共查询到20条相似文献,搜索用时 15 毫秒
1.
M. S. Ruderman 《Fluid Dynamics》1986,21(6):925-934
It is proposed to consider the propagation of surface waves along a tangential magnetohydrodynamic discontinuity in the particular
case where the fluid velocities on both sides of the interface are equal to zero. In [1] it was shown that waves called surface
Alfvén waves may be propagated along the surface separating a semi-infinite region without a field from a region with a uniform
magnetic field. The linear theory of surface Alfvén waves in a compressible medium was considered in [2]. In [3] the damping
of surface Alfvén waves as a result of viscosity and heat conduction was investigated. The propagation of low-amplitude nonlinear
surface Alfvén waves in an incompressible fluid in the absence of dissipative processes is described by the integrodifferential
equation obtained in [4]. By means of a numerical solution of this equation it was shown that a perturbation initially in
the form of a sinusoidal wave will break. The breaking time was determined. In this paper the equation derived in [4] is extended
to the case of a viscous fluid. It is shown that the equation obtained does not have steady-state solutions. The propagation
of periodic disturbances is investigated numerically.
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 94–104, November–December, 1986.
The author wishes to thank L. S. Fedorov for assisting with the calculations. 相似文献
2.
G. A. Khabakhpashev 《Journal of Applied Mechanics and Technical Physics》2005,46(6):807-817
Dynamics of three-dimensional disturbances of the interface between two fluid layers of different densities is considered
analytically and numerically. An evolutionary integrodifferential equation is derived, which takes into account long-wave
contributions of inertia of the layers and surface tension, small but finite amplitude of disturbances of the interface between
two incompressible immiscible fluids, gentle slopes of the lid and bottom, and nonstationary shear stresses at all boundaries.
Numerical solutions of this model equation for several (most typical) nonlinear problems of transformation of two- and three-dimensional
waves are obtained.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 45–57, November–December, 2005. 相似文献
3.
The far field asymptotics of internal waves is constructed for the case when a point source of mass moves in a layer of arbitrarily
stratified fluid with slowly varying bottom. The solutions obtained describe the far field both near the wave fronts of each
individual mode and away from the wave fronts and are expansions in Airy or Fresnel waves with the argument determined from
the solution of the corresponding eikonal equation. The amplitude of the wave field is determined from the energy conservation
law along the ray tube. For model distributions of the bottom shape and the stratification describing the typical pattern
of the ocean shelf eract analytic expressions are obtained for the rays, and the properties of the phase structure of the
wave field are analyzed.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 111–120, May–June, 1998.
This work was financially supported by the Russian Foundation for Basic Research (project No. 96-01-01120). 相似文献
4.
V. M. Teshukov 《Journal of Applied Mechanics and Technical Physics》2007,48(3):303-309
The classical shallow-water equations describing the propagation of long waves in flow without a shear of the horizontal velocity
along the vertical coincide with the equations describing the isentropic motion of a polytropic gas for a polytropic exponent
γ = 2 (in the theory of fluid wave motion, this fact is called the gas-dynamic analogy). A new mathematical model of long-wave
theory is derived that describes shear free-boundary fluid flows. It is shown that in the case of one-dimensional motion,
the equations of the new model coincide with the equations describing nonisentropic gas motion with a special choice of the
equation of state, and in the multidimensional case, the new system of long-wave equations differs significantly from the
gas motion model. In the general case, it is established that the system of equations derived is a hyperbolic system. The
velocities of propagation of wave perturbations are found.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 8–15, May–June, 2007. 相似文献
5.
The self-consistent motion of a fluid and elastically oscillating plates partially covering the fluid is simulated numerically
in the linear approximation. The problem is reduced to the simultaneous solution of the Laplace equation for the fluid and
the equation of elastic plate oscillations for the ice. The numerical and analytical solutions, the latter obtained from an
integral equation containing the Green’s function, are compared. To solve the problem numerically, the boundary element method
for the Laplace equation and the finite element method for the equation describing the elastic plate are proposed. The coefficients
of transmission and reflection of surface gravity waves from the floating plates are calculated. It is shown that the solution
may be quasi-periodic with characteristics determined by the initial values of the wave and ice-floe parameters. The ice floes
may exert a filtering effect on the surface wave spectrum, essentially reducing its most reflectable components.
Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 123–131, May–June,
2000. 相似文献
6.
