共查询到20条相似文献,搜索用时 15 毫秒
1.
V. A. Solonnikov 《Journal of Mathematical Sciences》2009,157(6):885-947
We consider the free boundary problem for the Navier–Stokes equations governing a nonstationary motion of a layer of a viscous
incompressible liquid that covers the surface of a rigid ball rotating around a fixed axis with constant angular velocity
ω. The liquid is subject to the gravitation force generated by the mass of the ball. The self-gravitation forces between the
liquid particles and capillary forces on the free surface are not taken into account. We consider the problem of stability
of the regime of the rigid rotation of the liquid with the same angular velocity and prove that it is stable if |ω| is less than a certain constant. Bibliography: 10 titles.
Translated from Problems in Mathematical Analysis
39 February, 2009, pp. 91–145. 相似文献
2.
The fluid flow through a rotating straight pipe is considered, the axis of rotation being perpendicular to the pipe axis. The flow of the fluid is taken as fully developed, i.e. the velocity field is assumed to be the same in all transverse cross sections of the pipe. The derivation presented applies to viscous and nonviscous incompressible fluids. For constant angular pipe velocity a simple and exact (Coriolis type) relationF=2Q(t) is derived between the forceF by which the fluid acts on the (unit length of the) pipe in the direction perpendicular to the two axes, the fluid mass flow rateQ(t) through the pipe, and the angular velocity. Variable angular velocities, i.e.
, introduce an additional term into the expression for the inertial forceF, which depends only on
and on known (constant) parameters; this term is known for given angular velocity(t). The flow configuration investigated here is an idealization of those appearing (over short space and time intervals) in the devices measuring mass flow rateQ(t) through the (Coriolis) forceF. Therefore the exact results derived here cast some light on the degree of precision one expects in these devices, where more complicated flow configurations are present than those looked at in this paper. 相似文献
3.
R. S. Srivastava 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,54(6):1073-1085
Fully developed laminar flow in a straight heated
rotating pipe which includes the influence of both, coriolis force
and buoyancy force, has been considered analytically. The solution
has been obtained in terms of series expansions; the solution is
therefore restricted to small values of the parameters involved. 相似文献
4.
V. V. Ramana Rao 《Proceedings Mathematical Sciences》1972,75(4):189-198
A theoretical analysis is made of the flow of a conducting viscous and incompressible fluid through a straight annular pipe of circular cross-section flowing under a constant pressure gradient. The pipe is rotated about an axis perpendicular to it and also there is imposed a uniform magnetic field transverse to the motion. The secondary flow pattern has been studied in detail for small values of angular velocity and Hartman number. 相似文献
5.
Peder A. Tyvand 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1984,35(4):592-597
Summary The linear theory by Reid [1] on gravity waves in a viscous liquid with surface tension is extended. Asymptotic formulae for the dispersion relation are derived. A critical Morton number equal to 0.044789 is found. Only in liquids with smaller Morton numbers, travelling ripples may exist with group velocity exceeding phase velocity.
Zusammenfassung Reid's lineare Theorie über Gravitationswellen in einer viskosen Flüssigkeit mit Oberflächenspannung wird erweitert. Abgeleitet werden asymptotische Formeln für das Verteilungsverhältnis und eine kritische Morton-Zahl gleich 0.044789 wird gefunden. Nur in Flüssigkeiten mit geringeren Morton-Zahlen existieren wandernde kleine Wellen mit einer Gruppengeschwindigkeit, die die Phasengeschwindigkeit überschreitet.相似文献
6.
We consider the motion of compressible viscous fluids around a rotating rigid obstacle when the velocity at infinity is non zero and parallel to the axis of rotation. We prove the existence of weak solution. 相似文献
7.
8.
Stokes’ and Seth’s solutions for the slow motion of a sphere in a viscous, incompressible liquid have been discussed from the viewpoint of the structure of the velocity field and its relation to the drag of the sphere. The problem is analysed from a different angle in this paper. It is believed that it throws more light on thephysics of the problem. 相似文献
9.
V. A. Solonnikov 《Journal of Mathematical Sciences》2008,152(5):713-740
The paper is devoted to justification of the potential energy minimum principle in the problem of stability of a uniformly
rotating viscous incompressible self-gravitating liquid. The capillary forces on the free boundary of the liquid are not taken
into account. It is proved that the regime of rigid rotation is stable if the second variation of the energy functional is
positive. The proof is based on the analysis of the evolution free boundary problem for perturbations in the velocity and
pressure of the rotating liquid. Bibliography: 15 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 348, 2007, pp. 165–208. 相似文献
10.
Analytical solution of the flow problem of a dusty viscous liquid through a circular pipe in case of axial symmetry is obtained when pressure gradient varies harmonically with time. It is found that the effect of the fine dust is to make the velocity of sedimentation zero and when dust is sufficiently coarse, the effect of the dust is equivalent to an extra frictional force proportional to the fluid velocity. 相似文献
11.
《Journal of Applied Mathematics and Mechanics》2002,66(2):239-243
The motions of a viscous incompressible fluid, rotating initially as a rigid body with constant angular velocity together with parallel walls which bound it, acted upon by suddenly starting longitudinal oscillations of one of the walls, are investigated. The walls make an arbitrary angle with the axis of rotation. In general, the solution is obtained in the form of the sum of an infinite series and is represented by an integral containing an elliptic function. A number of special cass of the motion of the wall is considered. The results obtained are used to investigate certain structures of the boundary layers on the walls. 相似文献
12.
