scholarly journals Air-Aided Shear on a Thin Film Subjected to a Transverse Magnetic Field of Constant Strength: Stability and Dynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-24 ◽  
Author(s):  
Mohammed Rizwan Sadiq Iqbal
Keyword(s):  
Magnetic Field ◽  
Inertial Force ◽  
Transverse Magnetic ◽  
Nonlinear Analyses ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Constant Strength ◽  
Long Time ◽  
The Stability ◽  
The One

The effect of air shear on the hydromagnetic instability is studied through (i) linear stability, (ii) weakly nonlinear theory, (iii) sideband stability of the filtered wave, and (iv) numerical integration of the nonlinear equation. Additionally, a discussion on the equilibria of a truncated bimodal dynamical system is performed. While the linear and weakly nonlinear analyses demonstrate the stabilizing (destabilizing) tendency of the uphill (downhill) shear, the numerics confirm the stability predictions. They show that (a) the downhill shear destabilizes the flow, (b) the time taken for the amplitudes corresponding to the uphill shear to be dominated by the one corresponding to the zero shear increases with magnetic fields strength, and (c) among the uphill shear-induced flows, it takes a long time for the wave amplitude corresponding to small shear values to become smaller than the one corresponding to large shear values when the magnetic field intensity increases. Simulations show that the streamwise and transverse velocities increase when the downhill shear acts in favor of inertial force to destabilize the flow mechanism. However, the uphill shear acts oppositely. It supports the hydrostatic pressure and magnetic field in enhancing films stability. Consequently, reduced constant flow rates and uniform velocities are observed.

Research on novel spatial structure of power generation of spherical robot

2020 ◽  
Vol 234 (6) ◽  
pp. 600-612
Author(s):  
Yuyi Zhai ◽  
Zihang Ding ◽  
Yunjia Liu ◽  
Shaohua Jin ◽  
Liang Kang
Keyword(s):  
Power Generation ◽  
Space Structure ◽  
Induced Voltage ◽  
Spherical Robot ◽  
Energy Harvesters ◽  
Long Time ◽  
The Stability ◽  
The One ◽  
Spherical Mobile Robot ◽  
Pipeline Model

Continuous energy supply is essential to spherical mobile robot in the Antarctic investigation. This paper puts forward energy harvesters that can generate electricity from the wind to achieve the long time and the long range exploration. The major contribution is to present the preliminary models of the energy harvester which uses the law of electromagnetic induction, and meanwhile the spatial structures about generating electricity are analyzed, and the influence of different structures on the power generation and efficiency will be obtained. In order to get the characteristics of power generation efficiency, this paper designs one element pipeline model and two element pipeline model, and then the motion of magnet in harvester will be simulated in different installed structures and wind speed. The varying rules of induced voltage are concluded at last. Finally, experiments are implemented based on the simulated model. The experimental results verify the dependability of different structural schemes of the robot and the validity of induced voltages’ varying rules. The results show that the induced electromotive force value obtained by the one element pipeline structure model is larger than the two element pipeline model, but the stability of the latter is better. Through the research in this paper, it can provide a basis for selecting a suitable spherical robot space structure according to the environmental conditions to improve the endurance.

Long-time behaviour of a random inhomogeneous field of weakly nonlinear surface gravity waves

1983 ◽  
Vol 133 ◽  
pp. 113-132 ◽  
Author(s):  
Peter A. E. M. Janssen
Keyword(s):  
Wave Spectrum ◽  
Inhomogeneous Field ◽  
Time Behaviour ◽  
Phase Mixing ◽  
Weakly Nonlinear ◽  
Large Bandwidth ◽  
Long Time Behaviour ◽  
Homogeneous Wave ◽  
Long Time ◽  
The Stability

