Triad resonant instability of horizontally periodic internal modes

2020 ◽  
Vol 5 (3) ◽  
Author(s):  
Bruce R. Sutherland ◽  
Riley Jefferson
Keyword(s):  
Resonant Instability

scholarly journals Resonant Instability of Kink Oscillations in Magnetic Flux Tubes with Siphon Flow

Solar Physics ◽  
2021 ◽  
Vol 296 (6) ◽  
Author(s):  
Michael S. Ruderman ◽  
Nikolai S. Petrukhin
Keyword(s):  
Flow Velocity ◽  
Resonant Absorption ◽  
Tube Axis ◽  
Magnetic Tube ◽  
Transitional Layer ◽  
Threshold Velocity ◽  
Flux Tubes ◽  
Resonant Instability ◽  
Constant Magnitude ◽  
Magnetic Flux Tubes

AbstractWe study kink oscillations of a straight magnetic tube in the presence of siphon flows. The tube consists of a core and a transitional or boundary layer. The flow velocity is parallel to the tube axis, has constant magnitude, and confined in the tube core. The plasma density is constant in the tube core and it monotonically decreases in the transitional layer to its value in the surrounding plasma. We use the expression for the decrement/increment previously obtained by Ruderman and Petrukhin (Astron. Astrophys.631, A31, 2019) to study the damping and resonant instability of kink oscillations. We show that, depending on the magnitude of siphon-velocity, resonant absorption can cause either the damping of kink oscillations or their enhancement. There are two threshold velocities: When the flow velocity is below the first threshold velocity, kink oscillations damp. When the flow velocity is above the second threshold velocity, the kink oscillation amplitudes grow. Finally, when the flow velocity is between the two threshold velocities, the oscillation amplitudes do not change. We apply the theoretical result to kink oscillations of prominence threads. We show that, for particular values of thread parameters, resonant instability can excite these kink oscillations.

Paper 7: Control of Variable-Discharge Pumps and Dangers of Pipeline Resonance

1966 ◽  
Vol 181 (1) ◽  
pp. 144-174
Author(s):  
B. J. Cooper ◽  
D. Hartland ◽  
R. Lawson ◽  
A. M. Stone ◽  
R. D. Tyler
Keyword(s):  
Power Input ◽  
Small Region ◽  
Significant Loss ◽  
Pump Efficiency ◽  
Positive Slope ◽  
Simple Criterion ◽  
Wide Range ◽  
Resonant Instability ◽  
Organ Pipe ◽  
Computer Studies

The discharge and power input of Deriaz mixed-flow pumps and pump turbines can be controlled over a wide range without significant loss in efficiency by movement of the blades. The attainment of the highest pump efficiency involves a small region of positive slope in the head discharge graph. This paper examines the limitations of designing pumps which do not exhibit positive slope and the problems of governing if a positive-slope region is accepted. It is shown that operation in the positive-slope region can introduce a serious organ-pipe resonant instability in the pipeline. A simple criterion to determine whether or not such oscillations will occur is given. This stability criterion involves the dynamic characteristics of both the pump and the pipeline. Finally, computer studies of a particular Deriaz pump installation are presented. These underline the severity of the situation should resonance develop and show how it can be avoided by the use of an air bottle of appropriate design.

Resonant flow instability of space-charge waves in self-gravitating Lorentzian dusty plasma columns

2019 ◽  
Vol 97 (6) ◽  
pp. 651-655
Author(s):  
Myoung-Jae Lee ◽  
Young-Dae Jung
Keyword(s):  
Growth Rate ◽  
Space Charge ◽  
Dusty Plasma ◽  
Plasma Column ◽  
Flow Instability ◽  
Mode Analysis ◽  
Instability Mode ◽  
Resonant Instability ◽  
Charge Wave ◽  
Space Charge Wave

