Radiation of waves by a sphere harmonically oscillating to-and-fro in a viscous medium

The theory of the radiation of sound by a sphere in an ideal medium is presented in detail in [1–3]. The emission of waves by a sphere oscillating to-and-fro in a viscous incompressible liquid is analyzed in [4, 5]. The present paper gives a precise solution to the problem of the radiation of sound by a sphere oscillating in a viscous medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 101–106, September–October, 1970.     

Acoustomechanical constitutive theory for soft materials

Acoustic wave propagation from surrounding medium into a soft material can generate acoustic radiation stress due to acoustic momentum transfer inside the medium and material, as well as at the interface between the two. To analyze acoustic-induced deformation of soft materials, we establish an acoustomechanical constitutive theory by com-bining the acoustic radiation stress theory and the nonlinear elasticity theory for soft materials. The acoustic radiation stress tensor is formulated by time averaging the momen-tum equation of particle motion, which is then introduced into the nonlinear elasticity constitutive relation to construct the acoustomechanical constitutive theory for soft materials. Considering a specified case of soft material sheet subjected to two counter-propagating acoustic waves, we demonstrate the nonlinear large deformation of the soft material and ana-lyze the interaction between acoustic waves and material deformation under the conditions of total reflection, acoustic transparency, and acoustic mismatch.     

Unsteady Flow Through a Highly Porous Medium in the Presence of Radiation

The unsteady natural convection flow of a viscous and incompressible fluid through a porous medium with high porosity bounded by a vertical infinite stationary plate in the presence of radiation has been investigated. The fluid is assumed to be a gray, emitting and absorbing radiation, but non-scattering medium. The effects of the radiation parameter, Grashof number and permeability parameter of the medium on the velocity field as well as the effects of the radiation parameter and Prandtl number on the temperature field have been included in the analysis.     

Unsteady radiative-conductive heat transfer in a semitransparent selectively absorbing layer

Results of a numerical solution of the boundary-value problem of radiative-conductive heat transfer in a flat layer of a selectively absorbing and radiating medium are presented. The effect of the optical properties of the medium and the walls, the temperature of the source of radiation, and the relationship between the absorption spectra of the medium and the source of radiation on temperature distribution is studied. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 124–129, March–April, 2000.     

Radiation equilibrium temperature field in a gradient index medium with specular surfaces

The radiation equilibrium temperature field in a gradient index semitransparent absorbing-emitting gray medium is analyzed. The medium is bounded by two semitransparent specular surfaces and possesses a refractive index varying spatially or dependent on temperature. By discretizing the medium into many sublayers and adopting a linear refractive index approximation for each sublayer, the curved ray tracing technique is developed to solve the radiation transfer in medium. The temperature field at radiation equilibrium is obtained based on the energy conservation. The influences of refractive index distribution and optical thickness on the temperature field as well as the coupled effect of temperature and refractive index are examined. The results display the significant influences of gradient index on radiation transfer and the temperature distribution.     

Theory of magnetoacoustic wave generation by mechanical radiators

Aspects of the radiation of magnetoacoustic waves by an oscillating plane piston and by a radially pulsating cylinder and sphere are discussed. Expressions are derived for the magnetohydrodynamic perturbation fields in the medium. The radiation reaction forces acting on the given bodies are determined. The significant distinction between the theory of socalled magnetic sound generation and the theory of ordinary sound radiation is demonstrated. For example, the directivity pattern of a magnetic radially pulsating cylinder or sphere has a dipole character, whereas for ordinary sound generated by the same sources the pattern is isotropic, i.e., monopolar.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Flziki, No. 4, pp. 31–41, July–August, 1972.     

Convection due to the selective absorption of radiation in a porous medium

A model for convection due to the selective absorption of radiation in a fluid saturated porous medium is investigated. The model is based on a similar one introduced for a viscous fluid by Krishnamurti [x]. Employing this adapted model we show the growth rate for the linearised system is real. A linear instability analysis is performed. Global stability thresholds are also found using nonlinear energy theory. An excellent agreement is found between the linear instability and nonlinear stability Rayleigh numbers, so that the region of potential subcritical instabilities is very small, demonstrating that the linear theory accurately emulates the physics of the onset of convectionReceived: 10 February 2003, Accepted: 11 March 2003, Published online: 12 September 2003     

Calculation of the kinetics of propagation of a powerful light beam in a transparent dielectric with impurities

