Role of two-dimensional acoustic wave cutoff in the instability of subsonic MHD flows

One of the important factors affecting the structure of the natural vibrations and the conditions under which they build up in an inhomogeneous subsonic flow may be the cutoff of non-one-dimensional sound waves expressed in the strong reflection of such waves from the critical sections (caustics). In this study the case of natural two-dimensional acoustic perturbations in an inhomogeneous subsonic conducting gas flow in the presence of critical sections is subjected to an asymptotic analysis. Special attention is paid to the conditions of growth of the two-dimensional acoustic perturbations in the internal resonator formed by two critical sections and the walls of an MHD channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 26–36, March–April, 1988.The authors are grateful to seminar participants L. M. Biberman and G. A. Lyubimov for useful discussions.     

Stability of pipe flow with blowing

The stability of self-similar flows in a porous circular pipe [1–4] with respect to classical and self-similar perturbations of axisymmetric and nonaxisymmetric form is investigated. The case of blowing through the porous lateral surface is examined. Two formulations of the linear stability problem are considered and stability in the sense of self-similar evolution is also investigated. The limiting stability situations are analyzed. Relations for the critical values of the blowing rate parameters are presented for all the types of perturbations investigated. It is shown that nonaxisymmetric classical perturbations are the most dangerous.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 63–71, January–February, 1989.     

Ion distribution function at the boundary with an electrode

The ion distribution function is found in the case in which the Langmuir layer freely passes the ions incident from the plasma while the reverse ion flux is zero. These conditions are realized near the cathode in an arc discharge and at the surface of a probe operating on the ion branch of the characteristic. The electric field outside the Langmuir layer is assumed small. We obtain the connection between ion current and plasma density at the boundary with the electrode, the expressions for the ion mean kinetic energy and for the mean energy removed from the plasma by the ion, which differ markedly from the corresponding expressions in the Maxwellian distribution case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 47–54, May–June, 1969.     

Influence of the initial spatially inhomogeneous temperature perturbations on vibrational relaxation dynamics

The vibrational relaxation of a nonequilibrium molecular gas (T_V>T) plays an important role in the physics of gas lasers, laser chemistry [1], and plasma chemistry [2]. This paper is devoted to an analysis of the dynamics of V-T relaxation with spatially inhomogeneous perturbations of the translational temperature taken into account.Translated from Zhurnal Prikladnoi Mekhaniki i Technicheskoi Fiziki, No. 6, pp. 77–80, November–December, 1984.     

Plasma density and electeic field strength distributions at a boundary with an electrode

Close to the cathode in an arc discharge, or to the surface of a probe operating on the ionic branch of its characteristic, conditions are obtained under which the Langmuir layer freely passes ions coming from the plasma, while the reverse ion flow is virtually zero. The plasma density, ion distribution, and electric fieid-strength close to the electrode are found in the present paper. The extrapolated length is evaluated for the plasma density. The absolute value of the electric field strength increases logarithmically at the boundary with the electrode.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No, 2, pp. 4–6, March–April, 1970.     

Investigation of lateral forces and moments in the case of asymmetric gas flows in nozzles

Supersonic three-dimensional flows of a gas in a nozzle are studied. The main attention is devoted to the study of lateral forces and moments resulting from asymmetric perturbations of the contour of an axisymmetric conical or profiled nozzle or due to asymmetric perturbations of the parameters at some section of the nozzle. The approach is comprehensive — through a finite-difference numerical method, the method of small perturbations, and experimentally.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 70–85, March–April, 1980.     

Three-dimensional instability of an elliptic Kirchhoff vortex

The instability of a Kirchhoff vortex [1–3] with respect to three-dimensional perturbations is considered in the linear approximation. The method of successive approximations is applied in the form described in [4–6]. The eccentricity of the core is used as a small parameter. The analysis is restricted to the calculation of the first two approximations. It is shown that exponentially increasing perturbations of the same type as previously predicted and observed in rotating flows in vessels of elliptic cross section [4–9] appear even in the first approximation. As distinct from the case of plane perturbations [1-3], where there is a critical value of the core eccentricity separating the stable and unstable flow regimes, instability is predicted for arbitrarily small eccentricity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 40–45, May–June, 1988.     

