[Text] : статья / V.B. Bekezhanova // Journal of Applied Mechanics and Technical Physics. - 2011. - Vol. 52, Iss. 1. - p. 74-81DOI 10.1134/S0021894411010111
. -
Аннотация: An exact solution is obtained for the problem of steady flow in a system of two horizontal layers of immiscible fluids with a common interface. The stability of the flow is studied by a linearization method. It is shown that the occurrence of instabilities is due to the different governing parameters of the fluids (thickness, heating conditions, viscous and thermal conductivity of the fluids). It is found that under constant gravity conditions, the perturbations are monotonic, and in zero gravity, oscillatory thermocapillary instability occurs.
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Бекежанова, Виктория Бахытовна
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Найдено документов в текущей БД: 4
Convective instability of Marangoni-Poiseuille flow under a longitudinal temperature gradient
Numerical linearized MHD model of flapping oscillations
/ D. B. Korovinskiy [et al.] // Phys. Plasmas. - 2016. - Vol. 23, Is. 6, DOI 10.1063/1.4954388
. - ISSN 1070-664X
Кл.слова (ненормированные):
Dispersions -- Eigenvalues and eigenfunctions -- Linearization -- Magnetic fields -- Analytical estimates -- Current sheets -- Dispersion relations -- Gradient model -- Growth directions -- Initial perturbation -- Magnetic field components -- Mode dispersion -- Magnetohydrodynamics
Аннотация: Kink-like magnetotail flapping oscillations in a Harris-like current sheet with earthward growing normal magnetic field component Bz are studied by means of time-dependent 2D linearized MHD numerical simulations. The dispersion relation and two-dimensional eigenfunctions are obtained. The results are compared with analytical estimates of the double-gradient model, which are found to be reliable for configurations with small Bz up to values ? 0.05 of the lobe magnetic field. Coupled with previous results, present simulations confirm that the earthward/tailward growth direction of the Bz component acts as a switch between stable/unstable regimes of the flapping mode, while the mode dispersion curve is the same in both cases. It is confirmed that flapping oscillations may be triggered by a simple Gaussian initial perturbation of the Vz velocity. © 2016 Author(s).
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Держатели документа:
Space Research Institute, Austrian Academy of Sciences, 8042 Schmiedlstrasse 6, Graz, Austria
Saint Petersburg State University, Ulyanovskaya 1, Petrodvoretz, Russian Federation
Theoretical Physics Division, Petersburg Nuclear Physics Institute, Gatchina, Russian Federation
Institute of Computational Modelling, Russian Academy of Sciences, Siberian Branch, Krasnoyarsk, Russian Federation
Siberian Federal University, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Korovinskiy, D. B.; Ivanov, I. B.; Semenov, V. S.; Erkaev, N. V.; Kiehas, S. A.
Кл.слова (ненормированные):
Dispersions -- Eigenvalues and eigenfunctions -- Linearization -- Magnetic fields -- Analytical estimates -- Current sheets -- Dispersion relations -- Gradient model -- Growth directions -- Initial perturbation -- Magnetic field components -- Mode dispersion -- Magnetohydrodynamics
Аннотация: Kink-like magnetotail flapping oscillations in a Harris-like current sheet with earthward growing normal magnetic field component Bz are studied by means of time-dependent 2D linearized MHD numerical simulations. The dispersion relation and two-dimensional eigenfunctions are obtained. The results are compared with analytical estimates of the double-gradient model, which are found to be reliable for configurations with small Bz up to values ? 0.05 of the lobe magnetic field. Coupled with previous results, present simulations confirm that the earthward/tailward growth direction of the Bz component acts as a switch between stable/unstable regimes of the flapping mode, while the mode dispersion curve is the same in both cases. It is confirmed that flapping oscillations may be triggered by a simple Gaussian initial perturbation of the Vz velocity. © 2016 Author(s).
