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1.
A. A. Chesnokov 《Journal of Applied Mechanics and Technical Physics》2006,47(6):800-811
The problem of the decay of an arbitrary discontinuity for the equations describing plane-parallel shear flows of an ideal
fluid in a narrow channel is considered. The class of particular solutions corresponding to fluid flows with piecewise constant
vorticity is studied. In this class, the existence of self-similar solutions describing all possible unsteady wave configurations
resulting from the nonlinear interaction of the specified shear flows is established.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 34–47, November–December, 2006. 相似文献
2.
B. N. Elemesova 《Journal of Applied Mechanics and Technical Physics》1999,40(1):28-35
The plane-parallel unsteady-state shear gas flow in a narrow channel of constant cross section is considered. The existence
theorem of solutions in the form of simple waves of a set of equations of motion is proved for a class of isentropic flows
with a monotone velocity profile over the channel depth. The exact solution described by incomplete beta-functions is found
for a polytropic equation of state in a class of isentropic flows.
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 36–43, January–February, 1999. 相似文献
3.
A. P. Chupakhin 《Journal of Applied Mechanics and Technical Physics》1999,40(2):223-231
Partially invariant solutions of types (1, 2) and (1, 1) for gas-dynamic equations are regularly divided into two classes:
for the first class, the invariant independent variable is the time, i.e., this class contains barochronic solutions, and
for the second class, the invariant variable necessarily depends on spatial coordinates. The barochronic submodel of gas-dynamic
equations, as well as a passive subsystem for solutions of the second class, is integrated in finite form. In the latter case,
the invariant subsystem is reduced to an ordinary differential equation and quadratures. Integration of the submodels is illustrated
by a number of examples. The following common properties of barochronic gas flows are described: rectilinear trajectories
of gas particles, the possibility of collapse of density on a manifold, and stratification of the space of events.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 40–49, March–April, 1999. 相似文献
4.
S. V. Meleshko V. V. Pukhnachev 《Journal of Applied Mechanics and Technical Physics》1999,40(2):208-216
A family of partially invariant solutions of the Navier-Stokes equations of rank 2 and defect 2 is considered. These solutions
describe the three-dimensional unsteady motions of a viscous incompressible fluid in which the vertical velocity component
and the pressure are independent of the horizontal coordinates. In particular, they can be interpreted as flows in a horizontal
layer, one boundary of which is the free surface.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 24–33, March–April, 1999. 相似文献
5.
V. M. Teshukov 《Journal of Applied Mechanics and Technical Physics》1998,39(5):699-709
The problem of the decay of an arbitrary discontinuity (the Riemann problem) for the system of equations describing vortex
plane-parallel flows of an ideal incompressible liquid with a free boundary is studied in a long-wave approximation. A class
of particular solutions that correspond to flows with piecewise-constant vorticity is considered. Under certain restrictions
on the initial data of the problem, it is proved that this class contains self-similar solutions that describe the propagation
of strong and weak discontinuities and the simple waves resulting from the nonlinear interaction of the specified vortex flows.
An algorithm for determining the type of resulting wave configurations from initial data is proposed. It extends the known
approaches of the theory of one-dimensional gas flows to the case of substantially two-dimensional flows.
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 55–66, September–October, 1998. 相似文献
6.
S. V. Khabirov 《Journal of Applied Mechanics and Technical Physics》2009,50(2):207-212
This paper deals with one insufficiently studied submodel of invariant solutions of rank 1 of the equations of gas dynamics.
It is shown that, in cylindrical coordinates, the submodel without swirling reduces to a system of two ordinary differential
equations. For the equation of state with additional invariance, a self-similar system is obtained. A pattern of phase trajectories
is constructed, and particle motion is studied using asymptotic methods. The obtained solutions describe unsteady flows over
axisymmetric bodies with possible strong discontinuities.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 46–52, March–April, 2009. 相似文献
7.
