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.     

Development of perturbations at the interface between two liquids

The asymptotic behavior is studied in the case of large times of initially localized, one-dimensional, small perturbations of the interface between two liquids in the presence of a tangential velocity discontinuity, taking account of surface tension and the force of gravity. The asymptotic behavior of the perturbed region is found; i.e., on the plane x, t a sector is shown with vertex at the origin of the coordinates, inside of which the perturbations tend to infinity with increase of t, and outside of which the perturbations tend to zero, and the velocities of motion of the boundaries of the perturbed region are calculated. The conditions are shown for which the instability of the tangential discontinuity will not be absolute; i.e., when they are fulfilled, flows with a tangential velocity discontinuity can occur. For the case where the effect of the force of gravity can be neglected, these conditions are independent of the magnitude of the surface tension.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 46–49, September–October, 1977.     

Taylor instability in the discontinuity between two fluids in an electromagnetic field

The gravitational instability of the discontinuity between two compressible (or incompressible) fluids is investigated. The fluids are exposed to an electromagnetic field, and one of them is nonconducting, while the other has a finite conductivity. The magnetic Reynolds number is assumed to be small. It is shown that in contrast to the cases investigated in [1, 2], where compressible, infinitely conducting fluids were considered on both sides of the discontinuity, in the present case the electromagnetic field is not able to stabilize the discontinuity and the perturbations can propagate in fixed directions. The presence of walls inhibits the perturbation growth [2, 3], while their conductivity does not affect the instability of the discontinuity. The greatest perturbation growth is found to occur in a wave propagating along the magnetic field, when the electromagnetic field does not influence these perturbations in the case of incompressible fluids, but does influence them in the compressible case.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 24–28, September–October, 1976.The author wishes to express his appreciation to A. A. Barmin and A. G. Kulikovskii for suggesting the problem and for their continued interest in the work.     

Absolute, convective, and global instability of a magnetic liquid jet

An infinite or semi-infinite jet of non-conductive magnetic liquid in a uniform longitudinal magnetic field can be absolutely or convectively unstable for different values of the flow parameters. Though the higher field inhibits the absolute instability, this inhibition is maximum at some field intensity. A critical value of the surface tension exists, above which the instability is absolute for any intensity of the field. If the jet has a large but finite length and proper boundary conditions are held at its beginning and end, it is always globally unstable. The unstable global mode is based on a pair of waves that propagate in opposite directions and reflect from one into the other at the flow boundaries.     

Structure and stability of the interface in a magnetizable fluid

The problems of interface stability in magnetizable and polarizable fluids are considered in the case of the surface tension tensor dependent on the electromagnetic field strength. For describing this dependence the model proposed by A.N. Golubyatnikov (1986) is used. The investigation of the internal interface structure showed that for single-component systems, as a rule, the dependence of the surface tension on the field strength corresponds to surface phase properties paramagnetic in the normal and diamagnetic in the tangential direction. It is shown that within the framework of the model adopted the thermodynamic stability of the surface depends on the thickness of the interphase layer. Necessary stability conditions are obtained for plane interfaces in media with a constant magnetic permeability outside the interphase layer. The problem of stability of the horizontal free surface of an ideal magnetic field in an external magnetic field (similar to the problem of stability of the horizontal interface of two polarizable fluids in an external electric field) is solved for an arbitrary orientation of the external field relative to the interface. The stability loss is now accompanied by qualitative effects absent in the case of the surface tension tensor independent of the electromagnetic field strength.     

Flows of a conducting incompressible liquid in an arbitrary region with a strong magnetic field

A general solution is obtained describing the flow of a conducting liquid in an arbitrary region, which is bounded by nonconducting walls, in the case when it is possible to neglect inertial and viscous forces in comparison with the magnetic field, as well as the induced magnetic field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 144–150, May–June, 1973.     

Motion of a drop with allowance for thermocapillary forces

A study is made of the motion of a drop in a viscous medium of nonuniform temperature when the dependence of the surface tension on the temperature at the interface of the two media gives rise to additional tangential stresses leading to thermocapillary convection in fluids. The motions of a spherical drop and a deformed drop (when the surface of the drop is determined in the process of finding the solution) are considered. The shape of the drop surface is calculated for different values of the parameters of the problem. Dependences are obtained for the Reynolds number of the thermocapillary drift of drops in the absence of body forces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 80–86, July–August, 1982.     

