Two fundamental modes of disturbances and their development in a plane plume above a horizontal heat source

Experimental investigations are conducted on development of the disturbances which appear in the transition to turbulence in a natural convection plume above a horizontal line heat source in air. Both the power spectra of velocity and temperature in natural transition show that there seem to be two fundamental modes of disturbances. One is an outstanding peak about 0.8 Hz and the other a small one about 1.1 Hz in the spectra. The disturbances of these fundamental frequencies are observed as anti-symmetric modes around the entrance to the transition region. The disturbance of the first fundamental frequency is a selectively amplified anti-symmetric mode in that area. In contrast, the disturbance of the second fundamental frequency is thought to be originated from a symmetric mode and then transformed into an anti-symmetric mode of the same frequency during its growth.     

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.     

Propagation of a turbulent jet impinging on a plane surface in an external stream

The results of an investigation of the three-dimensional vortex zone which forms near a plane surface when a turbulent jet impinges on it in an external stream are presented. Problems of this kind occur, for example, in a study of the effects of the entry of exhaust gases into the air intakes of engines when aircraft with thrust reversers turned on fly through an airport and when vertical-take-off-and-landing aircraft move near the earth [1–3]. The structure of the vortex zone and the temperature distribution in it are established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 56–62, September–October, 1978.In conclusion, the author thanks A. N. Sekundov and S. Yu. Krasheninnikov for attention to the work and a discussion of its results.     

Propagation of plane surface waves over an underwater obstacle and a submerged plate

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 55–62, May–June, 1991.     

Propagation of disturbances in a two-phase magnetic particle dispersion

The propagation of one-dimensional vertical perturbations of the magnetic particle concentration in a liquid-particle or gas-particle disperse medium in an external uniform magnetic field, oriented parallel or antiparallel to the force of gravity, is considered. The propagation of linear disturbances is analyzed. Linear stability criteria for layers of magnetized particles fluidized with a gas or liquid are found. The propagation of nonlinear long (kinematic) concentration waves in a medium containing dispersed magnetized particles is investigated. It is shown that in the kinematic wave approximation the propagation of the nonlinear concentration perturbations can be described by the Burgers equation. The formation of regions with a sharp change in concentration (shock fronts) is analyzed. The structure of the shock front, in particular its width, is found. It is shown that a magnetic field leads to broadening of the shock front, thus preventing the formation of concentration discontinuities and hence leading to the smearing of the boundaries of the inhomogeneities formed in the fluidized bed. This provides a basis for a qualitative explanation of the stabilization of developed nonuniform fluidized beds of magnetic particles in a magnetic field.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 76–83, July–August, 1992.     

Propagation of plane surface waves over a rectangular step with overhang and over a partially capped rectangular trench

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 40–46, September–October, 1991.     

Propagation of plane elastic waves at a plane interface between two electro-microelastic solid half-spaces

This work is concerned with the wave propagation and their reflection and transmission from a plane interface between two different electro-microelastic solid half-spaces in perfect contact. It is found that there exist five basic waves in an infinite electro-microelastic solid, namely an independent longitudinal micro-rotational wave, two sets of coupled longitudinal waves influenced by the electric effect, and two sets of coupled transverse waves. The existence of the two sets of coupled longitudinal waves is new. In the absence of microstretch and electric effects, these two coupled longitudinal waves reduce to a longitudinal displacement wave of micropolar elasticity. Amplitude and energy ratios of various reflected and transmitted waves are presented when (i) a set of coupled longitudinal wave is made incident and (ii) a set of coupled transverse wave is made incident. Numerical computations have been performed for a particular model and the variations of amplitude and energy ratios are obtained against the angle of incidence. The results obtained are depicted graphically. It has been verified that the sum of energy ratios is equal to unity at the interface and the amplitude ratios of reflected and transmitted waves depend upon the angle of incidence, frequency and elastic properties of the media. Results of some earlier workers have also been reduced from the present formulation.     

Propagation of a Dugdale crack at the edge of a half plane

This work deals with the propagation of a Dugdale crack at the edge of a half plane. The corresponding singular integral equation is solved semi-analytically. The expressions of the stress intensity factor and of the crack gap are deduced. A propagation criterion deduced from the revisited Griffith theory (Ferdjani and Marigo in Eur J Mech A Solids 53:1–9, 2015) is applied. The length of the process zone is calculated and compared with the literature results. The presented results show the evolution of the applied load with the crack length for different values of the ratio of the critical length of the Dugdale model to the initial crack length. The shape of the crack gap is also presented. Finally, a comparison between the Griffith and Dugdale models is performed.     

