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Stability of quasistatic equilibrium state of an inhomogeneous viscous layer on an inclined planeстатья
Информация о цитировании статьи получена из
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 28 мая 2015 г.
- Авторы: Bozhinskii A.N., Zeidis I.M.
- Журнал: Fluid Dynamics
- Том: 8
- Номер: 6
- Год издания: 1975
- Издательство: Maik Nauka/Interperiodica Publishing
- Местоположение издательства: Russian Federation
- Первая страница: 866
- Последняя страница: 869
- DOI: 10.1007/BF01014257
- Аннотация: Перевод Устойчивость квазистатического состояния равновесия неоднородного вязкого слоя на наклонной плоскости. Известия Академии наук — механика жидкости и газа, 1967, 2(3), 111–112. Другой перевод: Bozhinskii A., Zeidis I. Stability of a quasistatic equilibrium state of a nonhomogeneous viscous layer on an inclined plane [glaciology] // Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza. — 1973. — no. 6. — P. 20–4. A study is made of the stability against small perturbations [1] of a slow flow of an incompressible inhomogeneous linearly viscous liquid under the influence of a force of gravity on an unbounded inclined plane. Problems of such kind arise in glaciology when one estimates the stability of snow on mountain slopes or determines the catastrophic movement of a glacier; the results can also be applied to solifluction phenomena [2, 3]. Equations for perturbations of parallel flows of linearly viscous fluids in the case of a continuous variation of the viscosity and density across the flow were derived in [4]. An attempt to solve the hydrodynamic problem with allowance for a perturbation of the viscosity was made in [5]; however, in the equations for the perturbations, simplifications resulted in the neglect of terms that take into account perturbations of the viscosity. In the quasistatic formulation considered here in the case when allowance is made for perturbation of the density and viscosity, the equation for the perturbation amplitudes is an ordinary differential equation with variable coefficients; analytic solution of the equation is very difficult, even for long-wave perturbations. In this connection a study is made of the stability of a laminar model; the viscosity and density are constant within each layer. A similar hydrodynamic problem in the long-wave approximation was considered in [6]. In the present paper an exact solution is constructed in the quasistatic formulation for a two-layer model; the solution shows that the viscosity of the lower layer has an important influence on the stability. Essentially, instability is observed when the lower layer acts as a lubricant.
- Добавил в систему: Сократов Сергей Альфредович