Dynamic stabilization of thin plasma filaments

The Routh function is found for a fine plasma filament (toroidal and rectilinear), experiencing smooth long-wave hosepipe and constrictive perturbations in the case in which the external magnetic field is a combination of quadrupole and longitudinal fields. Different variants of dynamic stabilization of a filament are briefly discussed. Combined dynamic stabilization of a straight filament with an alternating current by means of constant quadrupole and longitudinal fields is investigated by averaging with respect to rapid oscillations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, pp. 24–31, January–February, 1970.In conclusion the author wishes to thank M. L. Levin for useful discussions and advice.     

Stability of Thermocapillary Flow in a Flat Layer with Allowance for the Soret Effect

The stability of thermocapillary two-component liquid flow is studied taking into account thermal diffusion. An explicit expression is obtained to construct neutral Marangoni numbers under the assumption of monotonicity of perturbations. The thermocapillary and hydrodynamic instability mechanisms are considered. It is shown that plane perturbations are the greatest hazard to the stability of return flow.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 86–92, September–October, 2005.     

The nonlinear evolution of two-dimensional and three-dimensional waves in mixing layers

The authors consider problems connected with stability [1–3] and the nonlinear development of perturbations in a plane mixing layer [4–7]. Attention is principally given to the problem of the nonlinear interaction of two-dimensional and three-dimensional perturbations [6, 7], and also to developing the corresponding method of numerical analysis based on the application to problems in the theory of hydrodynamic stability of the Bubnov—Galerkin method [8–14].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhldkosti i Gaza, No. 1, pp. 10–18, January–February, 1985.     

Stability of plane magnetohydrodynamic couette flow with asymmetrical velocity profile

The hydrodynamic stability of plane magnetohydrodynamic Couette flow with asymmetrical velocity profile formed by a transverse magnetic field is investigated within the framework of the linear theory. The complete spectrum of the small perturbations is studied for the characteristic Hartmann numbers. The perturbations are classified in accordance with their phase velocity at large wave numbers. It is established that the stability of the flow is controlled by only one type of perturbations. The critical parameters of the problem are determined. The instability in question recalls the instability of Hartmann flow against asymmetrical perturbations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 12–18, May–June, 1971.The author thanks M. A. Gol'dshtik for interest in the work and V. A. Sapozhnikov and V. N. Shtern for useful discussions.     

The stability of weakly ionized D-type waves in the case of an optically thick layer of ionized gas behind the wave front

The stability of weakly ionized D-type waves is discussed in the case of a layer of plasma behind the front of a Lyman continuum of hydrogen which is optically thick for quanta. It is shown that stable oscillations are possible. For the characteristic parameters of an interstellar gas, viscous effects may have a stabilizing influence only on shortwave perturbations with wavelength LL₀ (L₀ corresponds to neutral oscillations).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 12–16, November–December, 1971.     

The spectrum of small perturbations in plane couette-poiseuille flow

The spectrum of small perturbations of plane Couette-Poiseuille flow is studied. The perturbations are classified according to their behavior at large wave numbers. The changes in the spectrum are traced as the transition is made from Poiseuille to Couette flow at fixed Reynolds number. The behavior of the perturbations is considered as a function of the Reynolds number.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 63–67, March–April, 1971.The author wishes to thank M. A. Gol'dshtik for his attention to the paper, V. A. Sapozhnikov for useful discussions, and V. N. Shtern for his great assistance and help with the paper and for useful discussions.     

Perturbation of magnetic field by a nonstationary gamma-ray source

The perturbations of a magnetic field in the neighborhood of a nonstationary source of gamma rays, and also the radio emission associated with these perturbations, are investigated on the basis of the results from numerical integration of the system of Maxwell equations describing the space and time variations of the fields.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 141–146, March–April 1975.     

Influence of a floating elastic plate on the surfaceeffects of internal waves generated by motion of a source in a non-homogeneous liquid

Perturbations of the surface of an exponentially stratified liquid of finite depth, free or covered by an elastic plate, are studied on the assumption that the perturbations are caused by internal waves generated by the steady motion of a constant -intensity source. The dependence of the spatial distribution of perturbations on the plate properties, velocity and the submersion depth of the source is considered.Sevastopol. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 118–125, March–April, 1995.     

