Propagation of Alfvén-gravitational waves in a stratified perfectly conducting flow with transverse magnetic field

1972 ◽  
Vol 54 (2) ◽  
pp. 209-215 ◽  
Author(s):  
N. Rudraiah ◽  
M. Venkatachalappa
Keyword(s):  
Magnetic Field ◽  
Gravitational Waves ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic ◽  
Constant Coefficients ◽  
Downward Propagation ◽  
The Mean ◽  
Propagation Of Waves ◽  
The Waves ◽  
Vertical Height

Alfvén-gravitational waves are found to propagate in a Boussinesq, inviscid, adiabatic, perfectly conducting fluid in the presence of a uniform transverse magnetic field in which the mean horizontal velocity U is independent of vertical height z. The governing wave equation is a fourth-order ordinary differential equation with constant coefficients and is not singular when the Doppler-shifted frequency Ωd = 0, but is singular when the Alfvén frequency ΩA = 0.If Ω2d < Ω2A the waves are attenuated by a factor exp − [2ΩA(N2−Ω2d)½−Ω2d + Ω2A]z, which tends to zero as z → ∞. This attenuation is similar to the viscous attenuation of waves discussed by Hughes & Young (1966). The interpretation of upward and downward propagation of waves is given.

Propagation of internal gravity waves in perfectly conducting fluids with shear flow, rotation and transverse magnetic field

1972 ◽  
Vol 52 (1) ◽  
pp. 193-206 ◽  
Author(s):  
N. Rudraiah ◽  
M. Venkatachalappa
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Shear Flow ◽  
Gravitational Waves ◽  
Transverse Magnetic Field ◽  
Internal Gravity Waves ◽  
Transverse Magnetic ◽  
Critical Levels ◽  
Mean Flow ◽  
The Waves

The propagation of internal Alfvén-inertio-gravitational waves in a Boussinesq inviscid adiabatic perfectly conducting shear flow with rotation is investigated in the presence of a transverse magnetic field. It is shown that the effect of the rotational nature of electromagnetic force and Coriolis force is that linear momentum is not conserved anywhere in the fluid even at critical levels, whereas the angular momentum flux is conserved everywhere in the fluid except at the critical levels at which the Doppler-shifted frequency Ωd = 0, + ΩA or ± Ω ± (Ω2 + Ω2A)½, where ΩA is the Alfvén frequency and Ω is the Coriolis frequency, and the angular momentum is transferred to the mean flow there by Alfvén-inertio-gravitational waves. Asymptotic solutions to the wave equation are obtained near the critical levels and it is shown that the effect of the Lorentz force on the waves at the critical levels is to increase the process of critical layer absorption. The condition for neglection of rotation for higher frequency waves is also obtained and is found to be the same in both hydrodynamic and hydro-magnetic flows.

Effect of ohmic dissipation on internal Alfvén-gravity waves in a conducting shear flow

1974 ◽  
Vol 62 (4) ◽  
pp. 705-726 ◽  
Author(s):  
N. Rudraiah ◽  
M. Venkatachalappa
Keyword(s):  
Magnetic Field ◽  
Wave Equation ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Critical Level ◽  
Transverse Magnetic ◽  
Asymptotic Solutions ◽  
Ohmic Dissipation ◽  
Propagation Of Waves ◽  
The Waves

Internal Alfvén-gravity waves of small amplitude propagating in a Boussinesq, inviscid, adiabatic, finitely conducting fluid in the presence of a uniform transverse magnetic field in which the mean horizontal velocityU(z) depends on heightzonly are considered. We find that the governing wave equation is singular only at the Doppler-shifted frequency Ωd= 0 and not at the magnetic singularities Ωd= ± ΩA, where ΩAis the Alfvén frequency. Hence the effect of ohmic dissipation is to prevent the resulting wave equation from having magnetic singularities. Asymptotic solutions of the wave equation, which is a fourth-order differential equation, are obtained. They show the presence of the magnetic Stokes points Ωd= ± ΩA. The interpretation of upward and downward propagation of waves is also discussed.To study the combined effect of electrical conductivity and the magnetic field on waves at the critical level, we have used the group-velocity approach and found that the waves are transmitted across the magnetic Stokes points but are completely absorbed at the hydrodynamic critical level Ωd= 0. The general expression for the momentum flux is mathematically complicated but will be simplified under the assumption\[ \frac{\partial^2h}{\partial x^2}+\frac{\partial^2h}{\partial y^2}\gg \frac{\partial^2h}{\partial z^2}, \]wherehis the perturbation magnetic field. In this approximation we find that the momentum flux is not conserved and the waves are completely absorbed at Ωd= 0.The general theory is applied to a particular problem of flow over a sinusoidal corrugation and asymptotic solutions are obtained by applying the Laplace transformation and using the method of steepest descent.

