Shock Waves In Media Research Articles

Nonlinear diagnostic of a shallow sea stratified by density with weak dispersion and weak nonlinearity

The paper discusses the methodology for determining the parameters of the hydrophysical background of a shallow sea stratified by density. The background of this sea is characterized by quadratic nonlinearity - α, high-frequency dispersion -β and phase velocity of linear internal gravitational waves - c 0. In the framework of the theory of weakly-intensity shock waves in media with weak dispersion, expressions are obtained for calculating the parameters: α, β and c 0. The data for calculations are in-situ measurement of the spatial-temporal characteristics of the internal undular bores, traveling on the pycnocline of the shallow sea.

Dynamics of Shock Waves in Media with Longitudinal Stratification

In this paper, we consider the problems of the dynamics of plane shock waves in media with one-dimensional longitudinal density stratification. The rationale, features, and limits of applicability of the Whitham method for calculating the wave propagation parameters are discussed. The dependence of the velocity of a plane shock wave on the medium density ahead of its front is obtained for any wave intensity.

Shock waves in media with negative electromagnetic susceptibilities

The Fock–Kemmer theory of precursor shock wave speeds in classical field theory is extended to the case of media with negative electromagnetic susceptibilities.

Computation of shock waves in media with an interphase boundary by the CIP-CUP method on an adaptive grid

A numerical technique of computing shock waves in compressible media with movable deforming interphase boundaries including those of the gas-liquid type has been realized. The approach without explicit separation of the interphase boundary is applied. The CIP-CUP method is used for integrating the equations of gas dynamics. An adaptive grid of special kind (the soroban-grid) is utilized. Some results of testing the technique using one- and two-dimensional problems are given. Results of computation of impact of a jet on a thin liquid layer on a wall are presented.

Mechanism of the appearance of the cellular structure of a shock wave in the region of its ambiguous representation

The mechanism of the formation of the cellular structure for a planar shock wave in an equilibrium medium, which arises due to its ambiguous representation characterized by the fulfillment of the condition L > 1 + 2M, i.e., one of the linear criteria of the instability of the shock wave in media with arbitrary thermodynamic properties, has been considered. It has been shown that this process is based on “switching” between different types of the possible decay configurations, which occurs during the motion and interaction of the transverse waves moving along the shock wave front.

Stability and ambiguous representation of shock wave discontinuity in thermodynamically nonideal media

The nonlinear analysis of the behavior of a shock wave on a Hugoniot curve fragment that allows for the ambiguous representation of shock wave discontinuity has been performed. The fragment under consideration includes a section where the condition L > 1 + 2M is satisfied, which is a linear criterion of the instability of the shock wave in media with an arbitrary equation of state. The calculations in the model of a viscous heat-conductive gas show that solutions with an instable shock wave are not implemented. In the one-dimensional model, the shock wave decays into two shock waves or a shock wave and a rarefaction wave, which propagate in opposite directions, or can remain in the initial state. The choice of the solution depends on the parameters of the shock wave (position on the Hugoniot curve), as well as on the form and intensity of its perturbation. In the two-dimensional and three-dimensional calculations with a periodic perturbation of the shock wave, a “cellular” structure is formed on the shock front with a finite amplitude of perturbations that does not decrease and increase in time. Such behavior of the shock wave is attributed to the appearance of the triple configurations in the inclined sections of the perturbed shock wave, which interact with each other in the process of propagation along its front.

Сollimation of relativistic and nonrelativistic shock waves in medium with large-scale density gradient

Сollimation of relativistic and nonrelativistic shock waves in medium with large-scale density gradient

Optical shock waves in media with quadratic nonlinearity

We report the existence of optical shock waves in quadratic media with complex dispersion. By using a truncated Painleve method it is analytically shown that the second harmonic and fundamental fields can propagate into the unexcited region as a mutually trapped two-field shock wave. The conditions for the existence of this solution are determined.