F. Gallaire D. Gérard-Varet F. Rousset 《Archive for Rational Mechanics and Analysis》2007,186(3):423-475
We study the stability of two-dimensional solutions of the three-dimensional Navier–Stokes equations, in the limit of small
viscosity. We are interested in steady flows with locally closed streamlines. We consider the so-called elliptic and centrifugal
instabilities, which correspond to the continuous spectrum of the underlying linearized Euler operator. Through the justification
of highly oscillating Wentzel–Kramers–Brillouin expansions, we prove the nonlinear instability of such flows. The main difficulty
is the control of nonoscillating and nonlocal perturbations issued from quadratic interactions. 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.
V. V. Bublik 《Journal of Applied Mechanics and Technical Physics》2006,47(6):790-799
A system of the Navier-Stokes equations of two-dimensional motion of a viscous heat-conducting perfect gas with a polytropic
equation of state is considered. Regular, partially invariant solutions of rank 1 and defect 1 are studied. A sufficient condition
of their reducibility to invariant solutions of rank 1 is proved. All solutions of this class with a linear dependence of
the velocity-vector components on spatial coordinates are examined. New examples of solutions that are not reducible to invariant
solutions are obtained.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 23–33, November–December, 2006. 相似文献
10.
In the theory of nonlinear elasticity of rubber-like materials, if a homogeneous isotropic compressible material is described
by a strain–energy function that is a homogeneous function of the principal stretches, then the equations of equilibrium for axisymmetric deformations reduce to a separable
first-order ordinary differential equation. For a particular class of such strain–energy functions, this property is used
to obtain a general parametric solution to the equilibrium equation for plane strain bending of cylindrical sectors. Specification
of the arbitrary function that appears in such strain–energy functions yields some parametric solutions. In some cases, the
parameter can be eliminated to yield closed-form solutions in implicit or explicit form. Other possible forms for the arbitrary
constitutive function that are likely to yield such solutions are also indicated. 相似文献
11.
Yu. Yu. Bagderina A. P. Chupakhin 《Journal of Applied Mechanics and Technical Physics》2005,46(6):791-799
All invariant and partially invariant solutions of the Green-Naghdi equations are obtained that describe the second approximation
of shallow water theory. It is proved that all nontrivial invariant solutions belong to one of the following types: Galilean-invariant,
stationary, and self-similar solutions. The Galilean-invariant solutions are described by the solutions of the second Painleve
equation, the stationary solutions by elliptic functions, and the self-similar solutions by the solutions of the system of
ordinary differential equations of the fourth order. It is shown that all partially invariant solutions reduce to invariant
solutions.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 26–35, November–December, 2005. 相似文献
12.
A class of steady similarity solutions of the equations for viscous vortex cores which correspond to external inviscid similarity
solutions with a power-law variation of the circumferential velocityv-r
−m near the rotation axis is considered. It is found that if the Bernoulli function in external flow is constant, then these
solutions will exist only on a certain range of the indexm of the exponential. For eachm on this range there are two solutions.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 38–43, January–February,
1998.
The work was financially supported by the Russian Foundation for Fundamental Research (project No. 95-01-00483). 相似文献
13.
A. K. Khe 《Journal of Applied Mechanics and Technical Physics》2009,50(2):199-206
Spatial stationary flows over an even bottom of a heavy ideal fluid with a free surface are considered. Jump relations for
flows with a strong discontinuity are studied. It is shown that the flow parameters behind the jump are defined by a certain
curve which is an analog of the (θ, p) diagram in gas dynamics. A shock polar and examples of flows with a hydraulic jump
are constructed for a particular class of solutions.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 37–45, March–April, 2009. 相似文献
14.
L. V. Ovsyannikov 《Journal of Applied Mechanics and Technical Physics》1999,40(2):191-197
The notion of a “simple” solution of a system of differential equations that admit a local Lie group G of transformations
of the basic space is considered as an invariant H-solution of type (0, 0) with respect to the subgroup HυG. Such solutions
are attractive since they are described by explicit formulas that provide a clear physical interpretation for them. For gas-dynamic
equations with a polytropic gas law, all simple solutions that are not related to special forms of gas flow are listed. Examples
of simple solutions are given and the collapse phenomenon, which has been previously studied for barochronic flows, is described.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 5–12, March–April, 1999. 相似文献
15.