Long waves in two superposed layers of magnetic fluid

The equations and boundary conditions describing plane-parallel potential motions of two superposed layers of stably stratified magnetic fluid are formulated. The fluid is assumed to fill entirely a horizontal plane channel in the presence of a uniform longitudinal magnetic field induced by external sources. With reference to the case of long waves propagating over the interface between the upper and lower layers, it is shown that the action of the field may be interpreted as the result of an increase in the nondimensional surface tension by an amount proportional to the square of the undisturbed field. In the linear formulation the effect of the field on the evolution of a long-wave perturbation of the initially plane interface is investigated. Korteweg-de Vries equations with quadratic and cubic nonlinearities are derived and the action of the field on the internal solitary waves is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 126–133, May–June, 1993.     

Development of two- and three-dimensional perturbations in the case of an ionization instability in a channel with nonconducting walls

An lonization instability of a plasma bounded by nonconducting walls is investigated taking into account electron thermal conduction. The wave vector is considered directed at some angle to the magnetic field direction. Perturbations with a wave vector orthogonal to the magnetic field induction vector turn out to be most unstable. A relatively simple formula to compute the neutral curve separating the stability and instability domains is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 119–123, May–June, 1976.     

Transport phenomena in a knudsen molecular gas in a magnetic field

We consider the behavior of a strongly rarefied (Knudsen) polyatomic gas between two surfaces that have different temperatures in a magnetic field. We show that in the magnetic field H there can arise a flux of gas and a heat flux along the surfaces (odd functions in H), and also normal and tangential forces on the walls.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 124–130, January–February, 1979.     

磁场对激波冲击R22重气柱作用过程影响的数值模拟

为研究平面入射激波与磁化R22重质圆形气柱的作用过程,首先通过数值方法得到了不同初始条件下激波诱导R22气柱的Kelvin-Helmholtz (KH)及Richtmyer-Meshkov (RM)不稳定性导致的重气柱变形过程,并详细讨论了不同情况下透射激波在气柱内聚焦诱导射流的过程;然后在加入磁场的情况下,采用CTU+CT算法进行数值模拟,以保证数值结果满足任意时刻磁场的散度为零。计算结果表明:磁场对激波诱导R22气柱不稳定性具有抑制作用;法向磁场和流向磁场都可以很好地抑制RM不稳定性;对于KH不稳定性,法向磁场的控制效果更好,不仅可以抑制界面上涡串的卷起,还可以阻止主涡的发展,而流向磁场做不到后者;磁场对射流影响不大,射流处的磁能量可以一定程度上抑制射流的衰减,同时法向磁场可以减小聚焦时压力及速度峰值。     

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.     

Two-dimensional spreading of a cloud of conducting gas in a magnetic field self-similar solution

A self-similar solution of the problem on the spreading in a magnetic field of a cloud of conducting gas, having the shape of a cylinder of noncircular cross section, is constructed. The cylindrical surface of the gas is restrained by a nonconducting sheath that spreads according to a prescribed law. The shape of the transverse cross section of the cylindrical cloud is determined from the solution. Cross sections obtained for a concrete case are represented in graphic form.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 29–36, March–April, 1973.In conclusion the author thanks V. I. Khonichev for assistance with the numerical calculations.     

On the spectrum of magnetic field and scalar impurity fluctuations in acoustic turbulence

The fluctuations of a magnetic field in acoustic turbulence are examined. An equation is derived for the spectral tensor of homogeneous magnetic field fluctuations. In a certain limit case the spectrum of steady-state pulsations is obtained in the presence of an external source. It is shown that three kinds of spectra exist in an inertial subdomain, each of which corresponds to a definite domain in wave space. Analogous results have been obtained for the fluctuations of a homogeneous scalar impurity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 26–31, March–April 1971.In conclusion, the author grateful to R. Z. Sagdeev for discussing the results obtains at a seminar.     

