Oscillations of an ideal liquid acted upon by subface-tension forces. Case of a doubly connected free surface

Many articles have appeared on the problems of small oscillations of an ideal liquid acted upon by surface-tension forces. Oscillations of a liquid with a single free surface are treated in [1, 2]. Oscillations of an arbitrary number of immiscible liquids bounded by equilibrium surfaces on which only zero volume oscillations are assumed possible are investigated in [3], We consider below the problem of the oscillations of an ideal liquid with two free surfaces on each of which nonzero volume disturbances are kinematically possible. The disturbances satisfy the condition of constant total volume. A method of solution is presented. The problem of axisymmetric oscillations of a liquid sphere in contact with the periphery of a circular opening is considered neglecting gravity. The first two eigenfrequencies and oscillatory modes are found.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 64–71, May–June, 1976.In conclusion, the author thanks F. L. Chernous'ko for posing the problem and for his attention to the work.     

Instability of two-layer film flow along an inclined surface

In [1–3] the method of expansion in a small wave number is used to investigate stability of two-layer flows; the results are valid for the neutral curves and in their neighborhood. Here, the eigenvalue problem is solved numerically, the wave disturbances are considered over the entire region of instability and the effect of the governing parameters on the characteristics of the most unstable disturbances is established.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 10–18, March–April, 1992.     

Traveling disturbances in rotating-disk flow

The stability curves for traveling disturbances in rotating-disk flow are computed using the sixth-order system of incompressible linear stability equations. It is found that the neutral curve has two minima for disturbances with positive frequencies as found earlier by Malik (1986) for stationary disturbances. The upper branch minimum occurs at =–2.9, R=283.6 while the lower branch minimum occurs at =7.9, R=64.46 where R is the Reynolds number. There exists a critical angle of approximately –35.34° (which is about 15° from the direction of maximum wall shear) below which all the waves are linearly damped. The results also show that at high frequencies the wave number for lower branch neutral disturbances varies with Reynolds number like R ^–1 while for stationary waves it behaves like R ^–1/2. The eigenfunction distribution suggests that the structure of the nonstationary high-frequency lower branch neutral disturbances are different from the structure of the viscous stationary disturbances.This work was sponsored under NASA Contract NAS1-18240.     

Thermocapillary instability of a plane layer with a vertical temperature gradient

The oscillating disturbances in a plane layer with a temperature gradient are analyzed. It is shown that for heating from below taking the deformability of the free surface into account leads to the appearance of short-wave oscillatory instability, which becomes the most dangerous mode. Moreover, the interaction of the capillary and thermocapillary instability mechanisms results in the appearance of oscillating disturbances of a new type, which lead to equilibrium crisis at high Marangoni numbers. It is established that when the free boundary is heated, the onset of convection is possible only with respect to oscillatory disturbances.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 19–23, May–June, 1992.     

Asymptotic structure of inviscid disturbances in a thin shock layer

The WKB method, used in [4] to analyze the short-wave instability of a supersonic mixing layer, is employed to investigate various types of inviscid three-dimensional short-wave disturbances in a thin shock layer of perfect gas with arbitrary velocity and temperature distributions across the layer. Simple analytic expressions for the dispersion relations are obtained for neutral disturbances. The results of an asymptotic analysis are compared with direct numerical calculations for a simple model of the shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 72–79, November–December, 1988.     

Dynamical properties of heterogeneous surface layers. capillary wave scattering

The dynamics of a heterogeneous liquid surface constituting a two-dimensional disperse system is considered. One of the surface phases (the dispersed phase) forms circular regions of diameter comparable with the characteristic length of the mechanical disturbances within the continuous disperse medium. Inhomogeneous boundary conditions for the Navier-Stokes equations with a discontinuity on the surface phase contact line are formulated. Special attention is paid to the conditions on this line. An approximate method of solving the surface wave diffraction problem and the results for the case of transverse surface wave scattering are described. It is shown that if the wavelength is close to the dimensions of the two-dimensional dispersed particles and their concentration is sufficiently high, the energy of the scattered waves may exceed that dissipated in the vorticity layer. Thus, a new nonclassical mechanism of surfactant action on capillary wave damping is possible.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 129–137, January–February, 1991.     

Development of finite-amplitude two-dimensional and three-dimensional disturbances in jet flows

The laminar-turbulent transition zone is investigated for a broad class of jet flows. The problem is considered in terms of the inviscid model. The solution of the initial-boundary value problem for three-dimensional unsteady Euler equations is found by the Bubnov-Galerkin method using the generalized Rayleigh approach [1–4]. The occurrence, subsequent nonlinear evolution and interaction of two-dimensional wave disturbances are studied, together with their secondary instability with respect to three-dimensional disturbances.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 8–19, September–October, 1985.     

Propagation of disturbances in supersonic vibrationally nonequilibrium gas flows

The propagation of finite disturbances in nonequilibrium supersonic gas flows is investigated, and the effect of entropy and acoustic disturbances on the inversion characteristics of the medium is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 128–134, March–April, 1990.     

Stable nonlinear waves in a poiseuille flow

Nonlinear Tolmin-Schlichting waves are studied [1–8]. The investigation is carried out by means of a modified Stuart-Watson method [1–3]. In the case of a rigid regime of excitation terms to the fifth order are taken into account in expansions with respect to the amplitude of self-excited oscillations. The stability of self-excited oscillations with respect to two- and three-dimensional disturbances is examined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 40–45, September–October, 1978.The author thanks S. Ya. Gertsenshtein for attention to the work and discussion of the results.     