D. G. Arkhipov G. A. Khabakhpashev 《Journal of Applied Mechanics and Technical Physics》2007,48(4):508-518
The dynamics of disturbances of the interface between two layers of incompressible immiscible fluids of different densities
in the presence of a steady flow between the horizontal bottom and lid is studied analytically and numerically. A model integrodifferential
equation is derived, which takes into account long-wave contributions of inertial layers and surface tension of the fluids,
small but finite amplitude of disturbances, and unsteady shear stresses on all boundaries. Numerical solutions of this equation
are given for the most typical nonlinear problems of transformation of both plane waves of different lengths and solitary
waves.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 49–61, July–August, 2007. 相似文献
7.
All the possible traveling wave solutions of Whitham-Broer-Kaup (WBK) equation are investigated in the present paper. By employing phase plane analysis, transition boundaries are derived to divide the parameter space into several regions associated with different types of phase portraits corresponding to different forms of wave solutions. All the exact expressions of bounded wave solutions are obtained as well as their existence conditions. The mechanism of bifurcation between different waves with varying Hamiltonian value has been revealed. It is pointed out that as the periods of two coexisted periodic waves tend to infinity, they may evolve to two solitary waves. Furthermore, when their trajectories pass through the common saddle point, the two solitary waves may merge into a periodic wave, and its amplitude is nearly equal to the sum of the amplitudes of the two solitary wave solutions. 相似文献
8.
A. A. Chesnokov 《Journal of Applied Mechanics and Technical Physics》2000,41(4):593-603
We obtain new classes of invariant solutions of the integrodifferential equations describing the propagation of nonlinear
concentration waves in a rarefied bubbly fluid. For all the solutions obtained, trajectories of particle motion in phase space
are calculated. The stability of some flows is studied in a linear approximation. In several cases, the construction of solutions
reduces to an integrodifferential equation of the second kind, which can be solved by the iteration method.
Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41,
No. 4, pp. 21–32, July–August, 2000. 相似文献
9.
M. A. Kulesh V. P. Matveenko M. V. Ulitin I. N. Shardakov 《Journal of Applied Mechanics and Technical Physics》2008,49(2):323-329
A study is made of waves in a Cosserat continuum, whose strain state is characterized by independent displacement and rotation
vectors. The propagation of longitudinal and transverse bulk waves is considered. Wave solutions are sought in the form of
wave trains specified by a Fourier spectrum of arbitrary shape. It is shown that if the solution is sought in the form of
three components of the displacement vector and three components of the rotation vector which depend on time and the longitudinal
coordinate, the initial system is split into two systems, one of which describes longitudinal waves, and the other transverse
waves. For waves of both types, dispersion relations and analytical solutions in displacement are obtained. The dispersion
characteristics of the solutions obtained differ from the dispersion characteristics of the corresponding classical elastic
solutions.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 196–203, March–April, 2008. 相似文献
10.
The envelope modulation of a monoinductance transmission line is reduced to generalized coupled Ginzburg-Landau equations,
from which a single cubic-quintic Ginzburg-Landau equation containing derivatives with respect to the space variable in the
cubic terms is deduced. We investigate the modulational instability of the space wave solutions of both the system and the
single equation. For the generalized coupled Ginzburg-Landau system, we consider only the zero wave numbers of the perturbations
whose modulational instability conditions depend only on the coefficients of the system and the wave numbers of the carriers.
In this case, a modulational instability criterion is established, which depends on both the perturbation wave numbers and
the carrier. We also study the coherent structures of the generalized coupled Ginzburg-Landau system and present some numerical
results.
Published in Neliniini Kolyvannya, Vol. 9, No. 4, pp. 451–489, October–December, 2006. 相似文献
11.
The surface waves generated by unsteady concentrated disturbances in an initially quiescent fluid of infinite depth with an inertial surface are analytically investigated for two- and three-dimensional cases. The fluid is assumed to be inviscid, incompressible and homogenous. The inertial surface represents the effect of a thin uniform distribution of non-interacting floating matter. Four types of unsteady concentrated disturbances and two kinds of initial values are considered, namely an instantaneous/oscillating mass source immersed in the fluid, an instantaneous/oscillating impulse on the surface, an initial impulse on the surface of the fluid, and an initial displacement of the surface. The linearized initial-boundary-value problem is formulated within the framework of potential flow. The solutions in integral form for the surface elevation are obtained by means of a joint Laplace-Fourier transform. The asymptotic representations of the wave motion for large time with a fixed distance- to-time ratio are derived by using the method of stationary phase. The effect of the presence of an inertial surface on the wave motion is analyzed. It is found that the wavelengths of the transient dispersive waves increase while those of the steady-state progressive waves decrease. All the wave amplitudes decrease in comparison with those of conventional free-surface waves. The explicit expressions for the freesurface gravity waves can readily be recovered by the present results as the inertial surface disappears. 相似文献
12.