Hard excitation of auto-oscillations in a Hagen-Poiseuille flow

Sufficiently powerful perturbations of the flow of a liquid moving in circular pipes results in turbulence, starting with Reynolds numbers of the order of 2200–2300 [1]. It has been established theoretically [2, 3] that the flow of a viscous incompressible liquid in a pipe of circular section (Hagen-Poiseuille flow) is stable with respect to infinitesimally small perturbations for all Reynolds numbers. Attempts to obtain finite-amplitude flow instability by considering only two-dimensional perturbations [4, 5] were also unsuccessful. This paper shows that the considered flow is unstable with respect to three-dimensional perturbations of finite amplitude.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 181–183, September–October, 1984.The author wishes to express sincere gratitude to G. I. Petrov and S. Ya. Gertsenshtein for their interest in his work.     

Relaxation of a liquid layer under the action of capillary forces

The theory of creeping motion is used to study the relaxation of an infinite viscous fluid layer (membrane) of nonuniform thickness. The propagation of boundary perturbations in a semi-infinite layer under the action of surface-tension forces is also considered. The layer has at least one common boundary with a gas. It is found that relaxation processes of an infinite layer or the propagation of boundary perturbations inside a bounded layer are non-monotonic, and that wave-like surface perturbations always arise. Relaxation times are determined. Maximum distances are found over which separate regions of the layer can affect each other.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, pp. 73–77, January–February, 1970.The author wishes to thank V. G. Levich for discussions.     

Development of two-dimensional perturbations on the surface of a tangential discontinuity

A study is made of the asymptotic behavior at long times of initially localized small two-dimensional perturbations of the interface of two fluids in the presence of a tangential discontinuity of the velocity; surface tension is taken into account. The development of one-dimensional perturbations was considered earlier in [1]. The asymptotic behavior of the perturbed region is found, i.e., in the xyt space there is found a cone with apex at the origin such that perturbations tend to infinity with increasing t along rays within the cone, while perturbations tend to zero along the remaining rays. Conditions are found under which the instability of the tangential discontinuity is not absolute, i.e., when these conditions are satisfied, flows with tangential discontinuity of the velocity can take place. These conditions, like the shape of the cone, do not depend on the magnitude of the surface tension.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 12–16, May–June, 1979.     

Flexural perturbations of free jets of maxwell and Doi-Edwards liquids

Flexural perturbations of high-velocity free jets of drop liquids moving in air are reinforced by the fact that the air pressure on the concave sections of the jet surface is greater than on the convex sections. The linear and nonlinear stages of development of flexural perturbations were studied in [1–5] for viscous Newtonian fluids. The effect of elastic stresses in the fluid on the growth of flexural perturbations of jets was first examined in [6], where it was assumed in an analysis of the growth of small disturbances that surface tension was constant along the jet, i.e., the investigators actually studied a tensed string. The studies [7, 8] examined the linear stage of growth of flexural perturbations of jets of Maxwell liquids. Our goal here is to analyze the dynamics of long-wave flexural perturbations of jets of viscoelastic fluids in both the linear and nonlinear stages of development. The rheological behavior of the fluid is described by two models — the phenomenological (Maxwell) model and the physical-molecular (Doi-Edwards) model. It is shown that the disturbances are oscillatory in character in the nonlinear stage of development. Meanwhile, the results of calculations performed with the Maxwell (M) and Doi-Edwards (DE) rheological models in the given problem agree with each other quantitatively as well as qualitatively.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 43–53, November–December, 1986.     

Nonlinear stability of two-dimensional steady flows of an ideal fluid with constant vorticity and their axisymmetric analogs

Flows with constant vorticity are widely used as local models of more complicated flows [1]. In many cases, such flows are stable against finite two-dimensional perturbations. In particular, the inviscid plane-parallel Couette flow has the property of nonlinear stability. Similar treatment of a class of axisymmetric flows yields nonlinear stability of a spherical Hill vortex and inviscid Poiseuille flow in a circular tube with respect to axisymmetric perturbations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 16–21, October–December, 1981.