Stability of a floating lamina

The effect of an oscillating bottom area on a floating dock, simulated by a lamina, is studied by the method of [1]. It is demonstrated that the overturning moment acting on the dock from the direction of the liquid will be maximal at certain parameter values which characterize the location of the perturbed bottom region and the depth of the basin.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 170–172, January–February, 1977.     

Behavior of a floating elastic plate during vibrations of a bottom segment

The Wiener-Hopf technique is used to obtain an analytical solution for the problem of vibrations of a floating semi-infinite elastic plate due to earthquake-induced vibrations of a bottom segment. An explicit solution is obtained ignoring the inertial term. The surface-wave amplitudes and ice-plate deflection are studied numerically as functions of the frequency and position of the vibrating bottom segment, ice thickness, and fluid depth.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 98–108, March–April, 2005.     

Surface wave generation in the process of finite deformation of the bottom of a basin

The process of generation of three-dimensional irrotational fluid motions induced by small local finite-duration displacements of part of the bottom of a basin is considered within the framework of wave linear theory for a basin of constant depth. The solution of the problem and an expression for the total wave field energy are obtained using integral transforms. The general properties of the process of unsteady wave generation induced by short-term and slow deformations of the bottom are analyzed. Within the framework of the piston generation model the energy characteristics of axisymmetric waves are compared for two time laws of bottom deformation of identical duration. In general, it is shown that under certain conditions the nature and intensity of the wave process depend on both the time law and the duration of the deformation process.Sevastopol. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 151–156, March–April, 1996.     

Reflection of surface waves by a vertical step at the bottom of a basin

A study is made of the propagation of surface waves in a basin with a vertical step in the bottom. The problem is solved by fitting solutions on the horizontal boundary that continues the bottom of the shallow-water region of the basin; the factorization method is used. It is shown that the reflection of the waves depends on the wavelength of the incident waves and the difference between the two depths in the basin.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 181–185, January–February, 1984.     

Effect of periodic bottom roughness on gravitational waves in a liquid

The effect of a rigid bottom of periodic form on small periodic oscillations of the free surface of a liquid is considered with the assumption of low amplitude roughness. The methodologically most significant study in this direction, [1], will be utilized. In [1] the steady-state problem for flow over an arbitrarily rough bottom was studied. Other studies have recently appeared on small free oscillations above a rough bottom. Essentially these have considered the effect of underwater obstacles and cavities on surface waves in the shallow-water approximation (for example, [2], [3]). Liquid oscillations in a layer of arbitrary depth slowly varying with length were considered in [4]. However, these results cannot be applied to the study of resonant interaction of gravitational waves with a periodically curved bottom.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 43–48, July–August, 1984.     

Vibrations of a Floating Elastic Plate Due to Periodic Displacements of a Bottom Segment

The problem of the behavior of a floating elastic thin plate under periodic vibrations of a bottom segment is solved using a numerical procedure based on the Wiener-Hopf technique. The effects of the vibration frequency, the position of the vibrating bottom segment, and the fluid depth on the vibration frequencies of the fluid and plate are studied numerically.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 166–179, September–October, 2005.     

Polymer flooding of oil formations with bottom water

A quasi-one-dimensional model describing the process of polymer flooding of oil formations underlain by bottom water is proposed. The model is based on the assumption of instantaneous gravitational phase separation along the vertical and is a generalization of the hydrodynamic model previously considered in [1]. The self-similar solutions constructed show that in the case of polymer flooding of an oil formation the presence of bottom water leads to qualitative changes in the saturation and concentration distribution and has an important influence on both the running and the final oil output. The results obtained are consistent with the data of two-dimensional numerical modeling of the process [2] and indicate the possibility of more efficient exploitation of water-oil zones as a result of pumping thickened water into the formation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 84–90, May–June, 1986.     

Interaction between an acoustic wave and a disc

A numerical solution is obtained to the problem concerning a pressure measurement at the boundary between an ideal compressible fluid and a solid wall. It is assumedthat the fluid occupies a semiinfinite cylinder with a rigid bottom into which an elastic disc is inserted and heldfirmly around its edges. Motion is produced by a pressure wave originating at infinity. A finite-difference grid for this application is described and the results of actual calculations are shown.Deceased.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 84–91, January–February, 1972.The authors thank L. M. Flitman for reviewing the work.     