This study investigates the peristaltic flow of Eyring–Powell fluid in an endoscope. The governing equations for Eyring–Powell
are modeled in cylindrical coordinates under the assumption of long wavelength and low Reynolds number approximation. The
resulting nonlinear differential equations are solved analytically and numerically by employing perturbation method and shooting
technique. Numerical integration have been done for pressure rise and frictional forces. Comparative study have been made
for both the solutions to see the validity of the results. The effects of various emerging parameters are investigated for
five different peristaltic waves. (Basically peristaltic phenomena is a natural phenomena so it is not necessary that peristaltic
wave be always a sinusoidal wave it could be multisinusoidal, triangular, trapezoidal and square waves for example heartbeats.)
Streamlines have been plotted at the end of the article. 相似文献
13.
G. L. Komissarova 《International Applied Mechanics》2008,44(4):419-430
The properties of harmonic surface waves in a fluid-filled cylinder made of a compliant material are studied. The wave motions
are described by a complete system of dynamic equations of elasticity and the equation of motion of a perfect compressible
fluid. An asymptotic analysis of the dispersion equation for large wave numbers and a qualitative analysis of the dispersion
spectrum show that there are two surface waves in this waveguide system. The first normal wave forms a Stoneley wave on the
inside surface with increase in the wave number. The second normal wave forms a Rayleigh wave on the outside surface. The
phase velocities of all the other waves tend to the velocity of the shear wave in the cylinder material. The dispersion, kinematic,
and energy characteristics of surface waves are analyzed. It is established how the wave localization processes differ in
hard and compliant materials of the cylinder
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 72–86, April 2008. 相似文献
14.
A. D. Kosinov Y. G. Ermolaev N. V. Semionov 《Journal of Applied Mechanics and Technical Physics》1999,40(5):858-864
Nonlinear evolution of high-amplitude periodic disturbances in a boundary layer on a flat plate for Mach numberM=2 is studied. An anomalous downstream evolution of the disturbances is found, quasi-two-dimensional disturbances being most
unstable. The obtained phase velocities of the waves are 30–40% greater than the phase velocities of the Tollmien-Schlichting
waves. The nonlinear evolution of vortex waves is accompanied by an increase in steady disturbances from the source of controlled
vibrations. High-frequency disturbances decay, and a periodic wave train degenerates downstream into a quasiharmonic wave
train.
Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated
from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 91–98, September–October, 1999. 相似文献
15.
We consider the question of stability for planar wave solutions that arise in multidimensional conservation laws with only
fourth-order regularization. Such equations arise, for example, in the study of thin films, for which planar waves correspond
to fluid coating a pre-wetted surface. An interesting feature of these equations is that both compressive, and undercompressive,
planar waves arise as solutions (compressive or undercompressive with respect to asymptotic behavior relative to the un-regularized
hyperbolic system), and numerical investigation by Bertozzi, Münch, and Shearer indicates that undercompressive waves can
be nonlinearly stable. Proceeding with pointwise estimates on the Green's function for the linear fourth-order convection–regularization
equation that arises upon linearization of the conservation law about the planar wave solution, we establish that under general
spectral conditions, such as appear to hold for shock fronts arising in our motivating thin films equations, compressive waves
are stable for all dimensions d≧2 and undercompressive waves are stable for dimensions d≧3. (In the special case d=1, compressive waves are stable under a very general spectral condition.) We also consider an alternative spectral criterion
(valid, for example, in the case of constant-coefficient regularization), for which we can establish nonlinear stability for
compressive waves in dimensions d≧3 and undercompressive waves in dimensions d≧5. The case of stability for undercompressive waves in the thin films equations for the critical dimensions d=1 and d=2 remains an interesting open problem. 相似文献
16.
