共查询到20条相似文献,搜索用时 30 毫秒
1.
A variational method is used to study the shape of a self-gravitating fluid mass rotating with a prescribed angular momentum per unit mass. The model is of primary interest in astrophysics, where it is taken as a model of a star. Sharp estimates are obtained on the diameter of the rotating body in terms of the total mass M and parameter and W represent, respectively, the kinetic and potential energy. The cases of Q small (slowly rotating body) and Q large (rapidly rotating body) are dealt with separately. 相似文献
2.
Henry C. Wente 《manuscripta mathematica》1982,39(2-3):287-296
Consider an incompressible fluid body (in outer space) rotating about an axis with a given angular velocity , and which is in equilibrium relative to the potential energy of its own gravitational field and the surface energy due to surface tension. We show that such a body possesses a plane of symmetry perpendicular to the axis of rotation such that any line parallel to the axis and meeting the body cuts it in a line segment whose center lies on the plane of symmetry. This extends an earlier result of L. Lichtenstein [4].This work was done with the support of S.F.B. 72 while the author was a visitor at the University of Bonn 相似文献
3.
The axisymmetric free laminar jet of a power-law fluid 总被引:1,自引:0,他引:1
Robert W. Serth 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1972,23(1):131-138
Summary The solution of the boundary-layer equations for an axisymmetric free laminar jet of a power-law fluid is investigated. It is shown that similar solutions are possible only forn1/2, wheren is the exponent in the power-law model. Forn>1/2, the axial velocity decay is proportional to the (–1/2n–1) power of the distance downstream and the jet spreads at a rate proportional to the (1/2n–1) power of the distance. Forn=1/2, the velocity decay and the rate of spread are exponential. Experimental data are presented which demonstrate that the predicted exponential decay occurs in real fluids.
Nomenclature d orifice diameter - D characteristic length - f preliminary dependent variable - F final dependent variable - J momentum inx-direction - K coefficient in power law model - n exponent in power law model - Re generalized Reynolds number - u x-component of velocity;u o=characteristic velocity;u p =initial velocity;=u/u o;u m =velocity on centerline of jet. - v y-component of velocity; - x coordinate in axial direction; ; = distance from orifice in experimental jet - y coordinate in radial direction; - function of - function of - parameter in final similarity transformation - preliminary independent variable - final independent variable - fluid density - shear stress - stream function 相似文献
Zusammenfassung Ähnliche Lösungen der Grenzschichtgleichungen für einen achsensymmetrischen laminaren Strahl von Potenzgesetz-Flüssigkeiten werden gegeben. Diese Lösungen werden mit vorhandenen experimentellen Daten verglichen.
Nomenclature d orifice diameter - D characteristic length - f preliminary dependent variable - F final dependent variable - J momentum inx-direction - K coefficient in power law model - n exponent in power law model - Re generalized Reynolds number - u x-component of velocity;u o=characteristic velocity;u p =initial velocity;=u/u o;u m =velocity on centerline of jet. - v y-component of velocity; - x coordinate in axial direction; ; = distance from orifice in experimental jet - y coordinate in radial direction; - function of - function of - parameter in final similarity transformation - preliminary independent variable - final independent variable - fluid density - shear stress - stream function 相似文献
4.
《Journal of Computational and Applied Mathematics》1986,16(3):355-369
This paper considers the nature of stationary axisymmetric convection in a rotating layer of fluid heated from below. The nonlinear amplitude equation for the case of rigid boundaries is derived, and it is found that for certain ranges of the speed of rotation and Prandtl number subcritical instability is possible. The outer solution is matched with the inner solution (which can be expressed in terms of Bessel functions) and is similar to that described by Brown and Stewartson (1978). 相似文献
5.
We consider stationary axisymmetric solutions of the Euler–Poisson equations, which govern the internal structure of barotropic gaseous stars. We take the general form of the equation of states which cover polytropic gaseous stars indexed by and also white dwarfs. A generic condition of the existence of stationary solutions with differential rotation is given, and the existence of slowly rotating configurations near spherically symmetric equilibria is shown. The problem is formulated as a nonlinear integral equation, and is solved by an application of the infinite dimensional implicit function theorem. Oblateness of star surface is shown and also relationship between the central density and the total mass is given. 相似文献
6.
V. A. Solonnikov 《Journal of Mathematical Sciences》2010,166(1):91-105
The paper is concerned with the problem of stability of a uniformly rotating viscous incompressible self-gravitating liquid bounded by a rotationally symmetric free surface. It is proved that it is unstable if the second variation of the energy functional is not positive. Bibliography: 11 titles. 相似文献
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9.
N. B. Grigor'yeva 《Journal of Applied Mathematics and Mechanics》1999,63(6):985-987
Using the method developed in [1] for solving the problem of the conditional stability of MacLaurin ellipsoids, it is proved that Jacobi ellipsoids are stable under Dirichlet conditions for all case when Jacobian ellipsoids exist. 相似文献
10.