John A. Lewis 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1963,14(2):169-172
Zusammenfassung Eine obere Schranke für die Dämpfung der kleinen Schwingungen eines Pendels wird für den Fall erhalten, dass die Dämpfung durch eine zähe, in einem am Pendel angebrachten Gefäss enthaltene Flüssigkeit verursacht wird. Diese Schranke gilt für ein beliebiges Flüssigkeitsvolumen, vorausgesetzt, dass dessen Trägheitsmoment bezüglich desjenigen des Pendels klein ist. 相似文献
13.
14.
Zusammenfassung Das Problem der langsamen Querbewegung einer ebenen Platte in einer zähen Flüssigkeit ist zurückgeführt worden auf ein Problem der Elektrostatik. Die Geschwindigkeitskomponenten und der Druck können berechnet werden aus einer Funktion , die als die gleiche erscheint wie das elektrostatische Potential einer Platte unter konstantem Potential im Vakuum. Die Strömungsverhältnisse an einer Platte vom allgemeinen Umriss können mit Hilfe der Experimente auf Grund dieser Analogie bestimmt werden. Der Fall einer kreisrunden Platte wurde analytisch behandelt mit Hilfe der Abbildungen. 相似文献
15.
The pulsating viscous flow superposed on the steady laminar motion of incompressible fluid in a circular pipe 总被引:10,自引:0,他引:10
Shigeo Uchida 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1956,7(5):403-422
Summary An exact solution of pulsating laminar flow superposed on the steady motion in a circular pipe is presented under the assumption of parallel flow to the axis of pipe. Total mass of flow on time average is found to be identified with that given byHagen-Poiseuille's low calculated on the steady component of pressure gradient. The phase lag of velocity variation from that of pressure gradient increases from zero in the steady motion to 90° in the pulsation of infinite frequency. Integration of work for changing kinetic energy of fluid through one period is vanished, while that of dissipation of energy by internal friction remains finite and excess amount caused by the components of periodic motion is added to the components of steady flow.It is found that the given rate of mass flow is attained in pulsating motion by giving the same amount of average gradient of pressure as in steady flow, but that excess works to the steady case are necessary for maintenance of this motion.
Zusammenfassung Eine exakte Lösung der pulsierenden laminaren Strömung in einem Kreisrohr wird angegeben mit der Annahme, dass die Richtung dem Geschwindigkeitsvektor der Rohrachse parallel ist. Die Durchflussmenge stimmt überein mit der aus der stationären Druckgefällekomponente gerechneten Menge. Für die Erhaltung der Bewegung dagegen ist die der Dissipation entsprechende Extraarbeit notwendig. Die Quantität dieser Arbeit hängt ab von den Frequenzen der Stromschwingungen.相似文献
16.
R. Yu. Amenzadze 《Mechanics of Composite Materials》1976,12(2):274-277
The problem of the propagation of progressive waves in a tube made of a linearly viscoelastic material which encloses a viscous Newtonian liquid is examined. For numerical calculations, it is proposed that the behavior of the tube wall material be described by the Voigt model. Dispersion curves are constructed for this case.S. M. Kirov Azerbaidzhan State University, Baku. Translated from Mekhanika Polimerov, No. 2, pp. 317–321, March–April, 1976. 相似文献
17.
T. M. Atanacković Dj. S. Djukić 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1985,36(5):757-763
For a non-linear boundary value problem describing the shape of a heavy rotating chain a priori estimates of the maximal deflection are obtained. Also, for the transformed chain problem an extremum Variational principle and error estimates are presented.
Zusammenfassung Für eine nichtlineare Differentialgleichung, die die Form einer schwer rotierenden Kette beschreibt, werden a priori Abschätzungen der maximalen Ausbiegung erhalten. Dabei werden für ein transformiertes Ketten-Problem ein extremales Variationsprinzip und die Feller Abschätzung angegeben.相似文献
18.
C. J. Simpson K. Stewartson 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1982,33(3):370-378
A recent study of the unsteady boundary layer near the equator of a spinning sphere provided strong numerical evidence that the solution develops a singularity a finite time after the motion is initiated. In this paper we reformulate and complete the asymptotic structure proposed to describe this singularity. It is then self-consistent and provides convincing evidence of the accuracy of the computations and of the existence of the singularity.
Zusammenfassung Eine neuere Untersuchung über die nicht-stationäre Grenzschicht nahe am Äquator einer rotierenden Kugel ergab starke numerische Evidenz für das Auftreten einer Singularität in der Lösung nach einer endlichen Zeit, vom Beginn der Bewegung gerechnet. In dieser Arbeit wird die asymptotische Struktur zur Beschreibung der Singularität neu formuliert und ergänzt. Sie wird selbstkonsistent und gibt ein wichtiges Zeugnis für die Genauigkeit der Berechnungen und für die Existenz der Singularität.相似文献
19.
Zusammenfassung Es wird gezeigt, dass in elektrisch leitender Flüssigkeit bei zylindrischer Symmetrie die Radialkomponente des Magnetfeldes klein ist im Vergleich zur Axialkomponente, sobald die axiale Ausdehnung des Gefässes klein ist im Vergleich zu seinem Durchmesser. 相似文献