16.
A two-scale model of ion transfer in a porous medium is obtained for one-dimensional horizontal flows under the action of
a pressure gradient and an external electric field by the method of homogenization. Steady equations of electroosmotic flows
in flat horizontal nano-sized slits separated by thin dielectric partitions are averaged over a small-scale variable. The
resultant macroequations include Poisson’s equation for the vertical component of the electric field and Onsager’s relations
between flows and forces. The total horizontal flow rate of the fluid is found to depend linearly on the pressure gradient
and external electric field, and the coefficients in this linear relation are calculated with the use of microequations.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 162–173, July–August, 2008. 相似文献
17.
We consider the Navier–Stokes equations in a thin domain of which the top and bottom surfaces are not flat. The velocity fields
are subject to the Navier conditions on those boundaries and the periodicity condition on the other sides of the domain. This
toy model arises from studies of climate and oceanic flows. We show that the strong solutions exist for all time provided
the initial data belong to a “large” set in the Sobolev space H
1. Furthermore we show, for both the autonomous and the nonautonomous problems, the existence of a global attractor for the
class of all strong solutions. This attractor is proved to be also the global attractor for the Leray–Hopf weak solutions
of the Navier–Stokes equations. One issue that arises here is a nontrivial contribution due to the boundary terms. We show
how the boundary conditions imposed on the velocity fields affect the estimates of the Stokes operator and the (nonlinear)
inertial term in the Navier–Stokes equations. This results in a new estimate of the trilinear term, which in turn permits
a short and simple proof of the existence of strong solutions for all time. 相似文献
18.
R. V. Krechetnikov I. I. Lipatov 《Journal of Applied Mechanics and Technical Physics》1999,40(3):461-470
The propagation of disturbances in three-dimensional boundary layers under the conditions of a global and a local strong inviscid-viscous
interaction is analyzed. A system of subcharacteristics is found based on the condition for the pressure-related subcharacteristic,
and an algebraic relation that gives the propagation velocity of disturbances is obtained. The velocity of propagation of
disturbances is calculated for two- and three-dimensional flows. The studied problem is of great importance for accurately
formulating problems for three-dimensional unsteady boundary-layer equations and for constructing adequate computational models.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 116–127, May–June, 1999. 相似文献
19.
Ten objective rates, spinning or non-spinning, are critically examined from the viewpoint of Sturm's theorems in ordinary
differential equations. Upon developing implication relations of oscillatory, non-oscillatory, and disconjugate behavior,
we establish oscillation and non-oscillation criteria which pick out the objective stress rates that lead to oscillatory and
non-oscillatory responses in simple shear deformation, respectively. Among the hypoelastic equations associated with the spinning
objective rates examined, the Jaumann equation is an oscillatory minorant, the homogeneous Xiao–Bruhns–Meyers equation is
a non-oscillatory majorant, and the homogeneous Green–Naghdi equation is a disconjugate majorant. If (Sturm comparable) non-spinning
objective rates are also taken into consideration, then the Durban–Baruch equation becomes an oscillatory minorant, but the
other two equations remain to play the same roles. The Jaumann equation is a Sturm majorant for all the other nine homogeneous
hypoelastic equations, and the homogeneous Szabó–Balla-2 equation is a Sturm minorant for all the other nine homogeneous hypoelastic
equations. Most of the solutions of the zeroth-grade hypoelastic equations at simple shear have already been published, except
for those of Szabó and Balla, to which the closed-form solutions are derived here. Moreover, all solutions are extended to
include the effect of initial stresses.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
20.
V. M. Teshukov 《Journal of Applied Mechanics and Technical Physics》1998,39(1):12-23
An approximate system of equations that describe unsteady flow of an inviscid non-heat-conducting gas in a narrow channel
of varying area is derived. Generalized characteristics and hyperbolicity conditions are obtained for this system of equations.
In connection with characteristics theory, the average Mach number and the flow criticality condition are introduced. Exact
solutions that describe steady transonic channel flows are investigated.
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 15–27, January–February, 1998. 相似文献