A large number of studies have been dedicated to the interaction of powerful optical radiation with transparent dielectrics in the prebreakdown or breakdown regimes. However, the mechanism by which the material is destroyed has not been determined decisively, as indicated by the constant flow of new publications on this theme. Attempts to obtain destruction as the result of electron avalanche [1] give threshold power values orders of magnitude greater than experiment [2]. In connection with this, in recent years the accent has been to deal with the concept of microimpurities of foreign particles or inhomogeneities within the medium having dimensions so small that their presence and concentration is difficult to monitor. As it absorbs optical radiation, the microimpurity (inhomogeneity) is heated and warms the areas of the medium adjacent to itself, which areas then commence to absorb light with significantly more intensity than they did in the initial state [3]. As a result, increase in absorption within the medium commences, terminating in breakdown or destruction of the material around the inhomogeneity. In [4, 5] it was noted that an important role may be played in such a destruction mechanism by thermoelastic stresses in the medium, which factor was not considered in [3]. In [4, 5] it was proposed that the basic effect of thermoelastic stresses reduces to development of microfissures in the medium. However, thermoelastic stresses can lead to yet another effect — narrowing of the forbidden zone of the medium and increase (together with the analogous action of temperature growth) in the coefficient of absorption of the medium. In the present study, the kinetics of interaction of optical radiation with a dielectric medium containing spherical metal particles as an impurity will be calculated, and it will be shown that thermoelastic stresses produce a significant contribution to the increase in light absorption by the medium around a particle.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 60–66, September–October, 1978.     

Convection due to the selective absorption of radiation in a porous medium

A model for convection due to the selective absorption of radiation in a fluid saturated porous medium is investigated. The model is based on a similar one introduced for a viscous fluid by Krishnamurti [x]. Employing this adapted model we show the growth rate for the linearised system is real. A linear instability analysis is performed. Global stability thresholds are also found using nonlinear energy theory. An excellent agreement is found between the linear instability and nonlinear stability Rayleigh numbers, so that the region of potential subcritical instabilities is very small, demonstrating that the linear theory accurately emulates the physics of the onset of convection. Received February 10, 2003 / Accepted February 10, 2003/ Published online May 9, 2003 / B. Straughan     

Effect of radiation scattering on the melting and solidification of a flat layer of a translucent medium

The paper considers the effect of isotropic and anisotropic scattering of radiation on the melting (solidification) of a flat layer of a semitransparent medium between opaque surfaces. The mathematical model of the phase transition is the classical formulation of the Stefan problem. From results of numerical calculations it follows that radiation scattering has a significant effect on the rate of propagation of the phase transition front and formation of a temperature profile during melting (solidification) of a semitransparent medium.     

Dynamic interaction of an eccentric multipole cylindrical radiator suspended in a fluid-filled borehole within a poroelastic formation

Acoustic radiation and the dynamic field induced by a cylindrical source of infinite extent, undergoing angularly periodic and axially-dependent harmonic surface vibrations, while eccentrically suspended in a fluid-filled cylindrical cavity embedded within a fluid-saturated porous elastic formation, are analyzed in an exact manner. This configuration, which is a realistic idealization of an acoustic logging tool suspended in a fluid-filled borehole within a permeable surrounding formation, is of practical importance with a multitude of possible applications in seismo-acoustics. The formulation utilizes the novel features of Biot dynamic theory of poroelasticity along with the translational addition theorem for cylindrical wave functions to obtain a closed-form series solution. The basic dynamic field quantities such as the resistive and the reactive components of the modal acoustic radiation impedance load on the source in addition to the radial and transverse stresses induced in the surrounding formation by an eccentric pulsating/oscillating cylinder in a water-filled borehole within a water-saturated Ridgefield sandstone medium are evaluated and discussed. Special attention is paid to the effects of source eccentricity, excitation frequency, and mode of surface oscillations on the modal impedance values and the dynamic stresses. Limiting cases are considered and good agreements with available solutions are obtained.     

Wave forces on stationary slender bodies

A theory is presented for the prediction of the wave forces on ships and the pressure field on slender bodies vibrating in an acoustic medium. In both radiation and diffraction the flow in the near field is approximated by a sequence of two-dimensional problems supplemented with homogeneous components which account for longitudinal flow interactions. These are matched to three-dimensional far-field approximations represented by axial source distributions and two integral equations are solved for their strengths. The theory is valid from the incompressible long-wavelength limit to wavelengths comparable to the body beam. Comparisons of wave forces and the acoustic radiation impedance pressure are in very good agreement with exact solutions. It is shown that the asymptotic matching conserves energy.     

