Propagation of internal Alfvén—acoustic—gravity waves in a perfectly conducting isothermal compressible fluid

1976 ◽  
Vol 73 (1) ◽  
pp. 125-137 ◽  
Author(s):  
N. Rudraiah ◽  
M. Venkatachalappa ◽  
P. Kandaswamy
Keyword(s):  
Magnetic Field ◽  
Gravity Waves ◽  
Velocity Shear ◽  
Conducting Plane ◽  
Acoustic Gravity Waves ◽  
Electrically Conducting ◽  
Ray Trajectories ◽  
Compressible Atmosphere ◽  
Wave Normal ◽  
The Waves

Internal Alfvén-acoustic-gravity waves propagating in an isothermal, perfectly electrically conducting, plane stratified, inviscid, compressible atmosphere permeated by a horizontal stratified magnetic field in which the mean horizontal velocity U(z) depends on the height z only exhibit singular properties at the Doppler-shifted frequencies \[ \Omega_{d} = 0,\quad\pm\Omega_A,\quad\pm\Omega_A/(1+M^2)^{\frac{1}{2}},\quad\pm (\Omega_c/2^{\frac{1}{2}})[1+M^2\pm \{(1+M^2)^2 - 4\Omega^2_A/\Omega^2_c\}^{\frac{1}{2}}]^{\frac{1}{2}} \] where ΩA is the Alfvén frequency, Ωc the sonic frequency and M the magnetic Mach number. The phenomenon of critical-layer absorption is studied using the momentum-transport approach of Booker & Bretherton (1967), the wave-packet approach (which is a consequence of the WKBJ approximation) of Bretherton (1966) and the technique involving wave normal curves of McKenzie (1973). The absorption effects are also illustrated, following Acheson (1972), by drawing ray trajectories. We find that the waves are absorbed at the critical levels Ωd = ± ΩA and ± ΩA/(1 + M2)½, and in particular we observe that these levels do not act like valves as observed by Acheson (1972). We also conclude that the combined effect of velocity shear and density and magnetic-field stratification is to increase the number of absorption levels.

Propagation of hydromagnetic waves in a perfectly conducting non-isothermal atmosphere in the presence of rotation and a variable magnetic field

1978 ◽  
Vol 89 (4) ◽  
pp. 785-792 ◽  
Author(s):  
N. Rudraiah ◽  
M. Venkatachalappa
Keyword(s):  
Magnetic Field ◽  
Variable Magnetic Field ◽  
Acoustic Gravity Waves ◽  
Electrically Conducting ◽  
Plane Normal ◽  
Valve Effect ◽  
Hydromagnetic Waves ◽  
The Waves ◽  
Isothermal Atmosphere ◽  
The Magnetic Field

The propagation of internal Alfvén-inertio-acoustic gravity waves in a perfectly electrically conducting, stratified, inviscid, non-isothermal, rotating atmosphere permeated by a non-uniform magnetic field is investigated. These waves exhibit singular properties at the critical levels at which the magnetic field and the sound velocity are such that \[ (\omega^2 - S^2)\{(c^2+V^2)\omega^2-c^2S^2\}-(c^2+V^2)\overline{R}^2=0, \] where ω is the frequency of the waves, $S = kV_x + lV_y,\overline{R} = 2\Omega_z\omega$, Vx and Vy are the x and y components of the Alfvén velocity, k and l are the corresponding wavenumbers and c is the sonic velocity. These levels act like valves which permit waves to penetrate them from one side only and absorb them when they propagate from the other side. In contrast to the incompressible results of Acheson (1972), we show that the valve effect in compressible flow no longer requires the presence of non-zero components of rotation in the plane normal to the direction in which the medium varies. We find that the compressibility increases the probability of a valve effect and so increases the capacity of a hydromagnetic wave to propagate across a field line, rather than being absorbed at some critical level.