Propagation of interfacial waves near the critical depth level in a two-layer fluid system is investigated. We first present a generalized modified Kadomtsev-Petviashvili (gmKP) equation for weakly nonlinear and dispersive interfacial waves propagating predominantly in the longitudinal direction of a slowly rotating channel with gradually varying topography and sidewalls. For certain type of non-rotating channels, we find two families of periodic-wave solutions, which include solitarywave solutions and a shock-like solution as limiting cases, to the variable-coefficient gmKP equation. We also show that in this situation the gmKP equation has only unidirectional N-soliton solutions and does not allow soliton resonance to occur. In a rotating uniform channel, our small-time asymptotic analysis and numerical study of the gmKP equation show that, depending on the relative importance of the cubic nonlinearity to quadratic nonlinearity, the wavefront of a Kelvin solitary wave may curve either forward or backward, trailed by a small train of Poincaré waves. When these two nonlinearities almost balance each other, the wavefront becomes almost straight-crested across the channel, and the trailing Poincaré waves diminish. 相似文献
17.
G. A. Khabakhpashev O. Yu. Tsvelodub 《Journal of Applied Mechanics and Technical Physics》1999,40(5):831-840
A second-order differential model for three-dimensional perturbations of the interface of two fluids of different density
is constructed. An evolution equation for traveling quasistationary waves of arbitrary length and small but finite amplitude
is obtained. In the case of the horizontal bottom and lid, there are perturbations of the Stokes-wave type among steady-state
periodic solutions. For moderately long perturbations, solutions in the form of solitary waves which are in agreement with
the available experimental and analytical results are found. The problem of a smooth transition from the deep-fluid to the
shallow-fluid region is studied.
Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 62–72. September–October, 1999. 相似文献
18.
We study possible steady states of an infinitely long tube made of a hyperelastic membrane and conveying either an inviscid, or a viscous fluid with power-law rheology. The tube model is geometrically and physically nonlinear; the fluid model is limited to smooth changes in the tube’s radius. For the inviscid case, we analyse the tube’s stretch and flow velocity range at which standing solitary waves of both the swelling and the necking type exist. For the viscous case, we first analyse the tube’s upstream and downstream limit states that are balanced by infinitely growing upstream (and decreasing downstream) fluid pressure and axial stress caused by fluid viscosity. Then we investigate conditions that can connect these limit states by a single solution. We show that such a solution exists only for sufficiently small flow speeds and that it has a form of a kink wave; solitary waves do not exist. For the case of a semi-infinite tube (infinite either upstream or downstream), there exist both kink and solitary wave solutions. For finite-length tubes, there exist solutions of any kind, i.e. in the form of pieces of kink waves, solitary waves, and periodic waves. 相似文献
19.
Under investigation in this paper, with symbolic computation, is a forced variable-coefficient extended Korteweg–de Vries
equation, which can describe the weakly-nonlinear long internal solitary waves (ISWs) in the fluid with the continuous stratification
on density. By virtue of the Hirota bilinear method, multi-soliton solutions for such an equation with the external force
term have been derived. Furthermore, effects are discussed with the aid of the characteristic line: (I) Inhomogeneities of
media and nonuniformities of boundaries, depicted by the variable coefficients, play a role in the soliton behavior; (II)
Solitons change their initial propagation direction on the compact shock or anti-shock wave background in the presence of
the external time-dependent force, and the results present an extended view compared with that for the linear theory; (III) Combined
effects of the inhomogeneities and external force are regarded as the nonlinear composition of the independent influence induced
by the two factors. Those results could be expected to be helpful for the investigation on the dynamics of the ISWs in an
ocean or atmosphere stratified fluid. 相似文献
20.
Feimin Huang Jing Li Akitaka Matsumura 《Archive for Rational Mechanics and Analysis》2010,197(1):89-116
We are concerned with the large-time behavior of solutions of the Cauchy problem to the one-dimensional compressible Navier–Stokes
system for ideal polytropic fluids, where the far field states are prescribed. When the corresponding Riemann problem for
the compressible Euler system admits the solution consisting of contact discontinuity and rarefaction waves, it is proved
that for the one-dimensional compressible Navier–Stokes system, the combination wave of a “viscous contact wave”, which corresponds
to the contact discontinuity, with rarefaction waves is asymptotically stable, provided the strength of the combination wave
is suitably small. This result is proved by using elementary energy methods. 相似文献