On some exact solutions in magnetohydrodynamics with astrophysical applications

1972 ◽  
Vol 51 (1) ◽  
pp. 33-38 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Free Surface ◽  
Angular Velocity ◽  
Incompressible Fluid ◽  
Exact Solutions ◽  
Equilibrium Configuration ◽  
Constant Angular Velocity ◽  
Magnetohydrodynamic Equations ◽  
The Stability

Some exact solutions of the steady magnetohydrodynamic equations for a perfectly conducting inviscid self-gravitating incompressible fluid are discussed. It is shown that there exist solutions for which the free surface of the liquid is that of a planetary ellipsoid and rotates with constant angular velocity about its axis. The stability of the equilibrium configuration is not investigated.

Centrifugal waves

1960 ◽  
Vol 7 (3) ◽  
pp. 340-352 ◽  
Author(s):  
O. M. Phillips
Keyword(s):  
Free Surface ◽  
Angular Velocity ◽  
Circular Cylinder ◽  
Rigid Body ◽  
Water Depth ◽  
Frequency Equation ◽  
Rigid Rotation ◽  
Body Motion ◽  
Small Perturbations ◽  
The Stability

When a hollow circular cylinder with its axis horizontal is partially filled with water and rotated rapidly about its axis, an almost rigid-body motion results with an interior free surface. The emotion is analysed assuming small perturbations to a rigid rotation, and a criterion is found for the stability of the motion. This is confirmed experimentally under varying conditions of water depth and angular velocity of the cylinder. The modes of oscillation (centrifugal waves) of the free surface are examined and a frequency equation deduced. Two particular modes are considered in detail, and satisfactory agreement is found with the frequencies observed.

Stability of a Rotor Partially Filled With a Viscous Incompressible Fluid

1979 ◽  
Vol 46 (4) ◽  
pp. 913-918 ◽  
Author(s):  
S. L. Hendricks ◽  
J. B. Morton
Keyword(s):  
Angular Velocity ◽  
Circular Cylinder ◽  
Incompressible Fluid ◽  
Parametric Study ◽  
Viscous Incompressible Fluid ◽  
Constant Angular Velocity ◽  
Unstable Region ◽  
Stability Boundaries ◽  
System Parameters ◽  
Linear Spring

A hollow circular cylinder rotating with constant angular velocity and partially filled with a viscous incompressible fluid has been analyzed for stability. The analysis can be extended to apply to many different rotor geometries. The results of this analysis predict that over a range of operating speeds, the system is unstable. The extent of this unstable region is determined by the system parameters. The interplay between viscosity of the fluid and damping on the rotor is especially important in determining stability boundaries. A parametric study is presented for a rotor modeled as a cup in the middle of a symmetrically supported massless shaft. The rotor is subject to a linear spring and a linear damper. Rotor unbalance, gravity, and axial effects are considered negligible.

Separation and the Taylor-column problem for a hemisphere

1974 ◽  
Vol 66 (4) ◽  
pp. 767-789 ◽  
Author(s):  
J. D. A. Walker ◽  
K. Stewartson
Keyword(s):  
Angular Velocity ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Shear Layers ◽  
Constant Angular Velocity ◽  
Vertical Shear ◽  
Rossby Number ◽  
Ekman Number ◽  
Free Shear Layers ◽  
Taylor Column

A layer of viscous incompressible fluid is confined between two horizontal plates which rotate rapidly in their own plane with a constant angular velocity. A hemisphere has its plane face joined to the lower plate and when a uniform flow is forced past such an obstacle, a Taylor column bounded by thin detached vertical shear layers forms. The linear theory for this problem, wherein the Rossby number ε is set equal to zero on the assumption that the flow is slow, is examined in detail. The nonlinear modifications of the shear layers are then investigated for the case when ε ∼ E½, where E is the Ekman number. In particular, it is shown that provided that the Rossby number is large enough separation occurs in the free shear layers. The extension of the theory to flow past arbitrary spheroids is indicated.

