On the structure and stability of rapidly rotating fluid bodies in general relativity. III - Beyond the angular velocity peak

1979 ◽  
Vol 231 ◽  
pp. 219 ◽  
Author(s):  
E. M. Butterworth
Keyword(s):  
General Relativity ◽  
Angular Velocity ◽  
Rotating Fluid ◽  
Structure And Stability ◽  
Velocity Peak

Singularities in general relativity

1970 ◽  
Vol 48 (8) ◽  
pp. 970-980 ◽  
Author(s):  
J. Pachner
Keyword(s):  
High Pressure ◽  
General Relativity ◽  
Angular Velocity ◽  
Mass Density ◽  
Rest Mass ◽  
First Integrals ◽  
Einstein Equations ◽  
Rotating Fluid ◽  
Relativistic Limit ◽  
Local Observer

The problem of singularities is examined from the standpoint of a local observer. A singularity is defined as a state with an infinite proper rest mass density. It is proved that any inhomogeneity and anisotropy in the distribution and motion of a nonrotating ideal fluid accelerates collapse. Collapse is also inevitable in a rotating fluid in the case of extremely high pressure when the relativistic limit of the equation of state must be applied. In order to investigate the influence of rotation on the existence of singularities in incoherent matter the Einstein equations together with their first integrals are written out for the points on a vortex filament. They show that rotation decelerates the contraction of space not only in the direction perpendicular to the vector of the angular velocity, but indirectly also along this vector and can prevent the occurrence of a singularity. This conclusion is confirmed by the numerical integration of the Einstein equations. The paper concludes with a discussion of some cosmological implications.

scholarly journals Determining the Tangential Velocity profile of a Rotating Fluid in a Static Container using Navier–Stokes equations

2020 ◽  
Author(s):  
RAJDEEP TAH ◽  
SARBAJIT MAZUMDAR ◽  
Krishna Kant Parida
Keyword(s):  
Angular Velocity ◽  
Velocity Profile ◽  
Velocity Gradient ◽  
Stokes Equations ◽  
Tangential Velocity ◽  
Navier Stokes ◽  
Rotating Fluid ◽  
Navier Stokes Equations ◽  
Similar Principle ◽  
Tangential Velocity Profile

The shape of the liquid surface for a fluid present in a uniformly rotating cylinder is generally determined by making a Tangential velocity gradient along the radius of the rotating cylindrical container. A very similar principle can be applied if the direction of the produced velocity gradient is reversed, for which the source of rotation will be present at the central axis of the cylindrical vessel in which the liquid is present. Now if the described system is completely closed, the angular velocity will decrease as a function of time. But when the surface of the rotating fluid is kept free, then the Tangential velocity profile would be similar to that of the Taylor-Couette Flow, with a modification that; due to formation of a curvature at the surface, the Navier-Stokes law is to be modified. Now the final equation may not seem to have a proper general solution, but can be approximated to certain solvable expressions for specific cases of angular velocity.

scholarly journals Angular velocity of rotation of extended bodies in general relativity

1996 ◽  
Vol 172 ◽  
pp. 309-320
Author(s):  
S.A. Klioner
Keyword(s):  
General Relativity ◽  
Angular Velocity ◽  
Rigid Body ◽  
Rotational Motion ◽  
The Body ◽  
Astronomical Observations ◽  
Newtonian Approximation ◽  
Accurate Definition ◽  
Principal Axes ◽  
Definition Of

We consider rotational motion of an arbitrarily composed and shaped, deformable weakly self-gravitating body being a member of a system of N arbitrarily composed and shaped, deformable weakly self-gravitating bodies in the post-Newtonian approximation of general relativity. Considering importance of the notion of angular velocity of the body (Earth, pulsar) for adequate modelling of modern astronomical observations, we are aimed at introducing a post-Newtonian-accurate definition of angular velocity. Not attempting to introduce a relativistic notion of rigid body (which is well known to be ill-defined even at the first post-Newtonian approximation) we consider bodies to be deformable and introduce the post-Newtonian generalizations of the Tisserand axes and the principal axes of inertia.

A note on forward wakes in rotating fluids

1970 ◽  
Vol 42 (1) ◽  
pp. 219-223 ◽  
Author(s):  
K. Stewartson
Keyword(s):  
Angular Velocity ◽  
Azimuthal Angle ◽  
Rotating Fluid ◽  
Rotating Fluids ◽  
Uniform Velocity

The two studies by Professor Miles (1970a, b) on the motion of a rotating fluid past a body raise the important question of the determinancy of such flows, by theoretical arguments, which it seems worth while making more precise. Suppose we have a fluid which when undisturbed has a uniform velocityUin the directionOxand a uniform angular velocity Ω aboutOx. It is slightly disturbed, the resulting motion having velocity components (u+U,v, Ωr+w) relative to cylindrical polar axes (x,r, θ), centreOand in whichrmeasures distance fromOx, while θ is the azimuthal angle. Assuming thatu, v, ware sufficiently small for their squares and products to be neglected, and are independent of θ, the equations governing their behaviour reduce to

scholarly journals On Vortex Motion in a rotating fluid

1888 ◽  
Vol 7 ◽  
pp. 29-41
Author(s):  
C. Chree
Keyword(s):  
Angular Velocity ◽  
Compressible Fluid ◽  
Vortex Motion ◽  
Rotating Fluid

The object of the following paper is to consider the motion of one or more vortices in a compressible fluid, which is rotating as a whole with uniform angular velocity ω about an axis, taken as axis of z. To save space I shall when possible refer for results to a previous paper in the Proceedings, distinguishing the equations of that paper, Vol. V.; pp. 52–59, by the suffix a.

Rotating fluid masses in general relativity. II

1966 ◽  
Vol 62 (3) ◽  
pp. 495-501 ◽  
Author(s):  
R. H. Boyer
Keyword(s):  
General Relativity ◽  
Variational Principle ◽  
First Integrals ◽  
Constant Angular Velocity ◽  
Hydrodynamic Equations ◽  
Rotating Fluid ◽  
Axially Symmetric ◽  
Field Equations ◽  
Full Field ◽  
Specific Entropy

AbstractWe describe some properties of a stationary, isolated, axially symmetric, rotating body of perfect fluid, according to general relativity. We first specialize to the case of constant specific entropy and constant angular velocity. The latter condition is equivalent to rigidity in the Born sense; both conditions are consequences of a simple variational principle. The hydrodynamic equations can then be integrated completely. Analogous first integrals are given also for the case of differential rotation. No use is made of the full field equations.

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