Free‐Free Radiation from Dense Interstellar Shock Waves

We present detailed calculations of the free-free emission behind shock waves in media where the postshock gas may be optically thick at radio frequencies. Using a numerical shock code, we solve the free-free radiative transfer equation at frequencies of 1.5, 5, and 15 GHz for a family of planar shock models that cover a wide range of densities (1000 cm-3 ≤ n0 ≤ 109 cm-3) and shock velocities (30 km s-1 ≤ V0 ≤ 300 km s-1). These models also predict how different preshock magnetic fields and viewing angles affect the overall free-free emission. As the shock velocities and preshock densities increase, the free-free spectral indices generally rise from optically thin values (~-0.1) and approach optically thick ones (~2.0). We find that for V ≥ 120 km s-1, the ionized precursor produced by the emergent postshock UV radiation can itself become optically thick to free-free radiation when the preshock density exceeds 106 cm-3. We also find that for some combinations of shock parameters, the superposition of radiation from the precursor onto that of the postshock region can produce spectral indices exceeding 2.0. In addition, we find that magnetic fields can suppress the free-free radiation only if they are strong enough to lower the magnetosonic Mach number below 4 for V ≥ 100 km s-1. An observer who knows the resolved angular sizes, fluxes, and spectral indices of a thermal radio source can use our grids to determine the preshock density, shock velocity, and viewing angle to the source. Possible applications include HH objects, shocked cloudlets, and accretion shocks deep within molecular clouds. As an example, we use our results to predict shock parameters for HH 1-2 and several thermal radio sources in Cep A east. We find that the predicted shock parameters for HH 1 and 2 agree well with those inferred from optical line ratios and line profiles. Radio emission from sources in Cep A are explained reasonably well as arising from thermal radiation behind a dense, fast shock like one might expect from a stellar jet deeply embedded within the molecular cloud core.

Converging shock waves in media with decreasing density

Converging shock waves in media with decreasing density

On the refraction of shock waves

This paper discusses the refraction of plane shock waves in media with arbitrary equations of state. Previous work is reviewed briefly, then a rigorous definition of wave impedance is formulated. Earlier definitions are shown to be unsatisfactory. The impedance is combined with the boundary conditions at the media interface to study both head-on and oblique shock incidence. The impedance determines the nature of the reflected and transmitted waves, their intensities, and the fractions of energy and power that are reflected and transmitted. The refractive index is also defined and determines whether or not a wave will be refracted, and also helps determine whether the wave system will be regular or irregular. The fundamental law of refraction is derived and shown to be a consequence of the fact that an arbitrary point on a shock or an expansion wave follows a ray path of minimum time between any two points on the path. This is a generalization of Fermat's Principle to media that are deformed and convected by the waves propagating through them.

Self-action of wave packets in a nonlinear medium and femtosecond laser pulse generation

The review describes the present status of the physics of optical pulse self-action phenomenon. A brief analysis of linear propagation of ultrashort laser pulses in dispersive media and optical elements is given. Results on self-phase-modulation and on profile shock waves in media with various group velocity dispersion are presented. The problems of optical pulse compression and the possibilities to control their shape are discussed in detail. Particular attention is paid to the physical aspects of formation and interaction of optical solitons. Stochastic problems of temporal self-action are also discussed. In conclusion the promising directions in nonlinear optics of femtosecond laser pulses are discussed.

Theory of shock waves in media undergoing phase transitions

Theory of shock waves in media undergoing phase transitions

Mathematical simulation of Mach reflection of shock waves in media with different adiabatic indices

Some peculiarities of the processes of regular and Mach reflection at constant adiabatic index γ=cp/cv=1.4 were investigated theoretically in [1]. It was demonstrated that increase in incident-wave intensity above some value leads to the appearance of an internal compression discontinuity (Fig. 1) and a break in the reflected wave (at point h), both of which had been observed previously only in experiment [2–4]. In the present study the method described in [1] is used to study the influence of adiabatic index on these peculiarities of the Mach reflection process which lead to a significant increase in pressure (to a maximum value Pm) on the surface wedge in the vicinity of point i. Pressure and density curves along the wedge surface are presented. It is found that increase in γ leads to the same qualitative changes in the pressure and density curves on the surface as are observed upon increase in semiaperture angle of the wedge Β or upon decrease in Mach number Mf of the shock-wave front incident on the wedge ab. These similarities in the shock-wave reflection process were first noted in [5] for weak shock waves in which the internal compression discontinuity does not appear.

Propagation of weak shock waves in media with an arbitrary number of chemical reactions: PMM vol. 41, n≗ 6, 1977, pp. 1062–1071

Nonlinear asymptotic equations that describe the wave motions of two-phase media consisting of a gas and solid heavy particles suspended in it are derived. Within the framework of the theory developed, it is shown that there exists an exact mathematical analogy between the motions of two-phase and chemically active media. By means of this analogy, it is possible to pass from well-known results for chemically active media to two-phase systems without making any changes.

Propagation of magnetogasdynamic plane shock waves in an exponential medium

An analytic solution for propagation of strong plane magnetogasdynamic shock waves in a medium with density increasing exponentially under low pressure is obtained in this paper. The shock wave moves with variable velocity and the total energy of the wave is variable.