Home – Home – Jornals – Journal of Applied Mechanics and Technical Physics 2002 number 2

This paper continues previous
investigation of Galilean-invariant
equations of mathematical physics, which
was begun with the use of the Clebsch–
Gordan coefficients from the theory of
products of the represented group SO(3).
Complex systems of conservation laws and
thermodynamic identities are
constructed. Concrete examples are
given.

Exact solutions of Euler equations that
describe the motion of an ideal
incompressible fluid with quadratic
pressure are studied. The solutions are
described by explicit formulas and can
be physically interpreted. The dynamics
of a spherical fluid volume is studied
for specified initial velocity fields.
It is shown that under certain initial
conditions, the spherical volume can
evolve into a torus-shaped body, thereby
changing the connectivity of the region
occupied by the fluid.

The paper studies boundary‐value problems for dynamic-diffusion boundary layers occurring near a vertical wall at high Schmidt numbers and for dynamic boundary layers whose inner edge is adjacent to the dynamic-diffusion layers. Exact solutions for boundary layers at small and large times are derived. The well-posedness of the boundary-value problem for a steady dynamic-diffusion layer is studied.

The one-velocity motion of a gas–liquid
medium with a variable mass fraction of
the gas phase, which is equilibrium in
terms of phase pressures, is considered.
The existence conditions of nonlinear
periodic wave packets similar in
structure to roll waves in open inclined
channels are found. The structure of
travelling waves in the medium with
continuous addition of energy to the gas
phase is studied.

The stability of the equilibrium state
of a flat layer bounded by rigid walls
is studied using a microconvection
model. The behavior of the complex
decrement for long-wave perturbations
has an asymptotic character.
Calculations of the full spectral
problem were performed for melted
silicon. Unlike in the classical
Oberbeck–Boussinesq model, the
perturbations in the microconvection
model are not monotonic. It is shown
that for small Boussinesq parameters,
the spectrum of this problem
approximates the spectra of the
corresponding problems for a heat-
conducting viscous fluid or thermal
gravitational convection when the
Rayleigh number is finite.

Instability of a plane horizontal layer
of an incompressible binary gas mixture
stratified in the gravity field under
the action of a transverse temperature
gradient modulated in time is studied.
The case of solid impermeable boundaries
of the layer, where the flux of matter
vanishes, is considered. The analysis is
based on the Floquet method applied to
linearized equations of convection in
the Boussinesq approximation. It is
shown that there are regions of
parametric instability at finite
frequencies. In addition to the
synchronous or subharmonic response to
an external action, the instability may
be related to quasi-periodic
disturbances. Depending on the amplitude
and frequency, modulation can stabilize
the unstable basic state and also
destabilize the equilibrium of the
fluid. The threshold values of
convection for modulations of
temperature and translational vertical
vibrations are compared.

Results of the analysis of specific
features of the laminar–turbulent
transition in various subsonic shear
flows, which are caused by localized
stationary and nonstationary streamwise
structures, are presented. One mechanism
of flow turbulization is considered,
which involves the origination and
development of secondary high-frequency
disturbances in regions of flow
instability generated by its modulation
by streamwise structures. It is shown
that this process is identical in
different types of shear flows (boundary
layers and jets) and in flows of the
type of localized streamwise structures
(stationary or nonstationary).

It is shown that during excitation of
forced, resonant, inertial oscillations
of large amplitude in a rigidly rotating
fluid, the mechanism of formation of
tornado-like vortices is primarily of a
kinematic nature (advection of
circulation of the azimuthal component
velocity and stretching of vortex lines
by the poloidal components of the
velocity field that arise from
excitation of inertial oscillations).
The main parameters of the vortices are
obtained by solutions of model problems.
To excite such oscillations, it is
necessary to deliver energy far
exceeding the initial energy of the
rotating fluid. Therefore, inertial
oscillations by themselves cannot lead
to the occurrence of intense atmospheric
vortices. Nevertheless, such
oscillations can apparently play the
role of a trigger mechanism that
activates more complex processes of
vortex formation related to instability
of the atmosphere.

Experimental estimates are obtained for
the main parameters of tornado-like
vortices that arise from excitation of
forced axisymmetric inertial
oscillations of large amplitude in a
rigidly rotating fluid.

The effect of charged dust particles on
the structure of the plasma precursor of
a strong shock wave is studied. The
conditions of formation of a weak
discontinuity front are obtained. It is
shown that resonant modes can occur in
which the concentration of dust
particles in the neighborhood of the
front increases. In the case of
positively charged particles of dust,
the formation of a localized compaction
region in the form of a soliton "bunch"
is possible and the dependence of the
amplitude of the soliton on shock-wave
velocity is nonmonotonic. In the case of
negatively charged particles of dust, a
rarefaction wave is formed. The
indicated phenomena can substantially
affect the concentration of the neutral
component in a slightly ionized plasma.

The wave structure in active bubble
media in shock tubes with sudden changes
of profiles in the form of
"discontinuities" in cross section and a
one-phase liquid waveguide is analyzed
numerically. In axisymmetric
formulation, the paper studies wave
amplification due to reflection from a
wall and focusing at the butt-end of a
rigid rod aligned coaxially with the
channel. In this configuration, the
amplification effect results from two-
dimensional cumulation of the shock wave
after it leaves the annular channel and
reaches the butt-end of the rod. A Mach
configuration forms in the focus spot.
The geometrical characteristics of the
shock tube allow one to control (to some
extent) the amplification coefficient
and the coordinates of the focus spot.
In particular, it is shown that the wave
can be focused near the second
discontinuity of cross section — a rigid
wall (in the region of passage through
the interface to the waveguide) — and
intensified upon reflection. If the
waveguide radius is equal to the height
of the Mach stem, the reflected wave has
a maximum amplitude.