The dispersion characteristics and the resonant instability mode of the space-charge wave are investigated in a streaming Lorentzian dusty plasma column by using the normal mode analysis. The result shows that the non-thermal character of the Lorentzian cylindrical dusty plasma enhances the unstable property of the space-charge wave due to the beam–plasma interaction. It is found that the resonant growth rates of the space-charge wave increase with an increase of the harmonic-order of the root of the Bessel function. It is also found that the influence of the self-gravitation enhances the resonant growth rate of the space-charge wave of the Lorentzian cylindrical dusty plasma. In addition, it is found the resonant growth rate decreases with an increase of the radius of the dusty plasma column. The variation of the resonant instability mode due to the non-thermal character and geometric effects is also discussed.

scholarly journals Triadic resonances in precessing rapidly rotating cylinder flows

2015 ◽  
Vol 778 ◽  
Author(s):  
T. Albrecht ◽  
H. M. Blackburn ◽  
J. M. Lopez ◽  
R. Manasseh ◽  
P. Meunier
Keyword(s):  
Rotating Cylinder ◽  
Direct Numerical Simulations ◽  
Mode Shapes ◽  
Resonance Model ◽  
Rapid Rotation ◽  
Nutation Angle ◽  
Resonant Instability ◽  
Theoretical Predictions ◽  
Long Time ◽  
Good Agreement

Direct numerical simulations of flows in cylinders subjected to both rapid rotation and axial precession are presented and analysed in the context of a stability theory based on the triadic resonance of Kelvin modes. For a case that was chosen to provide a finely tuned resonant instability with a small nutation angle, the simulations are in good agreement with the theory and previous experiments in terms of mode shapes and dynamics, including long-time-scale regularization of the flow and recurrent collapses. Cases not tuned to the most unstable triad, but with the nutation angle still small, are also in quite good agreement with theoretical predictions, showing that the presence of viscosity makes the physics of the triadic-resonance model robust to detuning. Finally, for a case with $45^{\circ }$ nutation angle for which it has been suggested that resonance does not occur, the simulations show that a slowly growing triadic resonance predicted by theory is in fact observed if sufficient evolution time is allowed.

The mean electromotive force generated by elliptic instability

2012 ◽  
Vol 707 ◽  
pp. 111-128 ◽  
Author(s):  
K. A. Mizerski ◽  
K. Bajer ◽  
H. K. Moffatt
Keyword(s):  
Electromotive Force ◽  
Analytical Techniques ◽  
Accretion Discs ◽  
Dynamo Action ◽  
Flow Models ◽  
Euler Flow ◽  
Resonant Instability ◽  
Astrophysical Objects ◽  
The Mean ◽  
Tidal Deformations

AbstractThe mean electromotive force (EMF) associated with exponentially growing perturbations of an Euler flow with elliptic streamlines in a rotating frame of reference is studied. We are motivated by the possibility of dynamo action triggered by tidal deformation of astrophysical objects such as accretion discs, stars or planets. Ellipticity of the flow models such tidal deformations in the simplest way. Using analytical techniques developed by Lebovitz & Zweibel (Astrophys. J., vol. 609, 2004, pp. 301–312) in the limit of small elliptic (tidal) deformations, we find the EMF associated with each resonant instability described by Mizerski & Bajer (J. Fluid Mech., vol. 632, 2009, pp. 401–430), and for arbitrary ellipticity the EMF associated with unstable horizontal modes. Mixed resonance between unstable hydrodynamic and magnetic modes and resonance between unstable and oscillatory horizontal modes both lead to a non-vanishing mean EMF which grows exponentially in time. The essential conclusion is that interactions between unstable eigenmodes with the same wave-vector $\mathbi{k}$ can lead to a non-vanishing mean EMF, without any need for viscous or magnetic dissipation. This applies generally (and not only to the elliptic instabilities considered here).

scholarly journals Near-resonant instability of geostrophic modes: beyond Greenspan's theorem

2020 ◽  
Vol 900 ◽  
Author(s):  
T. Le Reun ◽  
B. Gallet ◽  
B. Favier ◽  
M. Le Bars
Keyword(s):  
Resonant Instability

Abstract

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