The decay of a magnetohydrodynamic shock wave

Résumé On utilise l'analyse linéaire pour étudier les faibles perturbations non-isentropiques des équations relatives aux écoulements unidimensionnels et non-stationnaires d'un fluide non visqueux idéal, parfaitement conducteur de l'électricité et compressible, soumis à l'action d'un champ magnétique transversal. On utilise la solution générale de la perturbation non-isentropique d'un écoulement par ondes simples centrées pour déterminer la perturbation qui se manifeste lorsqu'une onde de choc magnétohydrodynamique, tout d'abord uniforme et de force arbitraire, rencontre le régime d'onde simple.Dans le cas limité d'un champ magnétique nul, la solution se réduit exactement à celle du problème correspondant de la dynamique classique des gaz. C'est la une confirmation de la validité de la théorie.

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This research was supported by National Science Foundation grant GP 87190.     

The motion of a non-uniform hydromagnetic shock wave

Sommaire Nous considérons un écoulement, unidimensionnel, non stationaire, non isentropique, d'un fluide parfait, parfaitement conducteur de l'électricité, soumis à l'action d'un champ magnétique pour une orientation transversale du champ et le mouvement non continu d'une onde de choc magnetohydrodynamique.

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This research was supported by a National Aeronautics and Space Administration general research grant to the University of Wisconsin.     

Magnetohydrodynamic shock wave decay

Summary A modified hodograph transformation is used to obtain an exact solution of the equations governing the one-dimensional unsteady flow of an ideal, inviscid, perfectly conducting compressible fluid, subjected to a transverse magnetic field. This solution is used to obtain an approximate representation of the path of an initially uniform shock wave which intersects a centered simple wave. In the limit of vanishing magnetic field, the solution reduces exactly to the solution of the corresponding problem for conventional gas dynamics.

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Résumé Une transformation hodographe modifiée est employée pour obtenir une solution exacte des équations relatives aux écoulements unidimensionnels non-stationnaires et non-isentropiques d'un fluide non visqueux idéal, parfaitement conducteur d'électricité et compressible, soumis à l'action d'un champ magnétique transversal. On utilise cette solution pour obtenir une représentation approximative de la trajectoire d'une onde de choc magnétohydrodynamique initialement uniforme, rencontrant une onde simple centrée.Dans le cas limite d'un champ magnétique nul, la solution se réduit exactement à celle du problème correspondant de la dynamique classique des gaz. C'est là une confirmation de la validité de la théorie.

     

Solitary wave and shock wave solutions to a second order wave equation of Korteweg-de Vries type

This paper obtains the solitary wave as well as the shock wave solutions to the second order wave equation of Korteweg-de Vries type that was first proposed in 2002. The ansatz method is used to retrieve these solutions. The domain restrictions as well as the parameter regimes are all identified in the process of obtaining the solution.     

Breaking of a weak shock wave on shallow water

A perturbation method is used to derive the fundamental equations and certain necessary and sufficient conditions for the breaking of weak shock waves encountered in the investigation of the one-dimensional and two-dimensional systems of equations of motion of shallow water.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 173, pp. 159–162, 1988.     

Self-similar convergence of a shock wave in a heat conducting gas

The problem of the convergence of a spherical shock wave (SW) to the centre, taking into account the thermal conductivity of the gas in front of the SW, is considered within the limits of a proposed approximate model of a heat conducting gas with an infinitely high thermal conductivity and a small temperature gradient, such that the heat flux is finite in a small region in front of the converging SW. In this model, there is a phase transition in the surface of the SW from a perfect gas to another gas with different constant specific heat and the heat outflow. The gas is polytropic and perfect behind the SW. Constraints are derived which are imposed on the self-similarity indices as a function of the adiabatic exponents on the two sides of the SW. In front of the SW, the temperature and density increase without limit. In the general case, a set of self-similar solutions with two self-similarity indices exists but, in the case of strong SW close to the limiting compression, there are two solutions, each of which is completely determined by the motion of the spherical piston causing the self-similar convergence of the SW.     

Oblique magnetohydrodynamic shock wave decay

Summary A modified hodograph transformation is used to obtain an exact solution of the equations governing the one-dimensional unsteady flow of an ideal, inviscid, perfectly conducting compressible fluid, subjected to an oblique magnetic field. This solution is used to obtain an approximate representation of the path of an initially uniform shock wave which intersects a centered simple wave. The solutions for the corresponding problems in the conventional, non-magnetic case and for a transverse orientation of the applied magnetic field are contained as special limiting cases of the solutions of the present paper. This provides a valuable check on the theory.

