Comments on heuristic models for electron turbulence

Summary The difficulties imposed by the largely nonlinear character of the differential equations governing turbulence resulted in many proposals for empirical models. We shall prove that some often used models are incorrect as they are clearly not properly normalized.

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Riassunto Le difficoltà imposte dal carattere largamente non lineare delle equazioni differenziali che regolano la turbolenza hanno dato come risultato molte proposte per modelli empirici. Si prova che alcuni modelli spesso usati non sono corretti poiché non possono essere normalizzati appositamente.

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Резюме Трудности, накладываемые нелинейным характером дифференциальных уравнений, описывающих турбулентность, приводят к большому числу эмпирических моделей. Мы доказываем, что некоторые часто используемые модели не являются корректными, так как они не нормированы надлежащим образом.

     

Similarity solutions of isothermal flows behind a MGD blast wave in an inhomogeneous medium

Summary Self-similar solutions of isothermal flows behind a cylindrical magnetogasdynamic blast wave have been obtained. A strong cylindrical shock wave generated by a sudden line source explosion in an inhomogeneous medium of electrically conducting gas has been studied. Numerical and analytical treatments have been presented and a uniformly valid distribution of pressure, density and velocity profiles has been determined and the magnetic-field effects on the flow distributions have been investigated. The shock propagation law is determined by extending Whitham’s rule for a MGD flow with infinite electrical conductivity.

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Riassunto Si sono ottenute soluzioni autosimili di flussi isotermici dietro un’onda espansiva, magnetogasdinamica, cilindrica. è stata studiata un’onda d’urto forte cilindrica generata da un’improvvisa esplosione a sorgente lineare in un mezzo non omogeneo di un gas elettricamente conduttore. Si presentano trattamenti numerici e analitici e si è determinata una distribuzione uniformemente valida dei profili di pressione, densità e velocità e si sono studiati gli effetti del campo magnetico sulle distribuzioni del flusso. La legge di propagazione dell’urto si determina estendendo la regola di Whitham per un flusso MGD con conduttività elettrica infinita.

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Резюме Получются самоподобные решения для изотермических потоков за цилиндрической магнитогазодимамической ударной. Исследется сильная цилиндческая ударная волна, которая обрзуетсяв резуль↦ате внеапного взрыва линейного истоника в неоднородной среде электрически проводящего газа. Проводятся численное и аналитическое рассмотрение. Определяжтся распредение давления, профили плотности и скорости. йсследуется влияние магнитного поля на распредение потока. Определется закон распространения ударной волны, обобшая правило Витама для магнитогазодинамического потока с бесконечной электрической проводимостью.

     

Numerical computation of transient shocked chemically reactive flows

Using the ability of the method of characteristics to evaluate shock fronts in an accurate manner, a formulation is presented which incorporates the effect of rapid exothermic chemical reactions in the flow. The formulation is applied to the computation of the unsteady reactive flow field behind a cylindrial expanding blast wave propagating in a mixture of hydrogen and oxygen. Details of the computational procedure are described. Results are presented for a sample problem and compared with those for the non-reactive case to illustrate the influence of chemical reactions.     

Diffraction of waves by semi-infinite breakwater using finite and infinite elements

A finite and infinite element model is derived to predict wave patterns around a semi-infinite breakwater in water of constant depth. Both circular and square meshes of elements are used. The wave theory used is that of Berkhoff. The appropriate boundary conditions for finite and infinite boundaries are described. The singularity in the velocity at the breakwater tip is modelled effectively using the technique of Henshell and Shaw originally developed in elasticity. The results agree well with the analytical solution. In addition the problem of waves incident upon a semi-infinite breakwater and parabolic shoal, where both diffraction and refraction are present, is solved. There is no analytical solution for this case. The combination of finite and infinite elements is found to be an effective and accurate technique for such problems.     

Instability of plasma waves in an electromagnetic field

Summary In the presence of a weak laser field the plasma scattering by electrons is discussed.

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Riassunto In presenza di un campo laser debole, si discute la diffusione del plasma mediante elettroni.

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Резюме В присутствии слабого лазерного поля обсуждается рассеяние плазмы на электронах.

     

Mesh effects on the computation of non-linear gravity waves of arbitrary discharge

Numerical computations of non-linear gravity waves are presented and the effects of mesh variations on the results are discussed. Waves are regarded as two-parameter families (λ,A)_Q of arbitrary discharge Q, and computations are carried out using a new Kantorovich algorithm. Mesh effects are to a large extent dependent on the particular wave region under consideration. Three such regions are identified and typical examples are computed and discussed.     

Transmission and reflection of waves in a one-dimensional disordered array

We study wave propagation in a one-dimensional disordered array of scattering potentials. We calculate the mean and the variance of the resistance of the array, defined as the ratio of reflected to transmitted intensity, for a rather wide class of probability distributions characterizing the disorder. Our method is based on a mapping of the wave propagation onto the motion of a two-dimensional oscillator which is perturbed parametrically.     

Double-grid Chebyshev spectral elements for acoustic wave modeling

Highly accurate algorithms are needed for modeling wave propagation phenomena in realistic media. The spectral element methods, either based on a Chebyshev or a Legendre polynomial basis, have shown their excellent properties of high accuracy and flexibility in describing complex models outperforming other techniques. In contrast with standard grid methods, which use dense spatial meshes, spectral element methods discretize the computational domain in a very coarse mesh. With constant-property elements, this fact may in some cases reduce seriously the computational efficiency. For instance, if the medium is finely heterogeneous, it may need to be described in a much finer way than the acoustic wave field. The double-grid approach presented in this work is a viable way for overcoming this lack of the method and for handling problems where the medium changes continuously or even sharply on the small scale. The variation in the properties is taken into account by using an independent set of shape functions defined on a temporary local grid in such a way that either the small scale fluctuations are accurately handled, without the need of a global finer grid, and the macroscopic wave field propagation is solved with no loose of computational efficiency.     

Direct noise computation of adaptive control applied to a cavity flowSimulation directe de l'atténuation par contrôle adaptatif du rayonnement d'une cavité affleurée par un écoulement

The Large Eddy Simulation of closed-loop active flow control applied to a 3D cavity excited by a compressible airflow with a Mach number of 0.6 is presented. The control actuator is an idealized synthetic jet located at the upstream cavity edge, and the control function is supplied by a feedback LMS-type algorithm whose input is a pressure signal measured inside the cavity. The radiated sound, provided directly by the LES simulation, was shown to decrease substantially when active control was applied. A simultaneous reduction of the vertical velocity fluctuations in the shear layer was observed. The intensity of vortical structures inside the cavity was also reduced, although the general aspect of the recirculation zone was not modified. The direct noise computation technique, which supplies the pressure field by solving the fluid mechanics equations, is shown to constitute a powerful tool for studying active aeroacoustic noise control. To cite this article: O. Marsden et al., C. R. Mecanique 331 (2003).     

Modélisation probabiliste d'une expérience ultrasonore : calcul de la dispersion sur les mesures de célérité

This Note presents a probabilistic model of transient wave reflection at a fluid–solid interface. The configuration represents an ultrasonic experiment used for bone tissue evaluation. The parametric method is used to derive the probabilistic model for the mechanical parameters of the solid (bone); the associated random variables are derived according to the maximum entropy principle. A Monte Carlo simulation, associated with the Cagniard–de Hoop method to calculate the acoustic response, yields the probability density for an output ultrasonic parameter similar to the velocity of longitudinal waves in the solid. Results demonstrate the sensitivity of the probability density of this parameter to the experimental setup. To cite this article: K. Macocco et al., C. R. Mecanique 333 (2005).