Vertical immersion of a cylindrical floating solid

This paper is devoted to a study of the vortex-free (irrotational) motion of an ideal incompressible liquid during the vertical immersion of a cylindrical solid. In contrast to problems of impact [1] and the entry of a solid into water [2], the case here treated deals with continuous immersion involving a change in the shape of the free surface but with a constant width of the wetted surface of the solid. The coefficients of the time-dependent power series for the velocity potential, the equation of the free surface, and the pressure on the solid are determined, allowing for all the terms in the Cauchy-Lagrange equation. The results of calculations relating to the immersion of a bottom with an elliptical shape of the submerged part are presented.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 27–31, March–April, 1973.     

Effect of Boundary-Layer Thickness on the Structure of a Near-Wall Flow with a Two-Dimensional Obstacle

Results of physical and numerical experiments on investigating the effect of the depth of immersion of a two-dimensional obstacle with a square cross section into a developed turbulent boundary layer on the length of the separated flow region are presented. The numerical simulation is based on solving averaged Navier–Stokes equations with the use of the k– model of turbulence. The near-wall flow is visualized in the experiments, and the fields of mean and fluctuating velocities are measured. Flow regions where the results of numerical simulation agree with experimental data are determined. It is shown that the length of the recirculation flow region in the near wake increases with decreasing depth of immersion of the two-dimensional obstacle into the turbulent boundary layer.     

Wave front in the blunt body immersion problem

The immersion of a three-dimensional blunt convex body in a compressible fluid with nonpositive acceleration is considered in the linear formulation. It is shown that at every instant the perturbation zone will be convex. The fluid particle velocity and pressure are calculated at each point on the wave front. At every instant the wave front is wholly determined by the initial supersonic stage of propagation of the boundary of the body-fluid interaction zone.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 5–11, July–August, 1992.The author wishes to thank A. G. Khovanskii for his constant interest.     

Liquid equilibrium in a capillary of random form

A statistical analysis of depth distribution of droplets of a given volume is given for a capillary with radius varying randomly along the axis.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 149–152, November–December, 1974.     

Container for Localization of an Explosion of a Compact High–Explosive Charge with an Inert Shell

Results of an experimental study of fragmentation effects in the explosion and the piercing power of the fragments of inert masses in the form of hemispherical aluminum and soft–steel shells enclosing the spherical charge of a high explosive under their action on flat steel, aluminum, steel–net, and claydite—concrete barriers are given. A design of the lightest spherical explosion–proof container with a load–carrying steel or glass–reinforced plastic shell protected by a splinter–proof layer capable of withstanding an explosion of a high–explosive charge (with a twofold safety factor) with an inert steel shell is proposed.     

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 a homogeneous plasma confined between two parallel planes

A study is made of the conditions of global instability of a collisionless plasma with a given distribution function.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 26–28, September–October, 1970.     

Rheological equations of state of weakly concentrated suspensions of rigid ellipsoidal particles

Rheological equations of state of dilute suspensions of rigid ellipsoidal particles (ellipsoids of revolution) are derived [1–4] from the vantage point of the structural-continuum approach, with attention given both to rotational Brownian motion of particles and to their inertia and the outer force fields. Interaction between particles is ignored in those treatments given the low concentration of the suspended particles. In this paper, the earlier findings [1–4] are generalized to higher concentrations. The effect of hydrodynamical interaction between particles on the rheological behavior of the suspension is treated in the light of the Simha approach [5].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 141–145, January–February, 1973.     

Effect of shock–wave loading on the properties of cryogenic TiNi — a shape–memory alloy

Results of an experimental study of the shock–wave deformation of TiNi and its effect on the crystallographic structure and temperature of austenite–martensite transformations are given. It is found that, for pressures of up to 2 GPa, shock–wave loading changes the defect structure and parameters of the lattice; however, this does not lead to a noticeable change in the temperature of the austenite–martensite transformation and the manifestation of the shapeNdash;memory effect.     