Dispersion of soluble matter in the hydromagnetic laminar flow between two parallel plates

1968 ◽  
Vol 64 (4) ◽  
pp. 1209-1214 ◽  
Author(s):  
A. S. Gupta ◽  
A. S. Chatterjee
Keyword(s):  
Magnetic Field ◽  
Diffusion Coefficient ◽  
Laminar Flow ◽  
Analytical Solution ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic ◽  
Parallel Plates ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
The Mean

AbstractThe paper presents an analytical solution for the dispersion of a solute in an electrically conducting fluid flowing between two parallel plates in the presence of a transverse magnetic field. It is shown that the solute is dispersed relative to a plane moving with the mean speed of the flow with an effective Taylor diffusion coefficient which decreases with increase in magnetic field.

scholarly journals On nonlinear Alfvén-cyclotron waves in multi-species plasma

2010 ◽  
Vol 77 (3) ◽  
pp. 385-403 ◽  
Author(s):  
ECKART MARSCH ◽  
DANIEL VERSCHAREN
Keyword(s):  
Magnetic Field ◽  
Kinetic Energy ◽  
Electric Field ◽  
Transverse Magnetic Field ◽  
Acoustic Waves ◽  
Mean Field ◽  
Transverse Magnetic ◽  
Longitudinal Electric Field ◽  
Mhd Turbulence ◽  
The Mean

AbstractLarge-amplitude Alfvén waves are ubiquitous in space plasmas and a main component of magnetohydrodynamic (MHD) turbulence in the heliosphere. As pump waves, they are prone to parametric instability by which they can generate cyclotron and acoustic daughter waves. Here, we revisit a related process within the framework of the multi-fluid equations for a plasma consisting of many species. The nonlinear coupling of the Alfvén wave to acoustic waves is studied, and a set of compressive and coupled-wave equations for the transverse magnetic field and longitudinal electric field is derived for waves propagating along the mean-field direction. It turns out that slightly compressive Alfvén waves exert, through induced gyro-radius and kinetic-energy modulations, an electromotive force on the particles in association with a longitudinal electric field, which has a potential that is given by the gradient of the transverse kinetic energy of the particles gyrating about the mean field. This in turn drives electric fluctuations (sound and ion-acoustic waves) along the mean magnetic field, which can nonlinearly react back on the transverse magnetic field. Mutually coupled Alfvén-cyclotron--acoustic waves are thus excited, a nonlinear process that can drive a cascade of wave energy in the plasma, and may generate compressive microturbulence. These driven electric fluctuations might have consequences for the dissipation of an MHD turbulence and, thus, for the heating and acceleration of particles in the solar wind.

Numerical study of the effect of transverse magnetic field on cylindrical and hemispherical CZ crystal growth of silicon

2010 ◽  
Vol 46 (4) ◽  
pp. 393-402 ◽  
Author(s):  
F. Mokhtari ◽  
A. Bouabdallah ◽  
A. Merah ◽  
S. Hanchi ◽  
A. Alemany
Keyword(s):  
Magnetic Field ◽  
Crystal Growth ◽  
Transverse Magnetic Field ◽  
Numerical Study ◽  
Transverse Magnetic

Heat Transfer in Liquid Metal at an Upward Flow in a Pipe in Transverse Magnetic Field

2020 ◽  
Vol 58 (3) ◽  
pp. 400-409
Author(s):  
N. A. Luchinkin ◽  
N. G. Razuvanov ◽  
I. A. Belyaev ◽  
V. G. Sviridov
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Liquid Metal ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic ◽  
Upward Flow
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