Scopus,
Смотреть статью,
WOS
Держатели документа:
Space Research Institute, Austrian Academy of Sciences, 8042 Schmiedlstrasse 6, Graz, Austria
Saint Petersburg State University, Ulyanovskaya 1, Petrodvoretz, Russian Federation
Theoretical Physics Division, Petersburg Nuclear Physics Institute, Gatchina, Russian Federation
Institute of Computational Modelling, Russian Academy of Sciences, Siberian Branch, Krasnoyarsk, Russian Federation
Siberian Federal University, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Korovinskiy, D. B.; Ivanov, I. B.; Semenov, V. S.; Erkaev, N. V.; Kiehas, S. A.
539.371
Т352
Т352
Термодинамически согласованные уравнения моментной теории упругости
[Текст] : статья / В. М. Садовский // Дальневосточный математический журнал. - 2016. - Т. 16, № 2. - С. 209-222
. - ISSN 1608-845X
Перевод заглавия: Thermodynamically consistent equations of the couple stress elasticity
Кл.слова (ненормированные):
упругость -- континуум Коссера -- моментные напряжения -- тензор кривизны -- термодинамически согласованная система -- elasticity -- Cosserat continuum -- Couple stresses -- curvature tensor -- thermodynamically consistent system
Аннотация: Для описания движения микрополярной среды, в которой наряду с поступательными степенями свободы реализуются независимые вращения частиц, выбирается естественная мера кривизны, представляющая собой характеристику деформированного состояния, не зависящую от пути его достижения. Показано, что часто используемая лагранжева мера кривизны со скоростью изменения, равной тензору градиентов угловой скорости, корректна только в геометрически линейном приближении. Методом внутренних термодинамических параметров состояния строятся нелинейные определяющие уравнения моментной теории упругости. В результате линеаризации этих уравнений в изотропном случае получаются уравнения континуума Коссера, в которых сопротивление материала изменению кривизны характеризуется не тремя независимыми коэффициентами, как в классической теории, а одним. Полная система уравнений динамики моментной среды при конечных деформациях и поворотах частиц приводится к термодинамически согласованной системе законов сохранения. С помощью этой системы получены интегральные оценки решений задачи Коши и краевых задач с диссипативными граничными условиями, гарантирующие единственность и непрерывную зависимость от начальных данных.
To describe motion in a micropolar medium, with the concurrent translational degrees of freedom and independent particle rotations, it is chosen to use natural measure of curvature that is a strain state characteristic independent of deformation method. It is shown that the common Lagrangian curvature measure with the rate of change equal to a tensor of angular velocity gradients is only applicable under geometrically linear approximation. The nonlinear constitutive equations of the couple stress theory are constructed using the method of internal thermodynamic parameters of state. The linearization of these equations in isotropic case yields the Cosserat continuum equations, where material resistance to the change in curvature is characterized by a single coefficient as against the three independent coefficients of the classical theory. The complete system of equations for the dynamics of a medium with couple stresses under finite strains and particle rotations reduces to a thermodynamically consistent system of laws of conservation. This system allows to obtain the integral estimates that guarantee the uniqueness and continuous dependence on the initial data of solutions of the Cauchy problems and the boundary-value problems with dissipative boundary conditions.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Садовский, Владимир Михайлович; Sadovskii V.M.
Перевод заглавия: Thermodynamically consistent equations of the couple stress elasticity
| УДК |
Кл.слова (ненормированные):
упругость -- континуум Коссера -- моментные напряжения -- тензор кривизны -- термодинамически согласованная система -- elasticity -- Cosserat continuum -- Couple stresses -- curvature tensor -- thermodynamically consistent system
Аннотация: Для описания движения микрополярной среды, в которой наряду с поступательными степенями свободы реализуются независимые вращения частиц, выбирается естественная мера кривизны, представляющая собой характеристику деформированного состояния, не зависящую от пути его достижения. Показано, что часто используемая лагранжева мера кривизны со скоростью изменения, равной тензору градиентов угловой скорости, корректна только в геометрически линейном приближении. Методом внутренних термодинамических параметров состояния строятся нелинейные определяющие уравнения моментной теории упругости. В результате линеаризации этих уравнений в изотропном случае получаются уравнения континуума Коссера, в которых сопротивление материала изменению кривизны характеризуется не тремя независимыми коэффициентами, как в классической теории, а одним. Полная система уравнений динамики моментной среды при конечных деформациях и поворотах частиц приводится к термодинамически согласованной системе законов сохранения. С помощью этой системы получены интегральные оценки решений задачи Коши и краевых задач с диссипативными граничными условиями, гарантирующие единственность и непрерывную зависимость от начальных данных.
