The Stability of a Warped Accretion Disc

1991 ◽  
Vol 9 (2) ◽  
pp. 249-250
Author(s):  
Colin S. Coleman ◽  
Sanjiv Kumar
Keyword(s):  
Binary Star ◽  
Compact Object ◽  
Shear Velocity ◽  
Major Effect ◽  
Accretion Disc ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Quadrupole Field ◽  
Surface Boundary Conditions ◽  
The Stability

AbstractAn accretion disc becomes warped when subjected to a torque which is misaligned with the disc plane. Such torques may be caused by Lense-Thirring precession near a spinning compact object, or the quadrupole field of a binary star. Here the flow in an adiabatic warped disc is modelled as a two-dimensional shear layer with linear velocity profile and free surface boundary conditions, and is investigated by means of a linear stability analysis.The flow is found to be unstable whenever it contains a critical layer, i.e., a level at which the shear velocity is equal to the phase velocity. The instability occurs over a broad wavenumber range and has a typical dimensionless growth rate ≈ 0.1 for both the compressible and incompressible cases. These waves grow with a time-scale of about one orbital period, and are likely to have a major effect on the disc viscosity.

Comparison of Two Base-Potentials for a Slender-Body Method

2012 ◽  
Author(s):  
Mahmoud Alidadi ◽  
Sander Calisal
Keyword(s):  
Three Dimensional ◽  
Slender Body ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Wave Elevation ◽  
Surface Boundary Conditions ◽  
Perturbation Potential ◽  
Order Of Magnitude ◽  
Body Method

The effects of two base-potentials on the accuracy of a slender-body method are studied in this paper. In the formulation for this method which is developed for the slender ships, the velocity potential is decomposed into a base-potential and a perturbation potential. Then using an order of magnitude analysis, the three-dimensional flow problem is simplified into a series of two-dimensional problems for the perturbation potential. These two-dimensional problems are solved with the linearized free surface boundary conditions, using a mixed Eulerian-Lagrangian method. Finally for the two base-potentials, the numerical wave elevation along a Wigleyull are compared with the experimental results.

Time-Domain Simulations of Radiation and Diffraction Forces

2010 ◽  
Vol 54 (02) ◽  
pp. 79-94 ◽  
Author(s):  
Xinshu Zhang ◽  
Piotr Bandyk ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Three Dimensional ◽  
The Body ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Strip Theory

Large-amplitude, time-domain, wave-body interactions are studied in this paper for problems with forward speed. Both two-dimensional strip theory and three-dimensional computation methods are shown and compared by a number of numerical simulations. In the present approach, an exact body boundary condition and linearized free surface boundary conditions are used. By distributing desingularized sources above the calm water surface and using constant-strength flat panels on the exact body surface, the boundary integral equations are solved numerically at each time step. The strip theory method implements Radial Basis Functions to approximate the longitudinal derivatives of the velocity potential on the body. Once the fluid velocities on the free surface are computed, the free surface elevation and potential are updated by integrating the free surface boundary conditions. After each time step, the body surface and free surface are regrided due to the instantaneous changing wetted body geometry. Extensive results are presented to validate the efficiency of the present methods. These results include the added mass and damping computations for a Wigley III hull and an S-175 hull with forward speed using both two-dimensional and three-dimensional approaches. Exciting forces acting on a Wigley III hull due to regular head seas are obtained and compared using both the fully three-dimensional method and the two-dimensional strip theory. All the computational results are compared with experiments or other numerical solutions.

A numerical nonlinear analysis of two-dimensional ventilating entry of surface-piercing hydrofoils with effects of gravity

2010 ◽  
Vol 658 ◽  
pp. 383-408 ◽  
Author(s):  
VIMAL VINAYAN ◽  
SPYROS A. KINNAS
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Numerical Scheme ◽  
Suction Side ◽  
Nonlinear Boundary Conditions ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Surface Boundary Conditions ◽  
Dimensional Boundary ◽  
Nonlinear Free Surface

The presence of the free surface adds an element of difficulty to the development of numerical and theoretical methods for the performance prediction of surface-piercing hydrofoils. Existing methods of analysis for two-dimensional surface-piercing hydrofoils or blade sections of a surface-piercing propeller solve either a linear problem, assuming a thin section and ventilated surface along with linear free-surface boundary conditions, or a nonlinear problem in a self-similar setting. Both these approaches cannot be used when the effects of gravity are important, which is the case when a craft is operating at low speeds. A two-dimensional boundary-element-method-based numerical scheme is presented here that overcomes these drawbacks by solving the fully ventilated flow past a surface-piercing hydrofoil of finite dimensions and includes the whole gamut of nonlinear free-surface interactions. The unique aspect of the numerical scheme is that fully nonlinear boundary conditions are applied on the free surface which allows for the accurate modelling of the jet generated on the wetted boundary and the ventilated surface formed on the suction side as a result of the passage of the hydrofoil through the free surface. Moreover, the effects of gravity can be considered to take into account the influence of the Froude number. Ventilated-surface shapes predicted by the present scheme are compared with existing experimental results and are shown to be in good agreement.

