Short dipole in a uniaxial medium

Summary The paper considers the radiation properties of a short dipole in a lossy uniaxial medium. A quantity T(r) called the transmission parameter is defined in terms of the integrated Poynting vector on a spherical surface of radius r. The variation of T(r) is studied as a function of r. One of the main findings of the paper is that T(r) is inversely proportional to the half-length L of the dipole for r 0, while it is proportional to L ² for r . This behavior is explained in terms of the variation of the fields in the medium. One possible explanation of the much discussed paradoxical behavior of the input resistance of a short dipole is offered in the light of the results obtained in this paper.     

Turbulent wake in a stratified medium

The problem of determining the form of the turbulent wake being formed behind a selfpropelled body in a medium with density varying in the direction of the effect of gravity is considered. The schematic picture of wake development behind a moving object is the following: Initially, diffusion is identical in all directions, and the wake broadens symmetrically; diffusion becomes strongly anisotropic with recession from the object, it diminishes in the vertical direction under the effect of gravity, and the wake becomes flattened; turbulent mixing within the wake results in the production of a more homogeneous density distribution within the volume occupied by the wake than in the surrounding medium; such a fluid volume turns out to be removed from the equilibrium state and tends to return to the equilibrium state under the effect of gravity; collapse of the wake occurs accompanied by its further expansion in the horizontal direction and the excitation of internal waves.Translated from ZhurnalPrikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 68–72, September–October, 1970.     

Two-dimensional inverse problem of thermoelasticity for a medium with an elastic discontinuity

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 26, No. 10, pp. 72–76, October, 1990.     

Uniqueness of uniaxial elastic-plastic interface motions

The uniaxial motion of interfaces between regions deforming elastically and regions deforming plastically is considered. The governing constitutive, stress-rate/strain-rate equations in both elastic and plastic regions are taken to be non-linear. Discontinuity relations across such interfaces are established by the repeated differentiation of existing relations. The relations given by previous workers (especially R.J. Clifton, T.C.T. Ting, E.H. Lee and Th. von Kármán) are discussed. The precise situations in which they hold are considered, and it is shown that some of these relations, while apparently derived for different situations, can, in certain circumstances, be shown to be equivalent. It has been shown that six essentially different types of motion can occur, and, when the constitutive equations are linear, each type of motion is unique. This result is extended to the non-linear situation, by means of an established local expansion procedure. For the case of a meeting interaction of stress waves carrying initially linear profiles, the previous (linear) analysis given by L.W. Morland and A.D. Cox fails to distinguish between certain types of motion. This motion is reconsidered and it is shown how non-linearity in the constitutive laws serves to determine uniquely the type of motion that takes place.     

Critical flow regime in a stratified medium

The equations for the single-point moments of second order of the velocity and temperature fields closed by means of semiempirical hypotheses are used to investigate the critical flow regime in a stratified medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhldkosti i Gaza, No. 2, pp. 156–159, March–April, 1979.     

Self-similar implosion of a continuous stratified medium

Abstract. The subject of this paper is the non perturbed self-similar implosion of a continuous stratified medium in cylindrical and spherical geometry. The main contribution is twofold. The first one is a condition on the initial density profile which guarantees that the integral of the internal energy over a fixed volume stays finite at the collapse. The second one is the proof that the self-similar implosion model partly restitutes the dynamics of an experiment of cylindrical implosion. Numerical values of the self-similar parameter are also given for various kind of stratified media in the two geometries. Received 8 March 1999 / Accepted 9 April 2001     

Two-dimensional free boundary layer in a stratified medium

Expressions for the fluctuation characteristics of shear flow in a stratified medium are obtained on the basis of the equations for the single-point second-order moments of the velocity and temperature fields and then closure of those equations by means of semiempirical hypotheses. The Prandtl equation, with the influence or Archimedean forces taken into account, is used to analyze plane jet flows and wake flows of a body, Numerical computations are carried out for a plane wake, and the results are compared with the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 71–79, July–August, 1977.     

Development of the region of a turbulized liquid in a stratified medium

The article discusses the plane unsteady-state problem of the development of a region of turbulent pulsations in an incompressible stratified liquid. At the initial moment of time, the energy of the turbulence is given inside a region of finite dimensions. A semiempirical system of equations describing this process is proposed. The article gives the data from numerical calculations, illustrating the original expansion of the region as a result of turbulent diffusion, its subsequent compression along a vertical (collapse) under the action of the forces of buoyancy, and the internal waves generated by the collapse.The work was reported at the International Symposium on Stratified Flows (Novosibirsk, August 29–31, 1972).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 45–52, May–June, 1974.     

Generation of dissipation-gravity waves during thermal convection in a stratified medium

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 49–55, May–June, 1991.     