Airfoil design using quasisolutions of inverse boundary-value problems

A mathematically rigorous approach to the solution of inverse boundary-value problems of aerohydrodynamics — problems in which the airfoil contour is found from the given distribution of the velocity as a function of the arc abscissa – is proposed. The approach is based on the notion of a quasisolution in the theory of improperly posed problems and involves a controlled modification of the initial data for the purpose of obtaining a unique solution in a given class of contours. The approach is explained with reference to the problem of designing an isolated airfoil in a plane steady ideal incompressible flow and is extended to the cases of subsonic gas flow and viscous incompressible flow. Some numerical results illustrating the possibilities of the method are also presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 5–13, May–June, 1988.The authors wish to thank G. Yu. Stepanov for frequent useful discussions and valuable advice.     

Impact of a figure of revolution in a stream of incompressible fluid with separation of a jet

The impact interaction of bodies with a fluid in a flow with jet separation has been considered in [1–3], for example. This investigation was in the two-dimensional formulation. The present paper considers the three-dimensional problem of impact of a figure of revolution in a stream of an ideal incompressible fluid with separation of a jet in accordance with Kirchhoff's scheme. A boundary-value problem is formulated for the impact flow potential and solved by the Green's function method. A method for constructing the Green's function is described. Expressions are given for the coefficients of the apparent masses. The results are given of computer calculations of these coefficients in the case of a cone using the flow geometry of the corresponding two-dimensional problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 176–180, November–December, 1980.     

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.     

Almost Periodic Solutions and Global Attractors of Non-autonomous Navier–Stokes Equations

The article is devoted to the study of non-autonomous Navier–Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous dynamical systems. Second, they have obtained conditions of convergence of non-autonomous Navier–Stokes equations. Third, a criterion for the existence of almost periodic (quasi periodic, almost automorphic, recurrent, pseudo recurrent) solutions of non-autonomous Navier–Stokes equations is given. Finally, the authors have derived a global averaging principle for non-autonomous Navier–Stokes equations.     

Optimization of Dynamic Plastic Deformation of Plates with a Complex Contour

A method for studying dynamic deformation of ideal rigid–plastic plates with a complex contour on a viscoelastic foundation is proposed. The method allows one to optimize the process of pulsed forming. The optimization parameters are the amplitude of the pulsed load, viscoelastic damping coefficients of the foundation, the surface density of the plate material, and the shape and supporting conditions of the edges. Numerical examples of simply– and doubly–connected plates are given. It is shown that different combinations of the control parameters of the process can ensure the same final shape of the plate formed.     

Action of an explosive plastic wave on a plate

The action of a transient loading on an infinitely elastic plate, freely covering the surface of an ideal compressible liquid, was discussed in [1–3]. A review of work on the dynamics of a plate under the action of a transient loading is given in [4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 131–136, July–August, 1976.     

Problems of optimizing multilayered spherical vessels

The problem of calculating a composite construction possessing defined optimal properties when compared with other constructions of the given type is considered in this paper in the case of spherical vessels in the domain of elastic strains.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 86–94, March–April, 1972.     

Nonresonance parametric interactions of surface waves in isotropic solid bodies

A solution in parametric approximation is given of the nonlinear interaction problem of Rayleigh surface waves propagating in a solid body with given elastic fields. Shortened equations that govern the modulation effect of the surface waves, and also expressions for the modulation index in terms of the third-order elasticity constant, are obtained.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 163–172, July–August, 1973.     

Numerical analysis of natural convection in a thin-walled cylindrical vessel with hemispherical end-plates completely filled with liquid

The results are given of calculations of convection in a thin-walled cylindrical vessel with hemispherical end-plates over the range of Rayleigh and Fourier numbers that correspond to the main regimes of unsteady laminar convection in the presence of a given heat flux.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 204–203, September–October, 1984.     

The free convection of a fluid with an initial vertical density gradient and lateral heating

Some results are given of an experimental investigation into the free convection in solutions with density which is nonuniform with height. It is shown that convective motion in solutions with a vertical density gradient and lateral heating is cellular in nature. The height of the cells is determined as a function of the temperature head and the density gradient.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 123–126, January–February, 1971.     

Vortex motion of a disperse mixture

A study is made of the motion of fine spherical particles in a given steady vortex flow of an incompressible fluid. The results are given of an investigation into the Lyapunov stability of a particle trajectory coincident with the vortex axis, and of trajectories from which the distance to the vortex axis is determined by the condition of equality of the radial components of the force of the phase interaction and of the centrifugal force which acts on the particle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 167–169, November–December, 1984.