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1.
By employing the method of multiple time scales, we derive here the transport equations for the primary amplitudes of resonantly interacting high-frequency waves propagating into a non-equilibrium gas flow. Evolutionary behavior of non-resonant wave modes culminating into shocks or no shocks, together with their asymptotic decay behavior, is studied. Effects of non-linearity, which are noticeable over times of order O(ε-1), are examined, and the model evolution equations for resonantly interacting multi-wave modes are derived. 相似文献
2.
S. A. Egorushkin 《Fluid Dynamics》1982,17(6):935-940
Special curves, called shock polars, are frequently used to determine the state of the gas behind an oblique shock wave from known parameters of the oncoming flow. For a perfect gas, these curves have been constructed and investigated in detail [1]. However, for the solution of problems associated with gas flow at high velocities and high temperatures it is necessary to use models of gases with complicated equations of state. It is therefore of interest to study the properties of oblique shocks in such media. In the present paper, a study is made of the form of the shock polars for two-parameter media with arbitrary equation of state, these satisfying the conditions of Cemplen's theorem. Some properties of oblique shocks in such media that are new compared with a perfect gas are established. On the basis of the obtained results, the existence of triple configurations in steady supersonic flows obtained by the decay of plane shock waves is considered. It is shown that D'yakov-unstable discontinuities decompose into an oblique shock and a centered rarefaction wave, while spontaneously radiating discontinuities decompose into two shocks or into a shock and a rarefaction wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 147–153, November–December, 1982. 相似文献
3.
We consider shock waves satisfying the viscous profile criterion in general systems of n conservation laws. We study S
i, j
dual-family shock waves, which are associated with a pair of characteristic families i and j. We explicitly introduce defining equations relating states and speeds of S
i, j
shocks, which include the Rankine–Hugoniot conditions and additional equations resulting from the viscous profile requirement.
We then develop a constructive method for finding the general local solution of the defining equations for such shocks and
derive formulae for the sensitivity analysis of S
i, j
shocks under change of problem parameters. All possible structures of solutions to the Riemann problems containing S
i, j
shocks and classical waves are described. As a physical application, all types of S
i, j
shocks with i>j are detected and studied in a family of models for multi-phase flow in porous media. 相似文献
4.
A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions. The obtained results show that such nonlinear wave equations admit richer classical and nonclassical symmetries, leading to the conservation laws and the reduction of the wave equations. Some exact solutions of the considered wave equations for particular cases are derived. 相似文献
5.
L. N. Lebedeva 《Fluid Dynamics》1976,11(6):968-971
Additional relationships must be used [1–3], in addition to those following from the main integral laws, in describing ionizing detonation waves, exactly as for ionizing shocks. These additional relationships are obtained from the requirement for the existence of wave structure. The structure of detonation waves ionizing a gas in an oblique magnetic field was investigated in [1, 2]. The case of a plane-polarized structure was considered, when the velocity vector and the magnetic field lie in a plane passing through the normal to the front. The structure of ionizing detonation waves is studied in this paper for the case when the wave is spatially polarized and both transverse magnetic field components vary in the structure. It is considered that the magnetic viscosity and a quantity reciprocal to the chemical reaction rate are much greater than the remaining dissipative coefficients in the layer representing the structure. Conditions for the existence of such a spatial structure are clarified. Plane-polarized ionizing detonation waves whose structure is not planar are also considered. When the characteristic length of magnetic field dissipation is much greater or much less than the characteristic length of the chemical reaction, the additional relationships assuring the existence of structure are written down explicitly or are investigated qualitatively.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 166–169, November–December, 1976. 相似文献
6.
Eric Varley 《Archive for Rational Mechanics and Analysis》1965,20(4):309-328
The general theory of simple waves in Green-elastic and Cauchy-elastic materials is given. Such waves generate three-dimensional unsteady deformations. Boundary conditions producing such waves are derived together with conditions under which shocks occur. The theory is used to illustrate conditions behind acceleration fronts moving into homogeneously deformed regions and also the modes of propagation of fronts moving into a simple wave. The steady flow of an elastic material past a rigid developable surface is discussed. Simple waves which are principal waves are also discussed. 相似文献
7.
