Equations of motion and equilibrium conditions for an ideal rotating fluid in parametrized post-Newtonian magnetohydrodynamics

Astrophysics ◽  
1986 ◽  
Vol 23 (3) ◽  
pp. 719-723 ◽  
Author(s):  
N. P. Bondarenko
Keyword(s):  
Equations Of Motion ◽  
Rotating Fluid ◽  
Equilibrium Conditions

scholarly journals Symmetry analysis of rotating fluid

2005 ◽  
Vol 47 (1) ◽  
pp. 65-74 ◽  
Author(s):  
K. Fakhar ◽  
Zu-Chi Chen ◽  
Xiaoda Ji
Keyword(s):  
Steady State ◽  
Infinite Number ◽  
Special Function ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Lie Theory ◽  
Rotating Fluid ◽  
Type Solution ◽  
Function Type ◽  
Basic Equations

AbstractThe machinery of Lie theory (groups and algebras) is applied to the unsteady equations of motion of rotating fluid. A special-function type solution for the steady state is derived. It is then shown how the solution generates an infinite number of time-dependent solutions via three arbitrary functions of time. This algebraic structure also provides the mechanism to search for other solutions since its character is inferred from the basic equations.

The motion of a rising disk in a rotating axially bounded fluid for large Taylor number

1995 ◽  
Vol 291 ◽  
pp. 1-32 ◽  
Author(s):  
Marius Ungarish ◽  
Dmitry Vedensky
Keyword(s):  
Exact Solution ◽  
Boundary Value Problem ◽  
Equations Of Motion ◽  
Taylor Number ◽  
Rossby Number ◽  
Rotating Fluid ◽  
Asymptotic Results ◽  
Dual Integral Equations ◽  
Wall Distance ◽  
Taylor Column

The motion of a disk rising steadily along the axis in a rotating fluid between two infinite plates is considered. In the limit of zero Rossby number and with the disk in the middle position, the boundary value problem based on the linear, viscous equations of motion is reduced to a system of dual-integral equations which renders ‘exact’ solutions for arbitrary values of the Taylor number, Ta, and disk-to-wall distance, H (scaled by the radius of the disk). The investigation is focused on the drag and on the flow field when Ta is large (but finite) for various H. Comparisons with previous asymptotic results for ‘short’ and ‘long’ containers, and with the preceding unbounded-configuration ‘exact’ solution, provide both confirmation and novel insights.In particular, it is shown that the ‘free’ Taylor column on the particle appears for H > 0.08 Ta and attains its fully developed features when H > 0.25 Ta (approximately). The present drag calculations improve the compatibility of the linear theory with Maxworthy's (1968) experiments in short containers, but for the long container the claimed discrepancy with experiments remains unexplained.

Low-Speed Controllability of Ships in Wind

1968 ◽  
Vol 12 (03) ◽  
pp. 181-200
Author(s):  
H. Eda
Keyword(s):  
Mathematical Model ◽  
Nonlinear Equations ◽  
Digital Computer ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Equilibrium Conditions ◽  
Region Of Stability ◽  
Nonlinear Equations Of Motion ◽  
Hydrodynamic Data ◽  
Relative Wind

Aerodynamic and hydrodynamic data for the Manner-class vessel, gathered in earlier experiments, were used to formulate a mathematical model representing the dynamic behavior of ships in wind. A digital computer was used to solve the eigenvalues of the system. Perturbation equations were linearized, with respect to equilibrium conditions, from nonlinear equations of motion. In addition, ship trajectory in certain wind conditions was examined by means of numerical solutions of the nonlinear equations of motion. Results indicate that the ship in bow wind tends, even without an autopilot system, to maintain its original course-with perturbation in yaw inducing yaw oscillations, the convergence of which depends upon the magnitude of relative wind velocity. It is shown that beam wind creates greater difficulties, although the use of an adequate autopilot increases the region of stability in wind of certain velocities (except in some conditions of relatively strong beam wind). An increase in rudder size is shown to improve controllability in wind significantly. Computations with and without the assumption of constant longitudinal speed indicate that the effect of surge motion on yaw and sway responses in wind is important, especially in beam wind.

Horizontal Pendulum With Sudden Changes in Platform Tilt

2011 ◽  
Author(s):  
Clark C. McGehee ◽  
Zach C. Ballard ◽  
Brian P. Mann
Keyword(s):  
Analytical Solutions ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Phase Correction ◽  
Method Of Averaging ◽  
Equilibrium Conditions ◽  
Ongoing Work ◽  
Approximate Analytical Solutions ◽  
Horizontal Pendulum ◽  
Platform Tilt

The equations of motion for a horizontal pendulum mounted to a rocking platform are developed. Equilibrium conditions are found as a function of the platform tilt angle. The equations are transformed to describe motion about the shifting equilibrium point, and an approximation for the amplitude and phase correction of the solution is developed using the method of averaging. This approximation is used to construct an iterative map that describes the pendulum angle and rotational velocity between each instance of platform rocking. Approximate analytical solutions are compared to numerical and experimental results, and ongoing work is discussed.