Interaction of an internal gravity current with a submerged circular cylinder

The problem of hydrodynamic loads due to the interaction of a gravity current propagating over a bottom channel with a submerged circular cylinder is studied experimentally. It was shown that in the examined range of parameters, the hydrodynamic loads are simulated after Froude. The hydrodynamic loads are maximal if the cylinder lies on the bottom, and they decrease rapidly with increase in the distance from the cylinder to the channel bottom. The effects of mixing and entrainment on the nature of the hydrodynamic loads are considered.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 81–90, March–April, 2005.     

Approximate solution of the problem of the bottom zone in a rarefied gas

The problem of the steady-plane monatomic rarefied gas flow around a semiinfinite bar is considered (the plane stationary case of the problem about the bottom zone). The problem is solved numerically at the level of the Krook relaxation model [1, 2]. A depenence of the gas density, velocity, and temperature in the whole flow domain on the space coordinates is obtained for supersonic and subsonic gas streams flowing around a body by using calculations on an M-20 electronic calculator.Khar'kov. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 139–143, January–February, 1972.     

Mathematical construction of a Reissner–Mindlin plate theory for composite laminates

A Reissner–Mindlin theory for composite laminates without invoking ad hoc kinematic assumptions is constructed using the variational-asymptotic method. Instead of assuming a priori the distribution of three-dimensional displacements in terms of two-dimensional plate displacements as what is usually done in typical plate theories, an exact intrinsic formulation has been achieved by introducing unknown three-dimensional warping functions. Then the variational-asymptotic method is applied to systematically decouple the original three-dimensional problem into a one-dimensional through-the-thickness analysis and a two-dimensional plate analysis. The resulting theory is an equivalent single-layer Reissner–Mindlin theory with an excellent accuracy comparable to that of higher-order, layer-wise theories. The present work is extended from the previous theory developed by the writer and his co-workers with several sizable contributions: (a) six more constants (33 in total) are introduced to allow maximum freedom to transform the asymptotically correct energy into a Reissner–Mindlin model; (b) the semi-definite programming technique is used to seek the optimum Reissner–Mindlin model. Furthermore, it is proved the first time that the recovered three-dimensional quantities exactly satisfy the continuity conditions on the interface between different layers and traction boundary conditions on the bottom and top surfaces. It is also shown that two of the equilibrium equations of three-dimensional elasticity can be satisfied asymptotically, and the third one can be satisfied approximately so that the difference between the Reissner–Mindlin model and the second-order asymptotical model can be minimized. Numerical examples are presented to compare with the exact solution as well as the classical lamination theory and the first-order shear-deformation theory, demonstrating that the present theory has an excellent agreement with the exact solution.     

Re-examined principles of thrust generation by a track on soft ground

Dr. Bekker’s first book Theory of land locomotion offers in fact two different concepts of thrust generation on soft ground with respect to the slip: (a) as the push of grousers causing horizontal soil “distortion” and (b) as the shear force in the failure plane linked with the shear deformation. Bekker preferred the second concept and backed it up by the unique shear-ring measuring technique. To clear up the matter, the author decided to re-examine the thrust generation by a track plate experimentally in field conditions. The tests have shown that the initial stage of thrust generation in compressible ground is always horizontal soil compression by grousers, which divides the soil under a track into separate blocks initially at rest. This compression increases at least to the transition point, when a block is sheared off simultaneously at the bottom and in both lateral planes and starts sliding along the channel formed by the preceding grouser. The analysis of these measurements enabled to define the compressive displacement of the face of the soil block (travel of the grouser) appurtenant to the mentioned transition point, useful to define the thrust–slip curve. The case may also be described by the conventional shear stress–shear displacement relationship, imagined to take place in the bottom failure plane, however, namely the “shear displacement” is rather an unusual quantity.     

Immersion of a floating deformed body

A study is made of the plane-eddyless motion of an ideal incompressible liquid with the vertical uniformly accelerated immersion of a body, whose bottom is deformed in accordance with a given law. The method of solution of [1] is used. Dependences are given for calculating the pressures, the forces of the resistance to the immersion, and the forms of the free surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 136–137, September–October, 1974.     