Sylvie Benzoni-Gavage 《Journal of Dynamics and Differential Equations》2002,14(3):613-674
Semi-discrete shock profiles are traveling wave solutions of hyperbolic systems of conservation laws under discretization in space. The existence of semi-discrete shocks has been investigated in earlier papers. Here the spectral stability of those nonlinear waves is addressed, and formulated in terms of a variational delay differential operator. Constructing a generalized Evans function, in infinite dimensions, it is shown how to derive stability criteria. Some examples are given when the criterion is fully explicit, e.g., for extreme Lax shocks. Additionally, connection is made with the alternative approach proposed by Chow, Mallet-Paret, and Shen (Journal of Differential Equations 1998), regarding the stability of traveling waves in general Lattice Dynamical Systems. 相似文献
8.
A. N. Norris 《Journal of Elasticity》1991,25(3):247-257
Several results are presented concerning symmetry properties of the tensor of third order elastic moduli. It is proven that a set of conditions upon the components of the modulus tensor are both necessary and sufficient for a given direction to be normal to a plane of material symmetry. This leads to a systematic procedure by which the underlying symmetry of a material can be calculated from the 56 third order moduli. One implication of the symmetry conditions is that the nonlinearity parameter governing the evolution of acceleration waves and nonlinear wave phenomena is identically zero for all transverse waves associated with a plane of material symmetry. 相似文献
9.
An experimental investigation was made of cavitation phenomena induced by underwater shock wave focusing applied to the extracorporeal microexplosion lithotripsy (microexplosion ESWL). Firstly an underwater microexplosion generated by detonation of a 10 mg silver azide pellet was studied and secondly underwater shock focusing and its induced cavitation phenomena were investgated. Underwater shock wave was focused by using a semi-ellipsoidal reflector in which a shock wave generated at the first focal point of the reflector was reflected and focused at the second focal point. It is found that an explosion product gas bubble did not produce any distinct rebound shocks. Meantime cavitation appeared after shock focusing at the second focal point where expansion waves originated at the exit of the reflector were simultaneously collected. A shock/bubble interaction is found to contribute not only to urinary tract stone disintegration but also tissue damage. The cavitation effect associated with the microexplosion ESWL was weaker in comparison with a spark discharge ESWL. The microexplosion ESWL is an effective method which can minimize the number of shock exposures hence decreasing tissue damage by conducting precise positioning of urinary tract stones.This article was processed using Springer-Verlag TEX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society. 相似文献
10.
We determine the nonclassical potential symmetries for a number ofequations that arise in the literature. A large number of these areobtained for some equations which only admit a single potential(classical) symmetry (e.g., the wave equation and the motion of wavesthrough some medium). However, we show that some of the exact solutionsinvariant under the nonclassical potential symmetries are equivalent toknown solutions but these solutions are not obtainable through theclassical point or potential symmetries. The Korteweg–deVries equation,it is shown, does not admit nonclassical potential symmetries – as inthe classical case. 相似文献
11.
Leonardo Seccia 《Continuum Mechanics and Thermodynamics》1995,7(3):277-296
We study the propagation of electromagnetic shock waves in an isotropic nonlinear dielectric medium. In order to select the physical shocks among all the mathematical solutions the usualLax conditions are applied. However, here they do not appear sufficient since strong shocks are present and the differential system is not strictly hyperbolic. So, two additional criteria are studied, theentropy growth condition and thereflection and transmission criterion, and a comparative analysis is developed. Finally, some experimental checks are suggested considering in particular the possible shape changes of an initial shock wave during its propagation. 相似文献
12.