To describe motion in a micropolar medium, with the concurrent translational degrees of freedom and independent particle rotations, it is chosen to use natural measure of curvature that is a strain state characteristic independent of deformation method. It is shown that the common Lagrangian curvature measure with the rate of change equal to a tensor of angular velocity gradients is only applicable under geometrically linear approximation. The nonlinear constitutive equations of the couple stress theory are constructed using the method of internal thermodynamic parameters of state. The linearization of these equations in isotropic case yields the Cosserat continuum equations, where material resistance to the change in curvature is characterized by a single coefficient as against the three independent coefficients of the classical theory. The complete system of equations for the dynamics of a medium with couple stresses under finite strains and particle rotations reduces to a thermodynamically consistent system of laws of conservation. This system allows to obtain the integral estimates that guarantee the uniqueness and continuous dependence on the initial data of solutions of the Cauchy problems and the boundary-value problems with dissipative boundary conditions.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Садовский, Владимир Михайлович; Sadovskii V.M.
On thermodynamically consistent form of nonlinear equations of the cosserat theory
/ V. M. Sadovskii // Eng. Trans. - 2017. - Vol. 65, Is. 1. - P201-208
. - ISSN 0867-888X
Кл.слова (ненормированные):
Cosserat continuum -- Curvature tensor -- Thermodynamically consistent system -- Boundary value problems -- Constitutive equations -- Cosserat continuum -- Couple stress theory -- Curvature tensors -- Dissipative boundary conditions -- Independent coefficients -- Nonlinear constitutive equations -- Thermodynamic parameter -- Thermodynamically consistent system -- Nonlinear equations
Аннотация: To describe motion in a micropolar medium a special measure of curvature is used that is a strain state characteristic independent of deformation process. The nonlinear constitutive equations of the couple stress theory are constructed using the method of internal thermodynamic parameters of state. The linearization of these equations in isotropic case yields the Cosserat continuum equations, where material resistance to the change in curvature is characterized by a single coefficient as against three independent coefficients of the classical theory. So, it turns out that the developed variant of the model gives an adequate description of generalized plane stress state in an isotropic micropolar medium, while the classical one describes this state only at a certain case. The complete system of nonlinear equations for the dynamics of a medium with couple stresses reduces to a thermodynamically consistent system of laws of conservation, which allows obtaining integral estimates that guarantee the correctness of the Cauchy problem and boundary-value problems with dissipative boundary conditions. © 2017, Polish Academy of Sciences. All rights reserved.
Scopus
Держатели документа:
Institute of Computational Modeling SB RAS, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Sadovskii, V.M.; Садовский, Владимир Михайлович
Кл.слова (ненормированные):
Cosserat continuum -- Curvature tensor -- Thermodynamically consistent system -- Boundary value problems -- Constitutive equations -- Cosserat continuum -- Couple stress theory -- Curvature tensors -- Dissipative boundary conditions -- Independent coefficients -- Nonlinear constitutive equations -- Thermodynamic parameter -- Thermodynamically consistent system -- Nonlinear equations
Аннотация: To describe motion in a micropolar medium a special measure of curvature is used that is a strain state characteristic independent of deformation process. The nonlinear constitutive equations of the couple stress theory are constructed using the method of internal thermodynamic parameters of state. The linearization of these equations in isotropic case yields the Cosserat continuum equations, where material resistance to the change in curvature is characterized by a single coefficient as against three independent coefficients of the classical theory. So, it turns out that the developed variant of the model gives an adequate description of generalized plane stress state in an isotropic micropolar medium, while the classical one describes this state only at a certain case. The complete system of nonlinear equations for the dynamics of a medium with couple stresses reduces to a thermodynamically consistent system of laws of conservation, which allows obtaining integral estimates that guarantee the correctness of the Cauchy problem and boundary-value problems with dissipative boundary conditions. © 2017, Polish Academy of Sciences. All rights reserved.
Scopus
Держатели документа:
Institute of Computational Modeling SB RAS, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Sadovskii, V.M.; Садовский, Владимир Михайлович