Waveboard Artifacts Generate Ghost Resonances Consistent with Equations for Predicting Ion Motion in Commercial Quadrupole Ion Traps

2005 ◽  
Vol 11 (1) ◽  
pp. 15-21 ◽  
Author(s):  
Kwenga F. Sichilongo ◽  
Bert C. Lynn
Keyword(s):  
Ion Trap ◽  
Ion Traps ◽  
Quadrupole Ion Trap ◽  
Stability Diagram ◽  
Two Dimensional ◽  
Quadrupole Field ◽  
Non Linear ◽  
Contour Plots ◽  
The Stability ◽  
Contour Surface

Real-time experiments involving fragmentation of the precursor molecular ion of n-butylbenzene ( m/z 134) to produce product ions C7H+7 ( m/z 91) and C7H+8 ( m/z 92), were used to observe the motion of ions in a commercial quadrupole ion trap. Initially, ghost resonance peaks were observed for excitation of the precursor ion at qz values of 0.4 and 0.5 on the qz axis of the stability diagram. Further experiments involving the generation of two-dimensional contour plots confirmed that these ghost peaks, which were in agreement with mathematical equations describing the motion of ions in a quadrupole field, arose due to waveboard artifacts. Two-dimensional contour surface plots showed non-linear secular frequency canyons from a qz value of 0.5 to higher values corresponding with higher drive radio frequency (rf) voltages on the stability diagram. This observation confirmed that ions are subjected to non-linear effects in this mass scan range. The octapole and hexapole field lines were observed at qz values of 0.65 and 0.78, respectively.

Thermal convection with large viscosity variations

1971 ◽  
Vol 47 (1) ◽  
pp. 113-125 ◽  
Author(s):  
K. E. Torrance ◽  
D. L. Turcotte
Keyword(s):  
Free Surface ◽  
Prandtl Number ◽  
Temperature Fields ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Temperature Dependent ◽  
Earth’S Mantle ◽  
Surface Boundary Conditions ◽  
Dependent Viscosity ◽  
Horizontal Wavelength

The influence of large variations of viscosity on convection in a layer of fluid heated from below has been investigated. Solutions for the flow and temperature fields were obtained numerically assuming infinite Prandtl number, free-surface boundary conditions, and two-dimensional motion of fixed horizontal wavelength. The effects of a temperature-dependent and a depth-dependent viscosity were each studied; calculations were also carried out using a temperature- and depth-dependent viscosity model appropriate to the earth's mantle.

Studies in the Stability of a Numerical Wave Tank Model for Generation and Propagation of Steep Nonlinear Long-Crested Surface Waves

2005 ◽  
Author(s):  
W. Parsons ◽  
R. E. Baddour
Keyword(s):  
Free Surface ◽  
Continuity Condition ◽  
Surface Boundary ◽  
Homogeneous Fluid ◽  
Surface Boundary Conditions ◽  
Curvilinear Coordinate ◽  
Underlying Causes ◽  
Steep Waves ◽  
The Stability ◽  
Numerical Beach

We are studying numerically the problem of generation and propagation of gravity long-crested waves in a tank containing an incompressible inviscid homogeneous fluid initially at rest with a horizontal free surface of finite extent and of infinite depth. A non-orthogonal curvilinear coordinate system, which follows the free surface is constructed which gives a realistic “continuity condition”, since it tracks the entire fluid domain at all times. A depth profile of the potential is assumed, and employed to perform a waveform relaxation algorithm to decouple the discrete Laplacian along dimensional lines, thereby reducing it’s computation over this total fluid domain. In addition, the full nonlinear kinematic and dynamic free surface boundary conditions are utilized in the algorithm, and a suitably tuned numerical beach is used to avoid reflections. It is well known that instability, in the form of generated spurious “sawtooth waves”, plagues this problem, leading to numerical overflow. This makes it very difficult to generate steep waves for sufficiently long simulation times. The authors have struggled with this problem for some time, with significant success, by employing an “aliasing filter”. This paper outlines our ongoing study of the stability of the model, including an analysis of the possible nature of the underlying causes including compatibility conditions. We conclude by giving a simple practical technique for greatly improving the stability.

A Model for the Simulation of Steady Spilling Breaking Waves

2003 ◽  
Vol 47 (01) ◽  
pp. 13-23
Author(s):  
R. Muscari ◽  
A. Di Mascio
Keyword(s):  
Stokes Equations ◽  
Turbulent Viscosity ◽  
Breaking Waves ◽  
Original Model ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Stable Algorithm ◽  
Surface Boundary Conditions

A numerical model for the simulation of two-dimensional spilling breaking waves is described. The model is derived from Cointe and Tulin's theory of steady breakers (Cointe & Tulin 1994), although some important changes have been introduced in order to obtain a stable algorithm when coupled with steady-state Reynolds averaged Navier-Stokes equations (RANSE) solvers. In particular, the shape of the breaker and its relation with the following wave height differ from the original model, and moreover, additional conditions for the tangential stress and the turbulent viscosity are proposed. The model has been implemented in a RANSE code, developed for the study of ship flows, through a modification in the free-surface boundary conditions below the breaker. This yields a simple but effective way to reproduce the breaker influence on the underlying flow. The algorithm was used for the simulation of the flow past a submerged hydrofoil. The numerical results are compared with the experimental data by Duncan (1983).

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