Physical mechanisms of the rogue wave phenomenon 总被引:8,自引:0,他引:8
A review of physical mechanisms of the rogue wave phenomenon is given. The data of marine observations as well as laboratory experiments are briefly discussed. They demonstrate that freak waves may appear in deep and shallow waters. Simple statistical analysis of the rogue wave probability based on the assumption of a Gaussian wave field is reproduced. In the context of water wave theories the probabilistic approach shows that numerical simulations of freak waves should be made for very long times on large spatial domains and large number of realizations. As linear models of freak waves the following mechanisms are considered: dispersion enhancement of transient wave groups, geometrical focusing in basins of variable depth, and wave-current interaction. Taking into account nonlinearity of the water waves, these mechanisms remain valid but should be modified. Also, the influence of the nonlinear modulational instability (Benjamin–Feir instability) on the rogue wave occurence is discussed. Specific numerical simulations were performed in the framework of classical nonlinear evolution equations: the nonlinear Schrödinger equation, the Davey–Stewartson system, the Korteweg–de Vries equation, the Kadomtsev–Petviashvili equation, the Zakharov equation, and the fully nonlinear potential equations. Their results show the main features of the physical mechanisms of rogue wave phenomenon. 相似文献
13.
Victor N. Nikolaevskiy 《Transport in Porous Media》2008,73(2):125-140
The Frenkel–Biot P-wave of the first type is a seismic longitudinal wave observed in rocks fully saturated with oil, water
or high-pressure gas. The P-wave of the second type is observed in unsaturated soils and other porous media saturated with
gas of low pressure. Their models include properties of the skeleton, that is, its elastic modules and its own viscosity.
If the non-linear terms are accounted for, the asymptotic analysis, usual for weak non-linear waves, might be applied to get
the wave spectrum evolution. The wetness of grains contacts in soils and such components of oil as tars or bitumen, which
attached to the skeleton, can be described by generalized viscous–elastic stress–strain connections. The latter are nominated
in such a way that creates the narrow frequency interval of wave of negative dissipation where the non-linear terms begin
to play the main role besides the neutral stability for waves of zero wave number. The corresponding case, relevant to single
continuum model, was analyzed in the literature. Here it is shown that the interpenetrating continua with interaction of the
Darcy type provide the dissipation sink in the wave evolution equation. This generalization, (Tribelsky, M.I.: Phys. Rev.
Lett. (2007, submitted)), can stabilize the asymptotic solution of the evolution equation, where the dispersion terms are
omitted. The asymptotic solution of the equation is invariant to initial conditions and it means a transformation of initial
wave spectra to unique one while wave is spreading in the viscous–elastic medium under consideration. This explains the phenomenon,
observed in wave tests at marine beach, when any dynamics action (impact, explosion, and ultrasound action) created at some
distance a wave of a single frequency (~25 Hz). 相似文献
14.
A new nonlinear evolution equation is derived for surface solitary waves propagating on a liquid-air interface where the wave motion is induced by a harmonic forcing. Instead of the traditional approach involving a base state of the long wave limit, a base state of harmonic waves is assumed for the perturbation analysis. This approach is considered to be more appropriate for channels of length just a few multiples of the depth. The dispersion relation found approaches the classical long wave limit. The weakly nonlinear dispersive waves satisfy a KdV-like nonlinear evolution equation with steeper nonlinearity. 相似文献
15.
L. van Wijngaarden 《Applied Scientific Research》1970,22(1):366-381
Asbtract The structure of shock waves in liquids containing gas bubbles is investigated theoretically. The mechanisms taken into account
are the steepening of compression waves in the mixture by convection and the effects due to the motion of the bubbles with
respect to the surrounding fluid. This relative motion, radial and translational, gives rise to dissipation and to dispersion
caused by the inertia of the radial flow associated with an expanding or compressed bubble. For not too thick shocks the dissipation
by radial motion around the bubbles dominates over the dissipation by relative translational motion, in mixtures with low
gas content. The overall thickness of the shock appears to be determined by the dispersion effect. Dissipation, however, is
necessary to permit a steady shock wave. It is shown that, analogous to undular bores, a stationary wave train may exist behind
the shock wave. 相似文献
16.
