Plane problem of wave motions occurring in a continuously stratified fluid during the flow around a submerged body

The plane stationary problem of wave motions occuring in the flow of a uniform inviscid incompressible gravity fluid with an arbitrary continuous (stable) change in density with depth around submerged sources and sinks of equal intensity is investigated in a linear formulation. An analysis of the structure of the wave motion in a flow with an arbitrary density change is performed in [1].Paper presented at the First Soviet-American Symposium on Internal Waves in the Ocean, Novosibirsk, December 3–8, 1976.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 148–152, July–August, 1978.     

Arbitrary body,close to a wedge,in a supersonic flow

The problem of supersonic flow around bodies close to a wedge was first discussed in the two-dimensional case in [1]. The shock wave was assumed to be attached, and the flow behind it to be supersonic; taking this into account, the angle of the wedge was assumed to be arbitrary. The surface of the body was also arbitrary, provided that it was close to the surface of the wedge. In solution of the three-dimensional problem, there was first considered flow around two supporting surfaces with only slightly different angles of attack [2], and then around a delta wing [3, 4]. In all these articles, the Lighthill method was used to solve the Hilbert boundary-value problem [5, 6]. A whole class of surfaces of bodies with arbitrary edges, under the assumption that the surface of the body was cylindrical, with generatrices directed along the flow lines of the unperturbed flow behind an oblique shock wave, was discussed in [7]. In the present work, the problem is regarded for a broad class of surfaces of bodies, using a new method which generalizes the results of [8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 109–117, July–August, 1974.The author thanks G. G. Chernyi for his direction of the work.     

Sensitivity of a supersonic boundary layer to acoustic disturbances

The results obtained by the authors in [1] are extended to the case of arbitrary angles of incidence of the external wave. This is not a trivial generalization, since the acoustic scattering undergoes a qualitative change. It is possible to distinguish two excitation channels: the first is connected with the diffraction of the acoustic wave by the spatial inhomogeneity resulting from the displacing action of the boundary layer, and the second with the presence of concentrated acoustic field sources associated with the scattering of the wave at the leading edge. The latter makes the principal contribution to the initial amplitude of the unstable modes when the angles of incidence of the sound are substantially different from zero. At low angles of incidence there is a singularity which can be revealed by introducing narrow intervals in the neighborhood of the limiting values of the wave numbers, where the two excitation channels are approximately equivalent. It is possible to obtain composite expressions for the initial amplitudes of the unstable modes uniformly valid for all angles of incidence of the acoustic wave.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 40–47, January–February, 1992.     

Approximate method of determining liquid oscillation frequencies in cavities of revolution

Variational methods [1–4], which require the use of computers, are widely used at present for determining the oscillation frequencies of liquid partially filling an arbitrary cavity of revolution. A technique is given in [5] for the approximate solution of this problem for a cavity which differs little from a cavity for which the solution is known. In the present paper we obtain an approximate first-order differential equation for the frequency squared, using the filling level as the independent variable. Calculations were made using this method for several cavities (sphere, cylinder with spherical base, cone with varying apex angles, torus). Comparison of these results with the results obtained experimentally by other theoretical methods shows that the proposed method is sufficiently accurate for engineering applications.The author wishes to thank I. V. Kolin for carrying out the calculations.     

Diffraction of an arbitrary acoustic wave by a strip of finite width

The problem of the diffraction of an arbitrary acoustic wave by a strip of finite width is solved. The solution is constructed by means of a generalization of the previously obtained integral for the problem of the diffraction of acoustic waves by a half-plane [5]. The problem of the diffraction of an arbitrary acoustic wave by the Riemannian manifold corresponding to the strip of finite width is first found. After this, by substitution of the values of the polar angle a solution is obtained for the reflected wave associated with diffraction on the Riemannian manifold, and then the boundary conditions on the surface of the strip are satisfied by means of a linear combination of these solutions. The problem of the diffraction of an arbitrary acoustic wave by a slit of finite width could be constructed in exactly the same way.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 171–175, March–April, 1991.     

Diffraction of a spherical acoustic wave on a cone

An exact analytic solution of the problem of diffraction of a plane acoustic wave on a cone of arbitrary aperture angle was obtained and studied in [1]. For the case of spherical wave diffraction on a cone a formula is known [2] which relates the solutions of the spherical and plane wave diffraction problems. This study will employ the results of [1, 2] to derive and investigate an exact analytical solution of the problem of diffraction of a spherical acoustic wave on a cone of arbitrary aperture angle. Results of numerical calculations will be presented and compared with analogous results for a plane wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 200–204, March–April, 1976.The author is indebted to S. V. Kochura for her valuable advice.     