Unsteady Rotating Flow in a Cylinder With a Free Surface

1968 ◽  
Vol 90 (4) ◽  
pp. 445-452 ◽  
Author(s):  
H. Goller ◽  
T. Ranov
Keyword(s):  
Free Surface ◽  
Angular Velocity ◽  
Stokes Equations ◽  
Constant Angular Velocity ◽  
Navier Stokes ◽  
Rotating Flow ◽  
Navier Stokes Equations ◽  
Surface Configuration ◽  
Simplifying Assumptions ◽  
Good Agreement

The investigation deals with the “spin-up” of the liquid partially filling a right circular cylinder which is impulsively accelerated from rest to a constant angular velocity. By application of certain simplifying assumptions, a simplification of the Navier-Stokes equations is obtained and numerically solved, obtaining the unsteady angular velocity distribution of the liquid and the configuration of the liquid’s free surface, as it approaches, asymptotically with time, a paraboloid. The simplifying assumptions are qualitatively verified by experiment. Measurement of the theoretically predicted free-surface configuration is obtained by an electrohydraulic servosystem designed and developed for the problem. Good agreement between experiment and theory is obtained.

Unsteady flows with a zero acceleration on the free boundary

2014 ◽  
Vol 754 ◽  
pp. 308-331 ◽  
Author(s):  
E. A. Karabut ◽  
E. N. Zhuravleva
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Incompressible Fluid ◽  
Exact Solutions ◽  
Unsteady Flows ◽  
Ideal Incompressible Fluid ◽  
Hopf Equation ◽  
New Approach

AbstractA new approach to the construction of exact solutions of unsteady equations for plane flows of an ideal incompressible fluid with a free boundary is proposed. It is demonstrated that the problem is significantly simplified and reduces to solving the Hopf equation if the acceleration on the free surface is equal to zero. Some examples of exact solutions are given.

scholarly journals Boundary-layer growth on a rotating and accelerating sphere

1987 ◽  
Vol 65 (1) ◽  
pp. 23-27 ◽  
Author(s):  
G. T. Karahalios ◽  
V. Theofilis
Keyword(s):  
Boundary Layer ◽  
Angular Velocity ◽  
Power Series ◽  
Incompressible Fluid ◽  
Skin Friction ◽  
Layer Growth ◽  
Constant Angular Velocity ◽  
Constant Acceleration ◽  
Analytic Expressions ◽  
Boundary Layer Growth

Boundary-layer growth on a sphere is studied when it is set into motion with constant acceleration and constant angular velocity, the latter being normal to the former. Analytic expressions are derived for the velocity components of the incompressible fluid in terms of a power series of the time of motion as well as for the skin friction.

Mathematical modeling of Couette flow in anomalous thermoviscous liquid

2011 ◽  
Vol 8 (1) ◽  
pp. 143-152
Author(s):  
S.F. Khizbullina
Keyword(s):  
Mathematical Modeling ◽  
Angular Velocity ◽  
Numerical Experiment ◽  
Temperature Dependence ◽  
Steady Flow ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Flow Regimes ◽  
Constant Angular Velocity ◽  
Coaxial Cylinders

The steady flow of anomalous thermoviscous liquid between the coaxial cylinders is considered. The inner cylinder rotates at a constant angular velocity while the outer cylinder is at rest. On the basis of numerical experiment various flow regimes depending on the parameter of viscosity temperature dependence are found.

Exact nonlinear wave solutions of the incompressible magnetohydrodynamic equations in a sheared magnetic field

1990 ◽  
Vol 44 (1) ◽  
pp. 25-32 ◽  
Author(s):  
Hiromitsu Hamabata
Keyword(s):  
Magnetic Field ◽  
Incompressible Fluid ◽  
Large Amplitude ◽  
Uniform Magnetic Field ◽  
Magnetohydrodynamic Equations ◽  
Wave Solutions ◽  
Field Lines ◽  
Incompressible Magnetohydrodynamic Equations ◽  
Physical Quantities ◽  
Nonlinear Wave Solutions

Exact wave solutions of the nonlinear jnagnetohydrodynamic equations for a highly conducting incompressible fluid are obtained for the cases where the physical quantities are independent of one Cartesian co-ordina.te and for where they vary three-dimensionally but both the streamlines and magnetic field lines lie in parallel planes. It is shown that there is a class of exact wave solutions with large amplitude propagating in a straight but non-uniform magnetic field with constant or non-uniform velocity.

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