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.

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 fluids with shear flow and rotation

1967 ◽  
Vol 30 (3) ◽  
pp. 439-448 ◽  
Author(s):  
Walter L. Jones
Keyword(s):  
Angular Momentum ◽  
Shear Flow ◽  
Gravity Waves ◽  
Shear Flows ◽  
Internal Gravity Waves ◽  
Vertical Transport ◽  
Wave Frequency ◽  
Slow Rotation ◽  
Critical Levels ◽  
Rotating System

In a rotating system, the vertical transport of angular momentum by internal gravity waves is independent of height, except at critical levels where the Doppler-shifted wave frequency is equal to plus or minus the Coriolis frequency. If slow rotation is ignored in studying the propagation of internal gravity waves through shear flows, the resulting solutions are in error only at levels where the Doppler-shifted and Coriolis frequencies are comparable.

Flat liquid metal jet affected by a transverse magnetic field

2021 ◽  
Vol 57 (2) ◽  
pp. 211-222
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Transverse Magnetic Field ◽  
Flow Characteristics ◽  
Transverse Field ◽  
Streamwise Velocity ◽  
Transverse Magnetic ◽  
Mean Flow ◽  
Square Duct ◽  
Oriented Parallel

A liquid metal flat jet immersed in a square duct under the influence of a transverse magnetic field is studied experimentally. Two cases are considered: when the applied magnetic field is oriented parallel (coplanar field) or perpendicularly (transverse field) to the initial plane of the jet. The main goal of the study is to investigate the mean flow characteristics and the stages of the jet's transformation. Signals of streamwise velocity at different locations are measured, which allows us to determine average velocity profiles and spatial-temporal characteristics of the velocity field. The two considered configurations are directly compared under the same flow regimes, with the same equipment. Figs 8, Refs 11.

Momentum transport by gravity waves in a perfectly conducting shear flow

1972 ◽  
Vol 54 (2) ◽  
pp. 217-240 ◽  
Author(s):  
N. Rudraiah ◽  
M. Venkatachalappa
Keyword(s):  
Magnetic Field ◽  
Gravity Waves ◽  
Critical Level ◽  
Critical Levels ◽  
Mean Flow ◽  
Critical Layers ◽  
The Mean ◽  
Pass Through ◽  
The Waves ◽  
Aligned Magnetic Field

Alfvén-gravitational waves propagating in a Boussinesq, inviscid, adiabatic, perfectly conducting fluid in the presence of a uniform aligned magnetic field in which the mean horizontal velocityU(z)depends on heightzonly are considered. The governing wave equation has three singularities, at the Doppler-shifted frequencies Ωd= 0, ± ΩA, where ΩAis the Alfvén frequency. Hence the effect of the Lorentz force is to introduce two more critical levels, called hydromagnetic critical levels, in addition to the hydrodynamic critical level. To study the influence of magnetic field on the attenuation of waves two situations, one concerning waves far away from the critical levels (i.e. Ωd[Gt ] ΩA) and the other waves at moderate distances from the critical levels (i.e. Ωd> ΩA), are investigated. In the former case, if the hydrodynamic Richardson numberJHexceeds one quarter the waves are attenuated by a factor exp{−2π(JH−¼)½} as they pass through the hydromagnetic critical levels, at which Ωd= ± ΩA, and momentum is transferred to the mean flow there. Whereas in the case of waves at moderate distances from the critical levels the ratio of momentum fluxes on either side of the hydromagnetic critical levels differ by a factor exp {−2π(J−¼)½}, whereJ(> ¼) is the algebraic sum of hydrodynamic and hydromagnetic Richardson numbers. Thus the solutions to the hydromagnetic system approach asymptotically those of the hydrodynamic system sufficiently far on either side of the magnetic critical layers, though their behaviour in the vicinity of such levels is quite dissimilar. There is no attenuation and momentum transfer to the mean flow across the hydrodynamic critical level, at which Ωd= 0. The general theory is applied to a particular problem of flow over a sinusoidal corrugation. This is significant in considering the propagation of Alfvén-gravity waves, in the presence of a geomagnetic field, from troposphere to ionosphere.

Effects of shear flow and transverse magnetic field on Richtmyer–Meshkov instability

2008 ◽  
Vol 15 (4) ◽  
pp. 042102 ◽  
Author(s):  
Jintao Cao ◽  
Zhengwei Wu ◽  
Haijun Ren ◽  
Ding Li
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic

Natural convection in horizontal pipe flow with a strong transverse magnetic field

2013 ◽  
Vol 720 ◽  
pp. 486-516 ◽  
Author(s):  
Oleg Zikanov ◽  
Yaroslav I. Listratov ◽  
Valentin G. Sviridov
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Transverse Magnetic Field ◽  
Metal Flow ◽  
Low Frequency ◽  
High Amplitude ◽  
Transverse Magnetic ◽  
Mean Flow ◽  
Horizontal Pipe ◽  
The Magnetic Field

AbstractLinear stability analysis and direct numerical simulations are conducted to analyse mixed convection in a liquid metal flow in a horizontal pipe with imposed transverse magnetic field. The pipe walls are electrically insulated and subject to constant flux heating in the lower half. The results reveal the nature of anomalous temperature fluctuations detected in earlier experiments. It is found that, at the magnetic field strength far exceeding the laminarization threshold, the natural convection develops in the form of coherent quasi-two-dimensional rolls aligned with the magnetic field. Transport of the rolls by the mean flow causes high-amplitude, low-frequency fluctuations of temperature.

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