Interior solutions for rotating fluid spheres

1985 ◽  
Vol 32 (8) ◽  
pp. 1857-1862 ◽  
Author(s):  
Patrick G. Whitman
Keyword(s):  
Rotating Fluid ◽  
Fluid Spheres ◽  
Interior Solutions

Slowly rotating fluid spheres in the Einstein–Yukawa theory

1983 ◽  
Vol 61 (9) ◽  
pp. 1324-1327
Author(s):  
K. D. Krori ◽  
A. R. Sheikh
Keyword(s):  
Analytic Solutions ◽  
The Other ◽  
Slow Rotation ◽  
Rotating Fluid ◽  
Physical Conditions ◽  
Fluid Spheres ◽  
Interior Solutions ◽  
Yukawa Theory

We introduce slow rotation to a solution given by Krori et al. which represents fluid spheres in the Einstein–Yukawa theory, and present two new analytic solutions which are nonsingular and satisfy physical conditions throughout the spheres. One of the interior solutions represents uniformly rotating spheres and the other represents differentially rotating spheres. We also match the interior and exterior solutions on the boundary.

Anisotropic fluid spheres satisfying the Karmarkar condition

2019 ◽  
Vol 34 (15) ◽  
pp. 1950113 ◽  
Author(s):  
Nayan Sarkar ◽  
Susmita Sarkar ◽  
Farook Rahaman ◽  
Ksh. Newton Singh ◽  
Hasrat Hussain Shah
Keyword(s):  
Compact Stars ◽  
Anisotropic Fluid ◽  
Stability Factor ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Suitable Form ◽  
Fluid Spheres ◽  
Interior Solutions ◽  
Tov Equation

In this paper, we present new physically viable interior solutions of the Einstein field equations for static and spherically symmetric anisotropic compact stars satisfying the Karmarkar condition. For presenting the exact solutions, we provide a new suitable form of one of the metric potential functions. Obtained solutions satisfy all the physically acceptable properties of realistic fluid spheres and hence solutions are well-behaved and representing matter distributions are in equilibrium state and potentially stable by satisfying the TOV equation and the condition on stability factor, adiabatic indices. We analyze the solutions for two well-known compact stars Vela X-1 (Mass = 1.77 M[Formula: see text], R = 9.56 km) and Cen X-3 (Mass = 1.49 M[Formula: see text], R = 9.17 km).

Banded Convection in Rotating Fluid Spheres and the Circulation of the Jovian Atmosphere

Icarus ◽  
1996 ◽  
Vol 122 (2) ◽  
pp. 242-250 ◽  
Author(s):  
Jean-Baptiste Manneville ◽  
Peter Olson
Keyword(s):  
Rotating Fluid ◽  
Fluid Spheres ◽  
Jovian Atmosphere

Comment on rotating fluid spheres

1984 ◽  
Vol 1 (3) ◽  
pp. 319-319 ◽  
Author(s):  
P G Whitman
Keyword(s):  
Rotating Fluid ◽  
Fluid Spheres

A new Legendre-type polynomial and its application to geostrophic flow in rotating fluid spheres

2010 ◽  
Vol 466 (2120) ◽  
pp. 2203-2217 ◽  
Author(s):  
Xinhao Liao ◽  
Keke Zhang
Keyword(s):  
Asymptotic Analysis ◽  
Rotation Axis ◽  
Spherical Geometry ◽  
Polar Coordinates ◽  
Rotating Fluid ◽  
Geostrophic Flow ◽  
Spherical Boundary ◽  
Essential Properties ◽  
Geostrophic Flows ◽  
Fluid Spheres

In rapidly rotating spheres, the whole fluid column, extending from the southern to northern spherical boundary along the rotation axis, moves like a single fluid element, which is usually referred to as geostrophic flow. A new Legendre-type polynomial is discovered in undertaking the asymptotic analysis of geostrophic flow in spherical geometry. Three essential properties characterize the new polynomial: (i) it is a function of r and θ but takes a single argument , which is restricted by 0≤ r ≤1 and 0≤ θ ≤ π , where ( r , θ , ϕ ) denote spherical polar coordinates with θ =0 at the rotation axis; (ii) it is odd and vanishes at the axis of rotation θ =0, and (iii) it is defined within—and orthogonal over—the full sphere. As an example of its application, we employ the new polynomial in the asymptotic analysis of forced geostrophic flows in rotating fluid spheres for small Ekman and Rossby numbers. Fully numerical analysis of the same problem is also carried out, showing satisfactory agreement between the asymptotic solution and the numerical solution.

scholarly journals Onset of Inertial Magnetoconvection in Rotating Fluid Spheres

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 41
Author(s):  
Radostin D. Simitev ◽  
Friedrich H. Busse
Keyword(s):  
Buoyancy Force ◽  
Wave Number ◽  
Leading Order ◽  
Rotating Fluid ◽  
Onset Of Convection ◽  
Azimuthal Magnetic Field ◽  
Magnetic Analysis ◽  
Azimuthal Wave Number ◽  
High Thermal Diffusivity ◽  
Fluid Spheres

The onset of convection in the form of magneto-inertial waves in a rotating fluid sphere permeated by a constant axial electric current is studied in this paper. Thermo-inertial convection is a distinctive flow regime on the border between rotating thermal convection and wave propagation. It occurs in astrophysical and geophysical contexts where self-sustained or external magnetic fields are commonly present. To investigate the onset of motion, a perturbation method is used here with an inviscid balance in the leading order and a buoyancy force acting against weak viscous dissipation in the next order of approximation. Analytical evaluation of constituent integral quantities is enabled by applying a Green’s function method for the exact solution of the heat equation following our earlier non-magnetic analysis. Results for the case of thermally infinitely conducting boundaries and for the case of nearly thermally insulating boundaries are obtained. In both cases, explicit expressions for the dependence of the Rayleigh number on the azimuthal wavenumber are derived in the limit of high thermal diffusivity. It is found that an imposed azimuthal magnetic field exerts a stabilizing influence on the onset of inertial convection and as a consequence magneto-inertial convection with azimuthal wave number of unity is generally preferred.

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