In this paper we investigate nonlinear interactions of narrowband, Gaussian-random, inhomogeneous wavetrains. Alber studied the stability of a homogeneous wave spectrum as a function of the width σ of the spectrum. For vanishing bandwidth the deterministic results of Benjamin & Feir on the instability of a uniform wavetrain were rediscovered whereas a homogeneous wave spectrum was found to be stable if the bandwidth is sufficiently large. Clearly, a threshold for instability is present, and in this paper we intend to study the long-time behaviour of a slightly unstable modulation by means of a multiple-timescale technique. Two interesting cases are found. For small but finite bandwidth – the amplitude of the unstable modulation shows initially an overshoot, followed by an oscillation around the time-asymptotic value of the amplitude. This oscillation damps owing to phase mixing except for vanishing bandwidth because then the well-known Fermi–Pasta–Ulam recurrence is found. For large bandwidth, however, no overshoot is found since the damping is overwhelming. In both cases the instability is quenched because of a broadening of the spectrum.

The onset of meandering in a barotropic jet

2001 ◽  
Vol 449 ◽  
pp. 85-114 ◽  
Author(s):  
N. J. BALMFORTH ◽  
C. PICCOLO
Keyword(s):  
Nonlinear Theory ◽  
Stability Boundary ◽  
Wave Model ◽  
Inviscid Limit ◽  
Reduced Model ◽  
Mean Flow ◽  
Single Wave ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
The Stability

This study explores the dynamics of an unstable jet of two-dimensional, incompressible fluid on the beta-plane. In the inviscid limit, standard weakly nonlinear theory fails to give a low-order description of this problem, partly because the simple shape of the unstable normal mode is insufficient to capture the structure of the forming pattern. That pattern takes the form of ‘cat's eyes’ in the vorticity distribution which develop inside the modal critical layers (slender regions to either side of the jet's axis surrounding the levels where the modal wave speed matches the mean flow). Asymptotic expansions furnish a reduced model which is a version of what is known as the single-wave model in plasma physics. The reduced model predicts that the amplitude of the unstable mode saturates at a relatively low level and is not steady. Rather, the amplitude evolves aperiodically about the saturation level, a result with implications for Lagrangian transport theories. The aperiodic amplitude ‘bounces’ are intimately connected with sporadic deformations of the vortices within the cat's eyes. The theory is compared with numerical simulations of the original governing equations. Slightly asymmetrical jets are also studied. In this case the neutral modes along the stability boundary become singular; an extension of the weakly nonlinear theory is presented for these modes.

Three-dimensional Rayleigh-Taylor instability Part 1. Weakly nonlinear theory

1988 ◽  
Vol 187 ◽  
pp. 329-352 ◽  
Author(s):  
J. W. Jacobs ◽  
I. Catton
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Taylor Instability ◽  
Initial Surface ◽  
Surface Slope ◽  
Cross Sectional ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Rayleigh Taylor Instability ◽  
The Stability

Three-dimensional weakly nonlinear Rayleigh-Taylor instability is analysed. The stability of a confined inviscid liquid and an overlying gas with density much less than that of the liquid is considered. An asymptotic solution for containers of arbitrary cross-sectional geometry, valid up to order ε3 (where ε is the root-mean-squared initial surface slope) is obtained. The solution is evaluated for the rectangular and circular geometries and for various initial modes (square, hexagonal, axisymmetric, etc.). It is found that the hexagonal and axisymmetric instabilities grow faster than any other shapes in their respective geometries. In addition it is found that, sufficiently below the cutoff wavenumber, instabilities that are equally proportioned in the lateral directions grow faster than those with longer, thinner shape. However, near the cutoff wavenumber this trend reverses with instabilities having zero aspect ratio growing faster than those with aspect ratio near 1.