Hypersonic flow past a wing at large angles of attack with detached shock wave

The thin shock layer method [1–3] has been used to solve the problem of hypersonic flow past the windward surface of a delta wing at large angles of attack, when the shock wave is detached from the leading edge (but attached to the apex of the wing) and the velocity of the gas in the shock layer is of the same order as the speed of sound. A classification of the regimes of flow past a delta wing at large angles of attack has been made. A general solution has been obtained for the problem of three-dimensional hypersonic flow past the wing allowing for nonequilibrium physicochemical processes of thermal radiation of the gas at high temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 149–157, May–June, 1985.     

Effect of the adiabatic exponent on the reflection of shock waves

The effect of the adiabatic exponent on certain features of shock-wave reflection is analyzed with particular reference to the nature of the dependence of the critical angle on the incident wave intensity. The latter is shown to increase with increasing shock-wave intensity. Limit cases of weak shock waves at any arbitrary adiabatic exponent and of strong shock waves with the adiabatic exponent equal to unity are analytically investigated. Results of calculations of the critical angle for various adiabatic exponents throughout the possible range of incident wave intensities are presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, pp. 62–66, January–February, 1970.     

Forces exerted by a weak shock wave on a wing of complicated shape in plan at supersonic velocities

A method is presented for calculating the supersonic distributed and total aerodynamic characteristics of a wing of complicated shape in plan, including a wing having the shape of an aircraft in plan which encounters a weak shock wave of arbitrary orientation. The problem is solved in the linear formulation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 121–127, July–August, 1982.     

Stokes waves on a cavity surface in a rotating fluid

The axisymmetric flow of an inviscid incompressible fluid rotating about a cavity with constant pressure is considered. Due to the centrifugal force, on the cavity surface waves may exist, in particular, waves with a break in the wave base where the cavity meridional sections form the angle 2/3, i.e. Stokes waves. A method of finding these waves from the boundary-value problem for the fluid velocity potential is described. For an infinite cavity, the dependence of the wave parameters on the cavitation number, calculated using the pressure in the cavity, is given.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 105–110, November–December, 1996.     

Theory of anomalous modes of regular reflection of shock waves

It is well known [1, 2] from numerical calculations of the reflection of a shock wave for a diatomic gass that in some cases regular reflection is accompanied by higher pressures than the pressure of normal reflection (anomalous modes of regular reflection). A theory explaining this phenomenon is presented in this paper. It is shown that if the adiabatic exponent is larger than some critical value, then for any shock wave intensity there exists a finite range of angles of incidence for which anomalous reflection modes occur. If the adiabatic exponent is smaller than this critical value, anomalous reflection occurs only for shock waves whose intensity is smaller than some characteristic value dependent on the adiabatic exponent. Explicit formulas are obtained which relate the angle and pressure of reflection of a shock wave to the initial parameters of the problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 117–125, September–October, 1973.The author thanks V. A. Belokon' for stimulating discussions.     

Development of taylor instability in compressible conducting media in a magnetic field

Article [1] is devoted to the investigation of the interface of viscous incompressible conducting media in the presence of a current and with a magnetic field with a small magnetic Reynolds number. Article [2] discusses the stability of a contact discontinuity in compressible media. In this article, in an analysis of the case of long-wave vibrations in the region z<0, the boundary condition is unsatisfactorily met. Therefore, in this part of it the author actually considered a problem with a mass force f=(0, 0, –g sign z) instead of f=(0, 0, –g). The present, article considers the stability of the interface of compressible conducting media in a magnetic field. It is postulated that the magnetic intensity can undergo a discontinuity at this boundary. The article gives the dependence of the maximal increment of the rise in the instability on the determining parameters. An analysis is made of the stability of a contact discontinuity as a function of the angles formed by the wave vector and the intensity of the magnetic field. The stabilizing effect of the walls on the stability is demonstrated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, 15–19, September–October, 1975.The author thanks A. G. Kulikovskii for his aid in stating the problem and for his continuing interest in the work.     

The existence of a discontinuity in the profile of a slow shock magnetohydrodynamic wave

An analysis is made of the structure of the profile of a slow shock magnetohydrodynamic wave of arbitrary intensity in a nonviscous medium. It is shown that the condition for the formation of a discontinuous profile coincides with the condition for the creation of an isothermal discontinuity in conventional gas dynamics.Translated from Zhurnal Prikladnoi Mekhanikii Tekhnicheskoi Fiziki, No. 2, pp. 3–9, March–April, 1971.The authors thank G. Ya. Lyubarskii for useful advice and discussions of the questions touched upon in this paper.     