The structure and dissipation of
moderate-amplitude pressure waves in a
liquid with bubbles of two dissimilar
gases (freon and helium) are
experimentally studied. It is shown that
introduction of a small (by volume)
quantity of helium bubbles with a high
thermal conductivity into a liquid with
poorly heat-conducting freon bubbles,
sharply increases the rate of damping of
solitary pressure waves.

Steady and unsteady waves propagating
over the surface of a thin layer of a
dilatant fluid moving over an inclined
plane, with rheological properties of
the fluid described by the Ostwald–de
Waele power law, are studied
analytically and numerically.

The physical basis of liquid-crystal
thermography, which allows visualization
and measurement of temperature and heat-
flux fields, are expounded. An
experimental technique and methods of
obtaining quantitative results are
described. Two approaches (monochromatic
and chromatic) to interpretation of
visualization data are considered.
Results illustrating the possibilities
of the method in an aerophysical
experiment are given.

The paper reports experimental results
on flow regimes with and without
cavities behind a rectangular sill in an
open channel. Photographs illustrating
the shapes of the free ends of the
cavities are given. It is shown that the
domains of existence of various flow
regimes overlap in the phase space of
problem parameters, which leads to
nonuniqueness of various functions of
the parameters. Quantitative information
is obtained for free surface profiles,
the discharge coefficient, and the
pressure on the flow bottom.

The numerical modeling of wave flows of
heterogeneous media with a three-
temperature scheme of interphase heat
and mass transfer involves the problem
of equation stiffness. A discrete model
of improved stability was developed to
describe these processes. Test
calculations of the interaction of a
shock wave with a bounded layer of a
mixture of a gas and droplets assuming a
discrete model over a wide range of
initial data showed that the stability
conditions do not depend on the rate of
interphase interaction (C-stability).

This paper studies the dynamic behavior
of simply and doubly connected elliptic
ideal rigid-plastic plates with simply
supported or clamped contours under
short-time intensive dynamic loads. It
is shown that there are several
mechanisms of dynamic deformation of
plates. For each mechanism, equations of
the dynamic behavior are obtained.
Operating conditions of these mechanisms
are analyzed. Analytical expressions for
the ultimate, "high" and "superhigh"
loads and the maximum final deflection
are obtained. Numerical examples are
given.

A model is proposed to calculate
stresses in a glass layer with gas
impurities heated by thermal infrared
radiation. Calculations were performed
for a layer with a diatomic impurity of
nitric oxide and a triatomic impurity of
water. It is shown that for the
radiation parameters and impurity
concentrations considered, the presence
of nitric oxide in the layer does not
influence its stress state, whereas the
presence of water leads to a certain
increase of stress. The stress state of
the layer is determined by the level of
thermal stresses, and the concentration
stresses and the stresses due to the
mass forces of radiation are negligible.
An increase in the rate of diffusion of
the diatomic impurity due to a change of
the radiation spectrum is accompanied by
an increase of thermal stresses.

This paper studies the dependence of the wavelength of localized plastic strain at the parabolic stage of strain hardening on the grain size in polycrystal aluminum. This dependence is determined in the grain-size range 10^-2 – 10 mm. The effect of the grain size on the character of the plastic-flow curve is studied.

This is a study of the effect of
structural and mechanical
characteristics of a composite material
on the stress–strain state of a
reflector antenna shaped as a composite
thin shell of revolution subjected to
gravity, wind, and temperature loads.
The boundary-value problem for the
system of partial differential equations
governing the behavior of this structure
is reduced to a sequence of boundary-
value problems for inhomogeneous systems
of ordinary differential equations with
variable coefficients. The resulting
stiff systems of equations are solved by
Godunov's method of discrete
orthogonalization.

Fragmentation of the structure of
lattice disorientations at high plastic
strains of metal crystals is studied.
The medium is modelled by the
geometrically nonlinear elastoplastic
Cosserat continuum. The points of the
continuum are identified with
dislocation cells with a frozen crystal
lattice.

New systems of pretwisted bars are
suggested, and their stability under a
conservative load is investigated. In
this paper, closed-form relationships
are obtained for the direct evaluation
of critical loads of pretwisted cross
bracings with different end connections
and an arbitrary ratio of the
dimensionless parameters of tension and
compression elements. The equation for
the critical loads is derived for
tension and compression braces with
different section properties, lengths,
and axial loading. It is found that the
critical load of a twisted brace is
higher than that of a nontwisted brace.
Parametric solutions are graphically
displayed to clarify the distinct
behavior, including the boundary
separating symmetric and antisymmetric
modes of buckling.

The plane problem of dynamic interaction
of a laminar viscous fluid flow and an
inextensible pliable fiber of finite
length is solved using the perturbation
method. Two types of rheological two-
dimensional flows — pure shear and
simple shear — are considered. Formulas
are obtained for the evolution of the
tensile force and the shape of the
fiber. Results of asymptotic and
numerical calculations are compared.

Elastic characteristics and propagation
velocities of ultrasonic waves in a TiC–
TiNi composite material are determined
by the ultrasonic resonance method. The
values of the elastic moduli of the
solid composite obtained are used to
estimate its plastic properties. The
effect of various additives on the
elastic and plastic properties of the
composite is studied.