The effects of boundary imperfections on convection in a saturated porous layer: near-resonant wavelength excitation

1989 ◽  
Vol 199 ◽  
pp. 133-154 ◽  
Author(s):  
D. A. S. Rees ◽  
D. S. Riley
Keyword(s):  
Porous Layer ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Resonant Forcing ◽  
Saturated Porous Layer ◽  
The Stability ◽  
Spatially Varying ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Complementary Study

Weakly nonlinear theory is used to study the porous-medium analogue of the classical Rayleigh-Bénard problem, i.e. Lapwood convection in a saturated porous layer heated from below. Two particular aspects of the problem are focused upon: (i) the effect of thermal imperfections on the stability characteristics of steady rolls near onset; and (ii) the evolution of unstable rolls.For Rayleigh-Bénard convection it is well known (see Busse and co-workers 1974, 1979, 1986) that the stability of steady two-dimensional rolls near onset is limited by the presence of cross-roll, zigzag and sideband disturbances; this is shown to be true also in Lapwood convection. We further determine the modifications to the stability boundaries when small-amplitude imperfections in the boundary temperatures are present. In practice imperfections would usually consist of broadband thermal noise, but it is the Fourier component with wavenumber close to the critical wavenumber for the perfect problem (i.e. in the absence of imperfections) which, when present, has the greatest effect due to resonant forcing. This particular case is the sole concern of the present paper; other resonances are considered in a complementary study (Rees & Riley 1989).For the case when the modulations on the upper and lower boundaries are in phase, asymptotic analysis and a spectral method are used to determine the stability of roll solutions and to calculate the evolution of the unstable flows. It is shown that steady rolls with spatially deformed axes or spatially varying wavenumbers evolve. The evolution of the flow that is unstable to sideband disturbances is also calculated when the modulations are π out of phase. Again rolls with a spatially varying wavenumber result.

Weakly nonlinear theory of fast steady-state magnetic reconnection

1988 ◽  
Vol 40 (1) ◽  
pp. 143-161 ◽  
Author(s):  
M. Jardine ◽  
E. R. Priest
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Boundary Conditions ◽  
Free Parameter ◽  
Diffusion Region ◽  
Slow Mode ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Special Cases ◽  
Field Lines

A family of models for fast steady-state reconnection has recently been presented by Priest and Forbes, of which the Petschek-like and Sonnerup-like solutions are special cases. This essentially linear treatment involves expanding about a uniform flow and field in powers of the external Alfvén Mach number Me, and hence is valid for small values of that parameter. To lowest order, the discrete slow-mode compressions attached to the diffusion region are straight, while downstream of them the plasma flows at simply the external Alfvén speed vAe and the field lines are straight. Here we present an extension of these solutions to the next order, which not only reveals that the wave itself is curved (as are the downstream magnetic field lines), but also that the downstream solution is sensitive to changes in the upstream boundary conditions. In the downstream solution there is a free parameter, which may be specified as a downstream boundary condition. Thus the boundary conditions at both the inflow and the outflow boundaries are crucial in determining the nature of the reconnection.

MHD Stability of Streaming Jet Using Artificial Intelligence Technique

2012 ◽  
Vol 28 (3) ◽  
pp. 453-459
Author(s):  
Mostafa A. M. Abdeen ◽  
Alfaisal A. Hasan
Keyword(s):  
Magnetic Field ◽  
Artificial Intelligence ◽  
Mathematical Formulation ◽  
Transverse Magnetic ◽  
Field Variation ◽  
Ann Model ◽  
Eigen Value ◽  
Mhd Stability ◽  
Artificial Neural Network Ann ◽  
The Stability

AbstractMathematical formulation for Magnetohydrodynamic (MHD) stability of a streaming cylindrical model penetrated by varying transverse magnetic field is presented. Eigen value relation is derived and discussed analytically. In the current paper, Artificial Neural Network (ANN) model, one of the artificial intelligence techniques, is developed to simulate the stability of streaming jet penetrated by magnetic field. The ANN results presented in the current study showed that ANN technique, with less effort and time, is very efficiently capable of simulating and predicting the effect of magnetic field variation and axial exterior field on the stability of the streaming jet. The influence of magnetic field has a stabilizing effect for all short and long wavelengths. However the streaming is strongly destabilizing.

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