scholarly journals Identification of linear slow sausage waves in magnetic pores

2007 ◽  
Vol 3 (S247) ◽  
pp. 351-354 ◽  
Author(s):  
I. Dorotovič ◽  
R. Erdélyi ◽  
V. Karlovský
Keyword(s):  
Magnetic Field ◽  
Gravity Waves ◽  
Morphological Changes ◽  
Average Rate ◽  
Linear Trend ◽  
Solar Interior ◽  
Small Scale ◽  
Temporal Area ◽  
Acoustic Gravity Waves ◽  
The Magnetic Field

AbstractThe analysis of an 11-hour series of high resolution white light observations of a large pore in the sunspot group NOAA 7519, observed on 5 June 1993 with the Swedish Vacuum Solar Telescope at La Palma on Canary Islands, has been recently described by Dorotovičet al. (2002). Special attention was paid to the evolution of a filamentary region attached to the pore, to horizontal motions around the pore, and to small-scale morphological changes. One of the results, relevant to out work here, was the determination of temporal area evolution of the studied pore where the area itself showed a linear trend of decrease with time at an average rate of −0.23 Mm2h−1during the entire observing period. Analysing the time series of the are of the pore, there is strong evidence that coupling between the solar interior and magnetic atmosphere can occur at various scales and that the referred decrease of the area may be connected with a decrease of the magnetic field strength according to the magnetic field-to-size relation. Periods of global acoustic, e.g.p-mode, driven waves are usually in the range of 5–10 minutes, and are favourite candidates for the coupling of interior oscillations with atmospheric dynamics. However, by assuming that magneto-acoustic gravity waves may be there too, and may act as drivers, the observed periodicities (frequencies) are expected to be much longer (smaller), falling well within the mMHz domain. In this work we determine typical periods of such range in the area evolution of the pore using wavelet analysis. The resulted periods are in the range of 20–70 minutes, suggesting that periodic elements of the temporal evolution of the area of this studied pore could be linked to, and considered as, observational evidence of linear low-frequency slow sausage (magneto-acoustic gravity) waves in magnetic pores. This would give us further evidence on the coupling of global solar oscillations to the overlaying magnetic atmosphere.

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.

Observational aspects of sunspot oscillations

2005 ◽  
Vol 364 (1839) ◽  
pp. 313-331 ◽  
Author(s):  
T.J Bogdan ◽  
P.G Judge
Keyword(s):  
Magnetic Field ◽  
Gravity Waves ◽  
Acoustic Gravity Waves ◽  
Ambient Magnetic Field ◽  
Intense Magnetic Field ◽  
Atmospheric Stratification

Oscillatory phenomena observed in sunspot umbrae and penumbrae are reviewed and critically discussed. A natural interplay between the thermal atmospheric stratification and the ordered collimation imposed by the intense magnetic field leads naturally to the characteristic properties of the umbral chromospheric and photospheric oscillations and their interpretation as low- β ( β =8 πp / B 2 ) slow magneto-acoustic-gravity waves guided along the ambient magnetic field.

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.

THE EFFECT OF FINITE CONDUCTIVITY ON GRAVITY WAVES IN A HORIZONTAL MAGNETIC FIELD

1965 ◽  
Vol 43 (4) ◽  
pp. 645-652 ◽  
Author(s):  
R. A. Wentzell ◽  
J. H. Blackwell
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Gravity Waves ◽  
Gravitational Force ◽  
Finite Conductivity ◽  
Horizontal Magnetic Field ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Infinite Conductivity ◽  
Mode Solution

A study has been made of the behavior of the plane interface between a vacuum and an electrically conducting fluid subject to a normal gravitational force and a magnetic field parallel to the interface. The system is examined for perturbations which bend the lines of force, without restriction to the extensively used idealization of infinite electrical conductivity. The eigenvalue spectra obtained, which are surprisingly different from the simpler ones corresponding to infinite conductivity, are examined by approximate and numerical techniques over the complete range of electrical conductivity from infinity to zero. The disappearance of a normal mode solution above a critical value of conductivity is an interesting feature of the effect of finite conductivity on magnetohydrodynamic stability.

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