Surface shape of a magnetic liquid drop near the edge of a magnetic wedge

The two-dimensional problem of the shape of the free surface of a magnetic fluid in a gravity field, a uniform external magnetic field and the nonuniform field of a magnetized metal wedge is considered. The results of numerically calculating the shape of the free surface of a magnetic liquid drop retained on an inclined plane by the field of a magnetizing wedge are presented. The changes in the shape of the free surface of an infinite volume of magnetic liquid near the edge of a wedge with increase in the external field are investigated. It is shown that for a certain critical field some of the magnetic liquid separates and adheres to the edge of the wedge. Experimental data on the determination of the maximum cross-sectional area of a drop retained by the magnetic field of a wedge and the critical rise of the magnetic liquid relative to the level outside the field are presented. The experimental and theoretical results are in agreement.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 113–119, July–August, 1992.The authors wish to thank V. V. Gogosov for useful discussions and his interest in the work.     

Stability of plane-parallel MHD flows in transverse magnetic field

We study within the framework of linear theory the stability of plane-parallel flows of a viscous, electrically conducting fluid in a transverse magnetic field. The magnetic Reynolds numbers are assumed small. The critical Reynolds number as a function of the Hartmann number is obtained over the entire range of variation of the latter. The small perturbation spectrum is studied in detail on the example of Hartmann flow. Neutral curves are constructed for symmetric and antisymmetric disturbances. The destablizing effect of a magnetic field is studied in the case of modified Couette flow. The results obtained agree with the calculations of Lock and Kakutani (where they meet) and are at variance with the results of Pavlov.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 3, pp. 127–131, May–June, 1970.The authors wish to thank M. A. Gol'dshtik for his interest in this study.     

Parametric excitation of waves on a liquid surface in the presence of an insoluble film

The presence of a film of surface-active agents leads to a change of the force acting on the surface of a liquid. This change does not lead to a simple decrease of the surface tension , and it is connected with the appearance of tangential forces acting on the free surface of the fluid [1]. The stability of the free surface of a liquid with a film of a surface-active agent in a variable gravitational field is examined. The linear formulation of the problem is solved. A solution is sought in the form of a series in powers of the small viscosity by the method of Laplace transforms in time and Fourier transforms in the x and y variables (the xy-plane coincides with the undisturbed liquid surface). An integrodifferential equation of the second-order with periodic coefficients is derived for the displacement of the surface from the equilibrium position. The solution is found by the method of averaging [2]. It is shown that the excitation energy should not be less than the energy dissipated in the system. It is shown that the presence of the film substantially increases the threshold of the instability.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 159–162, September–October, 1976.The authors thank G. Z. Gershuna for calling their attention to this problem.     

Structure of detonation waves,ionizing a gas,in the presence of an electromagnetic field. Cases of low magnetic viscosity

If behind a detonation wave, ionizing a gas, the magnetic Reynolds number is much greater than unity, then in order to describe such waves (just as for ionizing shock waves) complementary relations [1, 2] are necessary. These complementary relations are not the consequence of the basic integral laws, but can be found from a consideration of the wave structure. In [2], the structure of detonation waves, ionizing a gas, was investigated in an oblique magnetic field. It was supposed that the flow in a layer representing the structure is determined by the finite rate of the chemical reaction and the finite electrical conductivity. In the case when the characteristic length of the chemical reaction is much less than the characteristic dissipation length of the magnetic field, the complementary relations which ensure the existence of the structure are obtained in explicit form. The case is considered below when the characteristic length of the chemical reaction is much greater than the dissipation length of the magnetic field. In this case, the complementary relations are obtained in the explicit form.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 95–101, May–June, 1976.     

Structure of the fluid interface in an external magnetic field in the presence of a magnetizable surfactant

The structure of the flat interface between two conventional fluids in an external magnetic field in the presence of a magnetizable surfactant is investigated with account for the dependence of the free energy of the system on the surfactant concentration gradients and the bearing phase density. The dependence of the surface tension tensor components on the magnetic field strength is determined.     

The magnetic field in inhomogeneous turbulent flow

We consider a particular model of magnetohydrodynamic turbulents. The most fundamental assumption we make is that the velocity correlation time is negligible. By using a selective summation of the perturbation theory series an exact equation for the magnetic field is obtained when the mean square value of the velocity depends on coordinates, i.e., when the turbulence isinhomogeneous. The result makes it possible to obtain the macroscopic Maxwell's equations, i.e., the equations for the large-scale components of the electromagnetic field.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 12–18, January–February, 1971.In conclusion, the author thanks R. Z. Sagdeev and V. E. Zakharov for a discussion of the results.