Effect of an impermeable inclusion in the underlying highly permeable pressurized horizon on the conditions of ground water in an irrigated layer of soil

The problem of plane, nonpressurized, steady-state filtration through a layer of soil into an underlying pressurized horizon, which contains an impermeable section at the top, with uniform infiltration on the free surface is solved in a hydro-dynamic formation. A constructive solution of the problem is given with the help of the method of P. Ya. Polubarinova-Kochina; representations are obtained for the characteristic dimensions of the flow scheme and the depression. The case of limiting flow — no head in the bottom, highly permeable layer — studied in [1] is noted.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 3–5, May–June, 1986.The author thanks V. N. Emikh for useful remarks and discussions.     

Solitary stokes waves in heavy-fluid slit flow

Flow with a solitary Stokes wave is obtained as a result of solving the plane nonlinear problem of the steady flow of an ideal heavy incompressible fluid into a slit at the bottom of a vessel for a narrow range of Froude numbers on which there exists a solution with a jet surface descending monotonically to the slit [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 173–176, November–December, 1991.The authors are grateful to A. N. Ivanov and G. Yu. Stepanov for their assistance and useful discussions.     

Experimental verification of the gas-hydraulic analogy with reference to the dam-break problem

The results of an experimental study of dam-break waves for both a dry and a flooded bottom in the lower pool are compared with the first approximation of shallow-water theory. It is shown that this approximation adequately describes the height and velocity of the hydraulic jump in the lower pool for a flooded bottom, does not describe the undulations, and is inconsistent with the experimental data on the perturbation propagation velocity in the upper and, for a dry bottom, in the lower pool.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 143–152. Original Russian Text Copyright © 2004 by Bukreev, Gusev, A. A. Malysheva, and I. A. Malysheva.     

Onset of separation in hydrodynamic impact on a floating body

The vertical impact problem is considered for a body of revolution immersed in an ideal incompressible fluid bounded from below by a bottom in the shape of a surface of revolution. For a certain class of bodies it is proved that separation begins on the intersection between the wetted surface of the body and the meridional plane in which the shock impulse is located. As shown by the examples of spindle-shaped surfaces of revolution and an ellipsoid of revolution, separation can take place at one of two points on the boundary of the wetted surface of the body, one farther from and the other nearer to the point of application of the impulse.Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 99–104, November–December, 1996.     

Existence and uniqueness of a solution to a problem of steady composite waves on the surface of a liquid flowing over a wavy bottom

Composite waves on the surface of the stationary flow of a heavy ideal incompressible liquid are steady forced waves of finite amplitude which do not disappear when the pressure on the free surface becomes constant but rather are transformed into free nonlinear waves [1]. It will be shown that such waves correspond to the case of nonlinear resonance, and mathematically to the bifurcation of the solution of the fundamental integral equation describing these waves. In [2], a study is made of the problem of composite waves in a flow of finite depth generated by a variable pressure with periodic distribution along the surface of the flow. In [3], such waves are considered for a flow with a wavy bottom. In this case, composite waves are defined as steady forced waves of finite amplitude that, when the pressure becomes constant and the bottom is straightened, do not disappear but are transformed into free nonlinear waves over a flat horizontal bottom. However, an existence and uniqueness theorem was not proved for this case. The aim of the present paper is to fill this gap and investigate the conditions under which such waves can arise.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 88–98, July–August, 1980.     

Waves in an inhomogeneous fluid due to periodic pressures in the presence of a thin plate

The problem of motion of a two-layer fluid of finite depth subjected to pressure applied to its surface in the presence of a semiinfinite plate is considered in a linear formulation. Expressions governing the form of the originating surface and internal waves are obtained. Results are presented of a numerical computation of the elevation of the free surface and the interface caused by the application of the pressure.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 91–96, September–October, 1976.     

Interferometric study of natural convection in rectangular air cavities of various orientations

The results of an experimental investigation into the temperature profiles and heat transfer associated with natural convection in rectangular air cavities are presented, the angle of inclination varying from 0 (heating at the bottom) to 180° (heating at the top). The range of Rayleigh numbers was R=2.68·10³–2.57·10⁵, and n=H/d=5.06–18.3. The investigation was carried out by an optical method, using an IZK-454 interferometer. For a horizontal orientation of the cavity the heat-transfer data satisfy the relation N=0.216 R^0.25, for a vertical orientation N=0.144 R^0.3h^–0.129, where N is the Nusselt number. In the region of an inclination of 30° the heat transfer passes through a maximum under all conditions studied.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 89–93, July–August, 1972.