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Résumé Une transformation hodographe modifiée est employée pour obtenir une solution exacte des équations relatives aux écoulements unidimensionnels non-stationnaires et non-isentropiques d'un fluide non visqueux idéal, parfaitement conducteur d'électricité et compressible, soumis à l'action d'un champ magnétique oblique avec deux composantes différentes de zero. On utilise cette solution pour obtenir une représentation approximative de la trajectoire d'une onde de choc magnétohydrodynamique initialement uniforme, rencontrant une onde simple centrée. Les solutions pour le cas non magnétique et pour un champ transversal apparaissent comme des cas limites particuliers de la solution présentée ici, c'est là une confirmation de la validité de la theorie.

     

Asymptotic theory of the asymmetry parameters of a weak shock wave

A theory of the asymmetry parameters of a weak shock wave in a binary gas mixture, based on the expansion of the solutions of the Burnett equations in series in a small parameter of the shock wave intensity, that ensures the asymptotic accuracy of the required data, is given. The dependence of the solution on the characteristics of the mixture is examined. The known results for a polyatomic gas are refined and supplemented.     

Weak asymptotics of shock wave formation process

We construct an asymptotic (in a weak sense) solution corresponding to the shock wave formation in a special situation.     

The dissociation of a pure diatomic gas behind a strong normal shock wave

Zusammenfassung Die Arbeit behandelt das Problem der Dissoziation eines reinen diatomischen Gases durch einen starken geraden Verdichtungsstoss. Mit Hilfe einiger vereinfachender Annahmen und eines theoretischen Ausdruckes für die Dissoziationsgeschwindigkeit wird eine analytische Darstellung der Resultate erzielt. Der Einfluss der Erhitzung und der Kompression durch den Stoss wird eingehend diskutiert.

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The research reported in this document has been sponsored in part by the Air Research and Development Command, United States Air Force, under contract AF 61(514)1124, through the European Office, A.R.D.C.     

Vulcanization of mixtures of cured and raw rubbers in a shock wave

The authors show that current pulses arise in rubber mixtures and steel rods under the influence of a shock wave.All-Union Scientific-Research and Construction-Technological Institute of the Rubber Industry, Volzhskii. Translated from Mekhanika Polimerov, No. 2, pp. 348–349, March–April, 1974.     

Isothermal flow behind a shock wave propagating in the solar wind

A Parker-type blast wave, which is headed by a strong shock, driven out by a propelling contact surface, moving into an ambient solar wind having a strictly inverse square law radial decay in density, is studied. Assuming the self-similar flow behind the shock to be isothermal, approximate analytical and exact numerical solutions are obtained. There is a good agreement between the approximate analytical and exact numerical solutions. It is observed that the mathematical singularity in density at the contact surface is removed for the isothermal flow.     

The diffraction of a shock wave by an inclined body of revolution

Summary The interaction between a plane normal shock wave of arbitrary strength and a slender body of revolution, held with its axis at a small angle to the direction of propagation of the shock, is considered. The pressure field is determined by using the method of matched asymptotic expansions and the general results are applied to the problem of diffraction by an inclined circular cone.

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Zusammenfassung Es wird die Beeinflussung einer ebenen Stosswelle beliebiger Stärke durch einen schlanken Rotationskörper untersucht, dessen Achse einen kleinen Winkel mit der Ausbreitungsrichtung des Stosses bildet. Das Druckfeld wird mit Hilfe der abgestimmten asymptotischen Entwicklungen bestimmt, und die allgemeinen Resultate werden auf das Problem der Diffraktion durch einen angestellten Kreiskegel angewendet.

     

Computation of a shock wave structure in monatomic gas with accuracy control

The structure of a shock wave in a monatomic one-component gas was computed by solving the Boltzmann kinetic equation with accuracy controlled with respect to computational parameters. The hard-sphere molecular model and molecules with the Lennard-Jones potential were considered. The computations were performed in a wide range of Mach numbers with the accuracy no less than 3% for the shock front width and 1% for local values of density and temperature. The shock wave structure was studied in terms of macroscopic gas characteristics and in terms of the molecular velocity distribution function.