Helmut F. Bauer Julius Siekmann 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1971,22(3):532-542
Zusammenfassung Vorliegende Arbeit untersucht die Gleichgewichtsfiguren eines im schwerelosen Zustand rotierenden Systems, bestehend aus einer Gasblase und einem endlichen Flüssigkeitskörper. Das Gas wird von der Flüssigkeit eingeschlossen. Es wird die kritische Winkelgeschwindigkeit bestimmt, bei welcher die Oberfläche der Gasblase diejenige des umgebenden Flüssigkeitskörpers berührt. Das Problem ist von Bedeutung für Experimente in der für die Zukunft geplanten Orbit-Werkstatt. 相似文献
11.
V. A. Temnenko 《Journal of Mathematical Sciences》1996,82(2):3347-3350
We study the problem of the shape of an inextensible string rotating in a gravitational field. We discuss a method of solution
and present some results: bifurcation diagrams and equilibrium shapes of the string for certain values of the angular velocity
ω.
Translated fromDinamicheskie Sistemy, Vol. 11, 1992. 相似文献
12.
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
13.
14.
In this work, we study several routes of the transition to chaos from a steady axisymmetric vertical vortex in a rotating cylinder depending on thermal gradients and rotation rates. The analysis is done using nonlinear simulations. For a fixed rotation rate, the chaotic regime appears, as thermal gradients increase, after a sequence of supercritical Hopf bifurcations to periodic, quasiperiodic and chaotic flows in a scenario similar to the Ruelle–Takens–Newhouse route to chaos. For moderate values of the rotation rate we find vortices that tilt and move away from the center of the cylinder in a periodic, quasiperiodic and finally chaotic movement around the central axis. For larger rotation rates the axisymmetric vortex splits into two symmetric vortices that move periodically around the central axis, and lose the symmetry merging again in one non-axisymmetric vortex that moves around the central axis quasiperiodically and later chaotically. The transitions to chaos when the rotation rate is varied at fixed thermal gradients reveal also the appearance of periodic, quasiperiodic and chaotic states in different routes. Tilted single vortices, double vortices and more complex structures with multiple vortices are reported in this case. The transitions are studied through a force balance analysis. Results are of interest as they connect to the behavior of some atmospheric vertical vortices. 相似文献
15.
This work looks at the heat transfer effects on the flow of a second grade fluid over a radially stretching sheet. The axisymmetric flow of a second grade fluid is induced due to linear stretching of a sheet. Mathematical analysis has been carried out for two heating processes, namely (i) with prescribed surface temperature (PST case) and (ii) prescribed surface heat flux (PHF case). The modelled non-linear partial differential equations in two dependent variables are reduced into a partial differential equation with one dependent variable. The resulting non-linear partial differential equations are solved analytically using homotopy analysis method (HAM). The series solutions are developed and the convergence is properly discussed. The series solutions and graphs of velocity and temperature are constructed. Particular attention is given to the variations of emerging parameters such as second grade parameter, Prandtl and Eckert numbers. 相似文献
16.
The wellposedness problem for an anisotropic incompressible viscous fluid in R3,rotating around a vector B(t,x):=(b1(t,x),b2(t,x),b3(t,x)),is studied.The global wellposedness in the homogeneous case (B... 相似文献
17.
S. S. Chawla 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1979,30(5):789-795
Summary Fluid motion induced by the penetration of an oscillating axial magnetic field in a semi-infinite rotating fluid is considered. The redistribution of forces due to the generation of Maxwell stresses produce fluid fluctuations superposed on a steady motion. Estimates of the mean flow are obtained for different values of the mean applied magnetic pressure.
Zusammenfassung Die Flüssigkeitsbewegung, die durch das Eindringen eines oszillierenden achsialen Magnetfeldes in eine halb-unendliche rotierende Fluid-Masse induziert wird, wird untersucht. Die Neuverteilung der Kräfte, bedingt durch die Erzeugung von Maxwell-Spannungen, erzeugt Fluktuationen des Fluids, die der stationären Bewegung überlagert sind. Schätzungen der mittleren Geschwindigkeit für verschiedene Werte des mittleren magnetischen Druckes wurden erhalten.相似文献
18.
The boundary layer flow over a stretching surface in a rotating viscoelastic fluid is considered. By applying a similarity transformation, the governing partial differ-ential equations are converted in... 相似文献
19.
M. A. Page 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1982,33(6):752-762
Summary The flow of a rotating fluid past a split plate is examined in the limit of vanishing Rossby number to determine the nature of the StewartsonE
1/4-layers in the region of the gap between the plates. When the gap width is order unity it is established that the end regions have a radius ofO(E
1/4) and that they do not interact. However, when the gap width isO(E
1/4) there is an interaction between the two end regions, and the solution is calculated numerically for this case.
Zusammenfassung Es wird eine Drehströmung mit der Rossby-Zahl Null entlang zwei parallelen Platten untersucht, wobei die Spaltbreite die Größenordnung Eins hat. Es erhebt sich die Frage, ob in der Region zwischen den Platten eine StewartsonscheE 1/4-Schicht existieren kann. Es wird festgestellt, daß so eine Schicht nicht vorhanden sein kann; wenn jedoch die SpaltbreiteO(E 1/4) ist, dann wird der Spalt durch eine Stewartson-Schicht ausgefüllt. Die Lösung wird für diesen Fall berechnet, und der Effekt der Zähigkeit auf die Strömung zwischen den Platten wird gezeigt.相似文献
20.
《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