Controlling the Development of Stationary Longitudinal Structures in the Boundary Layer on a Flat Plate using Riblets

This paper reports results of experiments on controlling longitudinal structures in the boundary layer on a at plate. The longitudinal structures were generated by a controlled vortical disturbance of the external flow by means of a distributed susceptibility mechanism. It is shown that riblets reduce the intensity of both stationary and traveling disturbances. The linear and weakly linear stages in the development of disturbances in the boundary layer are the most favorable for the use of riblets.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 47–54, July–August, 2005.     

Structure of artificial disturbances induced by an external acoustic field in a supersonic boundary layer

The wave structure of the artificial disturbances generated by an external acoustic field in a supersonic boundary layer is investigated. The disturbances are classified with respect to phase velocity. Disturbances whose phase velocity in the direction of flow is greater than unity and waves located at the boundary of the discrete and continuous spectra are detected.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 82–86, May–June, 1989.     

Propagation of electromagnetic disturbances and stability of stationary states in media with a nonlinear ohm's law

The principles of propagation and development of small disturbances in nonlinear conducting media are studied.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 3–15, May–June, 1972.The author thanks G. A. Lyubimov and S. A. Regirer for their evaluation of basic results, and A. G. Kulikovski for his valuable advice.     

Development of Natural Disturbances in a Hypersonic Boundary Layer on a Sharp Cone

Experimental data on the location of the laminar—turbulent transition and development of natural disturbances in a laminar hypersonic boundary layer on a sharp thermally insulated cone with a half–angle of 7° are presented. The existence of the second mode of disturbances is confirmed. It is shown that the transition is determined by the first mode of disturbances. The experimental data are in good agreement with theoretical calculations.     

Velocity disturbance structure in the nonlinear stage of laminar-turbulent transition

The Herbert theory [1, 2] of laminar turbulent transition is generalized by taking into account the development of the secondary disturbances with allowance for their higher harmonics. The results of calculations of the development of three-dimensional pulsations, based on this theory, are in a agreement with the Herbert results in the initial stage of development and with the results of direct numerical modeling, obtained in this paper, and with experiment [3] in the later nonlinear stages of transition.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 3–9, November–December, 1993.     

Characteristics of an unstably localized disturbance in a compressed boundary layer

Experiments have demonstrated [1] that the transition of streamline-type flow into turbulent flow in a boundary layer occurs as a result of the formation and development of turbulent spots apparently arising from small natural disturbances. A study of the nonlinear evolution and interaction of localized disturbances requires knowledge of their characteristics to a linear approximation [2]. In the current work, results are presented of calculations of such characteristics for the first two unstable modes in a supersonic boundary layer on a two-dimensional plate (M = 4.5, T_w = 4.44).Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 50–53, January–February, 1976.     

Interaction between a supersonic boundary layer and acoustic disturbances

The development of disturbances in a boundary layer that have been induced by an external acoustic field are investigated. The problem is considered in the linear formulation. It is shown that the oscillations inside the supersonic boundary layer can have several times the intensity of the external disturbances. The susceptibility of the boundary layer to the acoustic disturbances increases with increasing Mach number. Cooling of the surface leads to a small decrease in the intensity of the longitudinal velocity oscillations in the layer. The effect of the parameters of the acoustic wave is considered, i.e., the effect of the frequency and phase velocity on the development of the disturbances.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 51–56, November–December, 1977.     

Linear response of a plasma in a magnetic field to localized initial vorticity

It is established that for three-dimensional disturbances the long-range effect is observed even in the absence of boundaries. The problem of the evolution of the electrodynamic and gas dynamic disturbances created by a localized vorticity source is considered. It is shown that acoustic disturbances of a nonlocal nature are formed. The spatial structure of the electric potential and the nonlocal electric field created by localized initial vorticity at a finite value of the Hall parameter is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 109–114, March–April, 1990.     

Steady disturbed viscous incompressible gas flows in a long cylinder with one closed end

There have been many studies of steady disturbed flows in rotating channels. In [1] the steady disturbed flow between two coaxial rotating cylinders was investigated. In [2, 3] the disturbances of Hagen-Poiseuille flow due to rotation of the pipe were considered. In this article other effects: the propagation of disturbances in a long rotating pipe and their interaction with the end face are examined.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 104–112, September–October, 1993.     

Natural oscillations arising from loss of stability in parallel flows of a viscous liquid under long-wavelength periodic disturbances

It was shown in [1] that a parallel flow with an arbitrary nonconstant velocity profile is unstable for long-wavelength spatially periodic disturbances along the flow. The present paper shows that this instability leads to a supercritical natural oscillation mode of the simple wave type. This mode is calculated using the Lyapunov-Schmidt method in the form given in [2], along with the asymptotic curve of the wavelengths [1]. If the long wavelength disturbances are the most dangerous (this occurs, for example, when there is a sinusoidal velocity profile), then the natural oscillation mode is stable for spatially periodic disturbances having the same wavelength.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 32–35, January–February, 1973.     

Experimental investigation of the development of harmonic disturbances in the boundary layer on a flat plate at mach number M=4

The development of three-dimensional wave packets artificially introduced into a boundary layer has been experimentally investigated. The measurements were made by the hot-wire anemometer method in the boundary layer on a flat plate at a Mach number M = 4. The artificial disturbances were introduced into the boundary layer by means of an electric discharge. A Fourier analysis of the data made it possible to obtain the wave characteristics of the plane waves. The composition of the disturbances was analyzed and those most dangerous from the instability standpoint were identified. The data obtained are compared with the results of experiments carried out at M = 2. The differences in the data are discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 54–58, November–December, 1990.