzed. It is shown that in this system the waves propagate with dispersion and dissipation, and for harmonic waves of infinitesimal amplitude there exists a range of wave numbers on which propagating modes do not exist. For waves of finite amplitude a nonlinear Schrödinger equation with a dissipative perturbation is obtained and its asymptotic solution is found. It is established that the presence of electrical conductivity and an applied magnetic field leads to a decrease in the amplitude and the frequency of the envelope of the wave train.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 104–108, September–October, 1990.     

Generation of secondary instability modes in the interaction of a Tollmien-Schlichting wave with isolated roughness

The infinite plane channel flow arising from the impingement of a plane instability wave of finite amplitude on isolated three-dimensional wall roughness is considered. The problem of the transformation of perturbations developing on the roughness in growing modes of secondary instability is solved. This problem describes the development of perturbations leading to the occurrence of a turbulent wedge. Simple relations describing the flow at large distances from the roughness are obtained. From these relations it follows that the angle at the vertex of the turbulent wedge is determined by the amplitude of the impinging wave, while the value of the perturbations generated is proportional to the roughness volume.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 28–38, May–June, 1995.The work was carried out with the financial support of the Russian Foundation for Fundamental Research (project No. 93-013-17613).     

Interaction of a Shock Wave with a Spherical Gas–Liquid Cluster

Experimental studies were performed of the interaction of a plane shock wave with a spherical gas–liquid cluster (polyurethane foam ball saturated with a bubbly liquid) in a vertical shock tunnel filled with a liquid. The cluster was shown to generate a solitary pressure wave of large amplitude.     

Resonance properties of two-dimensional wave disturbances in a boundary layer

The nonlinear development of disturbances of the traveling wave type in the boundary layer on a flat plate is examined. The investigation is restricted to two-dimensional disturbances periodic with respect to the longitudinal space coordinate and evolving in time. Attention is concentrated on the interactions of two waves of finite amplitude with multiple wave numbers. The problem is solved by numerically integrating the Navier-Stokes equations for an incompressible fluid. The pseudospectral method used in the calculations is an extension to the multidimensional case of a method previously developed by the authors [1, 2] in connection with the study of nonlinear wave processes in one-dimensional systems. Its use makes it possible to obtain reliable results even at very large amplitudes of the velocity perturbations (up to 20% of the free-stream velocity). The time dependence of the amplitudes of the disturbances and their phase velocities is determined. It is shown that for a fairly large amplitude of the harmonic and a particular choice of wave number and Reynolds number the interacting waves are synchronized. In this case the amplitude of the subharmonic grows strongly and quickly reaches a value comparable with that for the harmonic. As distinct from the resonance effects reported in [3, 4], which are typical only of the three-dimensional problem, the effect described is essentially two-dimensional.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 37–44, March–April, 1990.     

Propagation of modulated nonlinear waves in a relaxing gas-liquid mixture

The propagation of nonstationary weak shock waves in a chemically active medium is essentially dispersive and dissipative. The equations for short-wavelength waves for such media were obtained and investigated in [1–4]. It is of interest to study quasimonochromatic waves with slowly varying amplitude and phase. A general method for obtaining the equations for modulated oscillations in nonlinear dispersive media without dissipation was proposed in [5–8]. In the present paper, for a dispersive, weakly nonlinear and weakly dissipative medium we derive in the three-dimensional formulation equations for waves of short wavelength and a Schrödinger equation, which describes slow modulations of the amplitude and phase of an arbitrary wave. The coefficients of the equations are particularized for the considered gas-liquid mixture. Solutions are obtained for narrow beams in a given defocusing medium as well as linear and nonlinear solutions in the neighborhood of a diffraction beam. A solution near a caustic for quasimonochromatic waves was found in [9].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 133–143, January–February, 1980.