Numerical investigation of the propagation of a pulse of radiation with λ=10.6 μm through absorbing media

The passage of electromagnetic radiation through gaseous media is of special interest when reasonantly absorbing impurities are present in the gas. The interaction of radiation with such a medium can lead, for example, to a temporal decrease of the gas temperature or to its strong heating [1-3]. At the same time the index of refraction in the channel of the light beam is altered, which leads to a deviation of the light rays from the initial direction. The main characteristics of such thermal selfaction within the framework of linear absorption theory for steady and nonsteady processes have been discussed in [4-12]. Nonequilibrium processes in the medium upon absorption of resonant radiation were not taken into account. The effect of the kinetics of vibrational energy exchange on the state of a medium upon the propagation of radiation through a mixture of CO₂ and N₂ gases was first considered in [2, 13, 14]. However, the simplest models of vibrational energy exchange were used, and saturation of the absorbing transition P20 [10°0 00°1] in the CO₂ molecule was not taken into account. Thus linearized equations of vibrational kinetics were used in [13], and only one channel of relaxation of asymmetric vibrations of CO₂ and excited nitrogen was considered in [14]. The propagation of a pulse of radiation with =10.6 m through an absorbing medium is investigated and the influence of the saturation effect and nonlinear processes of vibrational energy exchange on the self-action of light beams of Gaussian profile is studied in this paper.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 14–19, May–June, 1984.     

Combined heat transfer in a boundary layer of a selectiviely absorbing medium on a permeable plate under the conditions of intense radiation heating

Results of a numerical study of unsteady radiative-convective heat transfer in a boundary layer on a thermally thin permeable plate in the presence of intense radiation heating from outside are reported. The conjugate formulation of the problem takes into account the thermal interaction between the plate and an external gas flow. We consider a turbulent flow of an emitting-absorbing medium with the selective character of absorption. Calculation results are analyzed with a view for clarifying the influence of the governing parameters, namely, the relative temperature of an external radiation source, the Stark number, and the injection parameter. The possibility of inversion of a convective heat flux on the plate under the conditions of high-level external radiation is found. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirisk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 126–133, September–October, 1998.     

Idea of a device for modeling localization phenomena in domains of arbitrary shape and a generalized localization theory

A conceptual diagram of a testing device is proposed where the medium filling a domain of a given (practically arbitrary) shape is subjected to a homogeneous simple shear until the medium becomes unstable. The diagram is based on that of a working prototype. It is proved that the instability occurs immediately after Hadamard’s inequality for the medium plastic response is violated. It is also proved that the onset of instability is necessarily accompanied by a localization of incremental plastic strains; the proof relies on the new theory of generalized localization developed in the present paper. The theoretical results obtained fill in significant logical gaps in the traditional strain localization theory suggested by Rice and his scientific school.     

Unsteady-state flow of a gas in a channel,resulting from the motion of a piston,with magnetohydrodynamic offtake of energy and luminescence of the gas

The present paper discusses the one-dimensional unsteady-state flow of a gas resulting from the motion of a piston in the presence of weak perturbing factors, with which the investigation of the perturbed (with respect to the usual self-similar conditions) motion reduces to the solution of ordinary differential equations, is indicated. The distributions of the parameters of the gas between the piston and the shock wave are found. The conditions under which there is acceleration or slowing down of the shock front are clarified. As an example, this paper considers the unsteady-state motion of a conducting gas in a channel with solid electrodes under conditions where electrical energy is generated, and the flow of a gas taking radiation into account, under the assumption of optical transparency of the medium. The theory developed is used to solve the problem of the motion of a thin wedge with a high supersonic velocity in an external axial magnetic field, taking account of the luminescence of the layer of heated gas between the wedge and the shock wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 17–25, September–October, 1970.     

Mathematical analysis of the radiation from a magnetic line source on a cylindrically capped wedge covered by a plasma sheath

Summary Radial eigenfunctions appropriate for the dielectric (or plasma) layered medium and air are used to obtain an exact solution of the problem of radiation from a magnetic line source (or a slotted antenna) on a conducting infinite wedge with a cylindrical cap covered by a dielectric (or plasma) sheath. In order to satisfy the boundary conditions at the interfaces between the dielectric (or plasma) and the air, it is necessary to expand the radial eigenfunctions of one medium in terms of those of the other.This method can be used to solve any other two dimensional diffraction or radiation problem involving a cylindrically capped wedge surrounded by a dielectric (or plasma) sheath.     

Transfer of energy from an evaporating drop in a vapor medium

The article considers the temperature distribution around an evaporating drop in a vapor medium. The transfer of energy is effected by molecular thermal conductivity, convection, and radiation. The mean length of the free flight path of the radiation considerably exceeds the characteristic distance at which the temperature changes. The times required for relaxation of the temperature to a steady-state value are determined, as well as the characteristic distances at which the temperature distribution changes.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 74–78, January–February, 1972.The authors thank V. G. Levich for his evaluation of the results obtained.