The motion generated by a slowly rising disk in an unbounded rotating fluid for arbitrary Taylor number

1994 ◽  
Vol 262 ◽  
pp. 1-26 ◽  
Author(s):  
D. Vedensky ◽  
M. Ungarish
Keyword(s):  
Equations Of Motion ◽  
Ekman Layer ◽  
The Body ◽  
Taylor Number ◽  
Present Formulation ◽  
Rotating Fluid ◽  
Asymptotic Results ◽  
Dual Integral Equations ◽  
Axis Of Rotation ◽  
Insight Into

The motion of a disk rising steadily parallel to the axis of rotation in a uniformly rotating unbounded liquid is considered. In the limit of zero Rossby number the linear viscous equations of motion are reduced to a system of dual integral equations which renders an ‘exact’ solution for arbitrary values of the Taylor number, Ta. The investigation is focused on the drag and the flow field. In the limits of small and large Ta the asymptotic results of the present formulation agree with – and extend – previous investigations by different approaches.A particular novel feature, for large Ta, is the contribution of the Ekman-layer flux to the outer motion. New insight into the structure of the Taylor column is gained; in particular, it is shown that the main part of the column is a ‘bubble’ of recirculating fluid, detached from the body and not communicating with the Ekman layer. However, it turns out that the essential discrepancy in drag between experiments (Maxworthy 1970) and previous theories cannot be attributed to the Ekman-layer suction effect.

Rigid-Body Approximations to Turbulent Motion in a Liquid-Filled, Precessing, Spherical Cavity

1972 ◽  
Vol 39 (1) ◽  
pp. 18-24 ◽  
Author(s):  
J. P. Vanyo ◽  
P. W. Likins
Keyword(s):  
Rigid Body ◽  
Viscous Liquid ◽  
Spherical Cavity ◽  
State Energy ◽  
Layer Structure ◽  
Equations Of Motion ◽  
Solid Sphere ◽  
Turbulent Motion ◽  
Rotating Fluid ◽  
Spherical Shells

Rigid-body approximations for turbulent motion in a liquid-filled, spinning and precessing, spherical cavity are presented. The first model assumes the turbulent liquid to spin and precess as a rigid solid sphere coupled to the cavity wall by a thin layer of massless viscous liquid. The second model replaces the layer of massless viscous liquid by a series of n concentric rigid spherical shells. The number and thickness of the shells can be varied so that the interior sphere varies from a negligible diameter to nearly the diameter of the cavity. Although these models do not provide solutions of the fluid equations of motion, they yield steady-state energy dissipation rates that compare favorably with existing experimental data associated with turbulent flow in such a cavity. The models also duplicate several other important features of rotating fluid flow theory. In particular, the motions of the concentric shells exhibit characteristics associated with a classic Ekman layer structure.

scholarly journals NUMERICAL MODELING OF THE PLANETARY BOUNDARY LAYER

2004 ◽  
Vol 3 (1) ◽  
pp. 74
Author(s):  
P. Oliveira ◽  
J. Soares ◽  
H. A. Karam ◽  
M. M. R. Pereira ◽  
E. P. Marques Filho
Keyword(s):  
Boundary Layer ◽  
Planetary Boundary Layer ◽  
Statistical Approach ◽  
Equations Of Motion ◽  
Simulation Models ◽  
The Other ◽  
Atmospheric Conditions ◽  
Equilibrium Conditions ◽  
Closure Models ◽  
Large Eddy

This work describes the major available techniques to simulate the time and space evolution of the planetary boundary layer. For homogeneous and equilibrium conditions the structure of the planetary boundary layer can be diagnosed from the Monin-Obukhov, Free Convection, Local and Mixed Layer Similarity theories. For the other atmospheric conditions the planetary boundary layer can be numerically simulated using first and second order closure models and large eddy models. The closure models take into consideration the traditional statistical approach. Large eddy simulation models are based on the filtered equations of motion and require the statistical approach to estimate subgrid turbulence.

scholarly journals NUMERICAL MODELING OF THE PLANETARY BOUNDARY LAYER

2004 ◽  
Vol 3 (1) ◽  
Author(s):  
P. Oliveira ◽  
J. Soares ◽  
H. A. Karam ◽  
M. M. R. Pereira ◽  
E. P. Marques Filho
Keyword(s):  
Boundary Layer ◽  
Planetary Boundary Layer ◽  
Statistical Approach ◽  
Equations Of Motion ◽  
Simulation Models ◽  
Atmospheric Conditions ◽  
Equilibrium Conditions ◽  
Closure Models ◽  
Eddy Simulation ◽  
Large Eddy

This work describes the major available techniques to simulate the time and space evolution of the planetary boundary layer. For homogeneous and equilibrium conditions the structure of the planetary boundary layer can be diagnosed from the Monin-Obukhov, Free Convection, Local and Mixed Layer Similarity theories. For the other atmospheric conditions the planetary boundary layer can be numerically simulated using first and second order closure models and large eddy models. The closure models take into consideration the traditional statistical approach. Large eddy simulation models are based on the filtered equations of motion and require the statistical approach to estimate subgrid turbulence.

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