Evolution of plane disturbances in hypoplastic granular materials

Received July 5, 2000 / Published online February 14, 2001     

Propagation of infinitesimal disturbances in a gas according to a relativistic kinetic model

Summary In this paper a kinetic model describing a relativistic gas is considered. The propagation of infinitesimal disturbances is studied. Given the frequency of the disturbance, the complex wave number is shown to exhibit a continuous spectrum. A detailed analysis, however, indicates the possibility of isolating, at least in an asymptotic sense, a sort of discrete spectrum imbedded in the continuum. The spectrum obtained by such asymptotic analysis is in agreement with the corresponding results for the Boltzmann equation.

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Sommario In questo lavoro viene considerato un modello cinetico per descrivere un gas relativistico. Viene studiata in particolare la propagazione delle onde di piccola ampiezza e si mostra che, data la frequenza del disturbo, il numero d'onda possiede uno spettro continuo. Un'analisi dettagliata mostra però la possibilità di isolare, almeno in senso asintotico, una specie di spettro discreto immerso nel precedente. Questo spettro ricavato dall'analisi asintotica è in accordo coi corrispondenti risultati noti per l'equazione di Boltzmann.

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Partially supported by G.N.F.M. of C.N.R. and M.P.I. contract number (40%) 20120201/81 - (A) - 218142055.     

Inhomogeneous electromagnetic plane waves in crystals

Summary The propagation of inhomogeneous, time harmonic, elliptically polarised, electromagnetic plane waves in non-absorbing, magnetically isotropic, but electrically anisotropic, crystals is considered. The electric displacement and the magnetic induction are assumed to have the forms D exp l(S · x–t) and B exp l(S · x–t), respectively, at the place x and time t, where D, S, B are Gibbs bivectors (complex vectors) and is real. The implications of Maxwell's equations for the various field quantities are interpreted simply and directly through the use of bivectors and their associated ellipses.The propagation of circularly polarised waves is considered in detail. For such waves the electric displacement bivector is isotropic: D · D = 0. In order that such waves may propagate it is found that either (i) D is parallel to the slowness bivector S, so that both D and S are isotropic and coplanar, or (ii) D is parallel to the magnetic induction bivector B, so that both D and B are isotropic and coplanar. It is shown that for type (ii) the secular equation must have a double root for the slowness and conversely if the secular equation has a double root then there exists an isotropic electric displacement right eigenbivector of the optical tensor.Both types of waves are possible in a biaxial crystal. They complement each other in the following way. For type (i) all but two great circles on the unit sphere are possible circles of polarisation for circularly polarised waves with D and S parallel. Each of the exceptional great circles is such that an optic axis is normal to the plane of the circle. These two exceptional circles are the only possible circles of polarisation for circularly polarised waves of type (ii) when D and B are parallel.The situation for uniaxial crystals is similar—the only essential difference being that for uniaxial crystals there is only one exceptional circle since there is only one optic axis.For isotropic crystals the situation is quite different. Circularly polarised waves of type (i) are not possible. All great circles on the unit sphere are possible circles of polarisation for circularly polarised waves of type (ii) with D and B parallel.     

An electromagnetic,plane stress-wave generator

This paper describes a unique device that has been developed for the transient loading of models along straight and curved boundaries and that operates by discharge of a high-energy, high-voltage capacitor bank. In its present configuration, this device can generate uniform pressures from 1500 psi (10 MPa) to pressures that approach 100,000 psi (690 MPa) and that rise from zero to maximum pressure in 2 μs and decay to approximately zero in another 2 μs. The transient stress-wave patterns in photoelastic models loaded with this device have been recorded by a dynamic polariscope. The dynamic polariscope presently in use is identical to a static polariscope except that the light source is of a short enough duration (½ μs) to photographically stop the movement of the photoelastic-fringe patterns caused by the stress wave. With the stress-wave generator and the dynamic polariscope, transient photoelastic patterns have been recorded in a number of models. These patterns indicate that the scatter from duplicate shots performed with this technique is on the order of 3 percent. This represents considerable improvement over the 15-percent scatter normally experienced with sheet-explosive loading techniques. This improvement and the rapid turnaround between shots (approximately 5 min) are distinct advantages this system has over other methods of dynamic loading.     

Propagation of disturbances in three-dimensional supersonic boundary layers

The propagation of disturbances in three-dimensional boundary layers under the conditions of a global and a local strong inviscid-viscous interaction is analyzed. A system of subcharacteristics is found based on the condition for the pressure-related subcharacteristic, and an algebraic relation that gives the propagation velocity of disturbances is obtained. The velocity of propagation of disturbances is calculated for two- and three-dimensional flows. The studied problem is of great importance for accurately formulating problems for three-dimensional unsteady boundary-layer equations and for constructing adequate computational models. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 116–127, May–June, 1999.