Natural convection from a vertical cylinder in a thermally stratified porous medium

The problem of non-Darcy natural convection adjacent to a vertical cylinder embedded in a thermally stratified porous medium has been analyzed. Nonsimilarity solutions are obtained for the case that the ambient temperature increases linearly with height of the cylinder. A generalized flow model was used in the present study to include the effects of the macroscopic viscous term and the microscopic inertial force. Also, the thermal dispersion effect is considered in the energy equation. Thus, the main aim of this work is to examine the effects of thermal stratification and non-Darcy flow phenomena on the free convection flow and heat transfer characteristics. It was found that the present problem depends on six parameters, namely, the local thermal stratification parameter ξ, the boundary effect parameter Bp, the modified Grashof number Gr^*, wall temperature exponent m, the curvature parameter ω, and the modified Rayleigh number based on pore diameter Ra _d . The impacts of these governing parameters on the local heat transfer parameter are discussed in great detail. Also, representative velocity and temperature profiles are presented at selected values of the thermal stratification parameter. In general, the local heat transfer parameter is increased with increasing the values of m, ω, and Ra _d ; while it is decreased with increasing the values of ξ, Bp, and Gr^*. Received on 19 May 1998     

Critical layer formation in a stratified medium with mean shear flows

The problem of the excitation of internal waves with a given wave number k and frequency in a stratified medium with shear flows is considered. The internal wave field of the form v(z)exp(–it+ikx) established as t in a medium without dissipation has a singular point at the level z=z₀ (critical level), at which the flow velocity U(z) coincides with the phase velocity /k. Dissipative effects (viscosity and heat conduction) smooth out this singularity. An exact solution of the model equation describing as t and zz₀ the field excited by oscillating sources activated at t=0 is constructed with allowance for dissipation. This makes it possible to describe the limiting steady-state field, determine the critical layer as the neighborhood of the critical level in which dissipation effects are important, and to estimate its width and the rate of convergence to the limiting steady-state regime. The asymptotic behavior of the fields is examined for Ri1, where Ri is the Richardson number. It is shown that when the well-known Miles stability condition Ri>1/4 is satisfied there are no natural oscillations with a critical level.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 82–93, May–June, 1990.     

Mixing in a stably stratified medium by horizontal shear near vertical walls

Stratified environmental flows near boundaries can have a horizontal mean shear component, orthogonal to the vertical mean density gradient. Vertical transport, against the stabilizing force of gravity, is possible in such situations if three-dimensional turbulence is sustained by the mean shear. A model problem, water with a constant mean density gradient flowing in a channel between parallel vertical walls, is examined here using the technique of large eddy simulation (LES). It is found that, although the mean shear is horizontal, the fluctuating velocity field has significant vertical shear and horizontal vorticity, thereby causing small-scale vertical mixing of the density field. The vertical stirring is especially effective near the boundaries where the mean shear is large and, consequently, the gradient Richardson number is small. The mean stratification is systematically increased between cases in our study and, as expected, the buoyancy flux correspondingly decreases. Even so, horizontal mean shear is found to be more effective than the well-studied case of mean vertical shear in inducing vertical buoyancy transport as indicated by generally larger values of vertical eddy diffusivity and mixing efficiency.     

Inhomogeneous inverse problem in finite elasticity

For a class of materials for which the principal strain directions always coincide with the principal stress directions one can determine the stress field in an inhomogeneously deformed body from given boundary conditions and a known strain field without knowing the constitutive equations. Each point of the inhomogeneously deformed body contains information such as that derived from an individual homogeneous identification test. The practically important two-dimensional case leads to a problem of solving a linear hyperbolic system where two differential equations describe the principal stress components. The problem can be reduced to that of integration along characteristics.Under a certain globality condition the existence, uniqueness, and correctness of the solution are guaranteed in the whole test piece. It is shown that the globality condition is closely related to whether or not the test piece is isotropic and elastic. The influence of experimental error on the correctness of problem formulation is discussed.

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Abstrakte Für die Klasse der Materialen, für welche die Grundspannungsrichtungen und die Grundverformungsrichtungen gleich sind, kann man das Spannungsfeld in einem inhomogen deformierten Körper für gegebene Randbedingungen und einem bekannten Verformungsfeld ohne Kenntnis der detailierten Form der Dehnungs-Spannungsgleichung bestimmen. Jeder Punkt des inhomogen deformierten Körpers liefert dieselbe Information wie ein individueller homogener Test. Der praktisch wichtige zweidimensionale Fall führt zu einem Problem der Lösung eines linear hyperbolischen Systems von zwei Differentialgleichungen für die Grundspannungskomponenten. Das Problem kann auf die Integration entlang der Charakteristik des Systems reduziert werden.Unter einer Bedingung der Globalität das die Existent, Eindeutigkeit und Richtigkeit der Lösung in der ganzen Testprobe gewährleistet sind. Es wird gezeigt, dass diese Globalitätsbedingung damit zusammenhängt eng, ob die Testprobe isotrop und elastisch ist. Der Einfluss der experimentellen Fehler auf die Richtigkeit der Formulation des Problems wird auch analysiert.