We examine the reflection and transmission phenomena of quasi-longitudinal plane(QP) waves in an AlN-ZnO laminated composite structure. The structure is designed under the influence of the initial stresses in which one carrier piezoelectric semiconductor(PSC) half-space is in welded contact with another PSC half-space.The secular equations in the transversely isotropic PSC material are derived from the general dynamic equation, taking the initial stresses into consideration. It is shown that the incident quasi-longitudinal wave(QP-mode) at the interface generates four types of reflected and transmitted waves, namely, QP wave, quasi-transverse(QSV) wave,electric-acoustic(EA) wave, and carrier plane(CP) wave. The algebraic equations are obtained by imposing the boundary conditions on the common interface of the laminated structure. Reflection and transmission coefficients of waves are obtained by implementing Cramer's rule. Profound impacts of the initial stresses and exterior electric biasing field on the reflection and transmission coefficients of waves are investigated and presented graphically. 相似文献
17.
圆柱形汇聚激波诱导 Richtmyer-Meshkov不稳定的 SPH 模拟 总被引:3,自引:3,他引:0
汇聚激波诱导不同物质界面的Richtmyer-Meshkov(RM)不稳定现象在惯性约束核聚变领域有重要的学术意义和工程背景.基于网格离散的宏观流体力学方法由于数值扩散问题往往需要高阶精度算法才能准确追踪界面演化,且对大变形和破碎合并等复杂界面追踪也极为困难.光滑粒子流体动力学(smoothed particlehydrodynamics,SPH)方法采用纯拉格朗日算法,可以有效克服上述难点.但经典SPH算法需采用人工黏性处理强间断,在激波间断处往往会出现严重的非物理振荡,对于涉及强冲击不稳定性问题,很难达到理想的模拟效果.本文采用基于HLL黎曼求解器的SPH算法,实现了对强激波和大密度比物质界面的有效分辨和追踪.一维数值校核证明了代码的可靠性、健壮性,并进一步模拟了二维圆柱形汇聚冲击波冲击四边形轻/重气界面诱导的RM不稳定性问题,与已有实验结果进行了对比,发现模拟结果与实验结果吻合.通过分析界面演化过程中的密度及压力变化,发现本文所采用的方法可准确地追踪激波与界面作用的复杂界面和波系演化规律.研究结果为进一步理解和解释汇聚冲击条件下的RM不稳定性机理奠定了基础. 相似文献
18.
A comparative analysis of two types of hyperelastic waves—plane waves (with plane front) and cylindrical waves (with curved
front)—is offered. The propagation of the waves is studied theoretically for quadratically nonlinear hyperelastic media and
numerically for a class of unidirectional fibrous composite materials. Hyperelasticity is described using the classical Murnaghan
potential and a structural model of the first order—the model of effective constants. The internal structure of materials
is described by this model and is at the micro-or nanolevels in numerical analysis. Particular attention is given to the evolution
of the wave profile. It is studied in three stages: (i) derivation of nonlinear wave equations, (ii) construction of solutions
in the form of plane and cylindrical waves, and (iii) numerical analysis of the evolution of these waves in composites with
microlevel (Thornel) or nanolevel (Z-CNT) fibers. The main similarities and differences between plane longitudinal and cylindrical
waves are shown. The most unexpected result is the striking difference between the evolution patterns numerically observed
for plane and cylindrical wave profiles
__________
Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 21–46, October 2006. 相似文献
19.
The collision of two blast waves is analyzed for the case of variable parameters of the gas behind the wave front and wave reflection at a plane, a cylindrical, and a spherical obstacle. The reflection of a blast wave from a nonmoving obstacle is investigated in detail. The problem of the collision of two shock waves with constant parameters behind the front is solved both in the symmetrical case (reflection from a nonmoving wall) and in the case of waves of different amplitudes by a system of algebraic relations for the compression shocks. The reflection of a strong point-source spherical shock wave from a wall has been treated in [1, 2]. The present article examines the initial stage of wave collision for an arbitrary distribution of the parameters behind the front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 41–48, September–October, 1971.The authors are grateful to V. P. Korobeinikov for a discussion of the results and to V. P. Kolgan for furnishing the numerical solutions. 相似文献