Numerical modeling of supersonic flow over wings with varying aspect ratio on a broad range of angles of attack using the law of plane sections

A method and a program based on it for solving the problem of flow in the neighborhood of bodies of different shapes introduced into a high-supersonic stream at arbitrary angles of attack are proposed. The equations of the law of plane sections are integrated by Godunov's method. It is shown that the region of applicability of Sychev's theory is much broader than indicated in [1].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 113–120, March–April, 1992.     

Unsteady reflection of a shock wave from a body with a cylindrical recess

In a number of cases of supersonic flow past bodies with recesses pulsations in the flow arise [1–3]. Experiments [4, 5] indicate that stabilization of the steady supersonic flow past the body with a recess on which a shock wave is incident takes place after a series of oscillations of the bow wave. Numerical calculation of the interaction of a supersonic jet with a cylindrical cavity [6] reveals that damped pressure pulsations arise inside the cavity if the jet is homogeneous, and undamped pulsations it is inhomogeneous. The authors explain the damping of the pulsations by the influence of artificial viscosity. This paper investigates experimentally and theoretically (by numerical methods) the oscillations of the bow shock wave and the parameters of the flow behind it in the case of unsteady reflection of a shock wave from a body with a cylindrical recess turned towards the flow. The problem is posed as follows. A plane shock wave with constant parameters impinges on a cylinder with a cavity. The unsteady flow originating from this interaction is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 199–202, September–October, 1984.     

Mode-III crack kinking under stress-wave loading

A horizontally polarized step-stress wave is incident on a semi-infinite crack in an elastic solid. At the instant that the crack tip is struck, the crack starts to propagate in the forward direction, but under an angle κπ with the plane of the original crack. In this paper a self-similar solution is obtained for the particle velocity of the diffracted cylindrical wave field. The use of Chaplygin's transformation reduces the problem to the solution of Laplace's equation in a semi-infinite strip containing a slit. The Schwarz-Christoffel transformation is employed to map the semi-infinite strip on a half-plane. An analytic function in the half-plane which satisfies appropriate conditions along the real axis, can subsequently be constructed. The Mode-III stress-intensity factor at the tip of the kinked crack has been computed for angles of incidence varying from normal to grazing incidence, for angles of crack kinking defined by -0.5?κ?0.5, and for arbitrary subsonic crack tip speeds.     

Pressure of an arbitrary acoustical wave on a plane

A study is made of the perturbed flow of a gas, brought about by a weak shock wave, falling on a fixed surface at an arbitrary angle. A solution determining the field of the velocities behind the front of the wave in an initially boundary-value problem with movable boundaries for a three-dimensional wave equation is obtained in the form of a double integral, containing an arbitrarily given function determining the parameters of the gas in the incident wave. The region of integration is a region included within an ellipse, whose relative eccentricity is equal to the sine of the angle of inclination of the front of the incident wave. A formula is obtained for the distribution of the pressure at the plane.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 114–116, January–February, 1975.     

Wave scattering from an interface crack in multilayered piezoelectric plate

This paper focuses on the theoretical basis for the study of wave scattering from an interface crack in multilayered piezoelectric media. The materials are taken to be anisotropic with arbitrary symmetry. Based on the Fourier transform technique together with the aid of the stiffness matrix approach, the boundary value problem of wave scattering is reduced to solving a system of Cauchy-type singular equations. The intensity factors and crack opening displacements are defined in terms of the solutions of the corresponding integral equations for any incident frequencies and incident angles. Numerical results are presented. The effects of incident frequencies and crack location on both the major and coupling intensity factors are illustrated. The influence of the piezoelectricity is also shown.     

Irregular reflection of a strong shock wave from a thin wedge

The problem of irregular reflection of a strong shock wave from a rigid wall has been studied [1–3] mainly within the framework of the linear theory. It has been found that near the front of a shock wave there exist a region of large gradients of gasdynamic parameters in which the linear theory is no longer valid [4]. In the present paper we consider the nonlinear problem of Mach reflection when there is interaction between a shock wave of high intensity and a thin wedge. The solution of the problem is constructed on the assumption that the ratio of densities along the front of the impinging shock wave is small [5, 6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 55–61, September–October, 1974.In conclusion, the authors wish to express their gratitude to A. A. Grib for his interest in the subject and to L. A. Rumyantsev for his help in carrying out the calculations.     

Effect of electron cyclotron waves on the structure of a weak collisionless shock wave

An analytic study is made of the structure of a weak collisionless shock wave propagating in a magnetized plasma at right angles to the magnetic field. Dissipation is produced by an instability associated with electron cyclotron oscillations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti 1 Gaza, No. 2, pp. 187–190, March–April, 1982.I thank V. B. Baranov for suggesting the problem and constant interest in the work, and also A. V. Ershov for discussing the results.