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.

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.

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.

Kompressionswellen in einer isothermen Atmosphäre mit vertikalem Magnetfeld

1966 ◽  
Vol 21 (7) ◽  
pp. 1098-1106 ◽  
Author(s):  
R. Lust ◽  
M. Scholer
Keyword(s):  
Magnetic Field ◽  
Strong Influence ◽  
Vertical Direction ◽  
Time Dependent ◽  
Solar Chromosphere ◽  
Magnetohydrodynamic Equation ◽  
One Dimensional ◽  
Spatial Dimensions ◽  
Propagation Of Waves ◽  
The Waves

The propagation of waves in the solar atmosphere is investigated with respect to the problem of the chromospheric spiculae and of the heating of the solar chromosphere and corona. In particular the influence of external magnetic fields is considered. Waves of finite amplitudes are numerically calculated by solving the time-dependent magnetohydrodynamic equation for two spatial dimensions by assuming axial symmetry. For the case without a magnetic field the comparison between one dimensional and two dimensional treatment shows the strong influence of the radial propagation on the steepening of waves in the vertical direction. In the presence of a magnetic field it is shown that the propagation is strongly guided along the lines of force. The steepening of the waves along the field is much larger as compared to the case where no field is present.

scholarly journals Intercomparison of AIRS and HIRDLS stratospheric gravity wave observations

2018 ◽  
Vol 11 (1) ◽  
pp. 215-232 ◽  
Author(s):  
Catrin I. Meyer ◽  
Manfred Ern ◽  
Lars Hoffmann ◽  
Quang Thai Trinh ◽  
M. Joan Alexander
Keyword(s):  
High Resolution ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Wave Spectrum ◽  
Horizontal Resolution ◽  
Wave Activity ◽  
Large Variability ◽  
Wave Event ◽  
The Waves

Abstract. We investigate stratospheric gravity wave observations by the Atmospheric InfraRed Sounder (AIRS) aboard NASA's Aqua satellite and the High Resolution Dynamics Limb Sounder (HIRDLS) aboard NASA's Aura satellite. AIRS operational temperature retrievals are typically not used for studies of gravity waves, because their vertical and horizontal resolution is rather limited. This study uses data of a high-resolution retrieval which provides stratospheric temperature profiles for each individual satellite footprint. Therefore the horizontal sampling of the high-resolution retrieval is 9 times better than that of the operational retrieval. HIRDLS provides 2-D spectral information of observed gravity waves in terms of along-track and vertical wavelengths. AIRS as a nadir sounder is more sensitive to short-horizontal-wavelength gravity waves, and HIRDLS as a limb sounder is more sensitive to short-vertical-wavelength gravity waves. Therefore HIRDLS is ideally suited to complement AIRS observations. A calculated momentum flux factor indicates that the waves seen by AIRS contribute significantly to momentum flux, even if the AIRS temperature variance may be small compared to HIRDLS. The stratospheric wave structures observed by AIRS and HIRDLS often agree very well. Case studies of a mountain wave event and a non-orographic wave event demonstrate that the observed phase structures of AIRS and HIRDLS are also similar. AIRS has a coarser vertical resolution, which results in an attenuation of the amplitude and coarser vertical wavelengths than for HIRDLS. However, AIRS has a much higher horizontal resolution, and the propagation direction of the waves can be clearly identified in geographical maps. The horizontal orientation of the phase fronts can be deduced from AIRS 3-D temperature fields. This is a restricting factor for gravity wave analyses of limb measurements. Additionally, temperature variances with respect to stratospheric gravity wave activity are compared on a statistical basis. The complete HIRDLS measurement period from January 2005 to March 2008 is covered. The seasonal and latitudinal distributions of gravity wave activity as observed by AIRS and HIRDLS agree well. A strong annual cycle at mid- and high latitudes is found in time series of gravity wave variances at 42 km, which has its maxima during wintertime and its minima during summertime. The variability is largest during austral wintertime at 60∘ S. Variations in the zonal winds at 2.5 hPa are associated with large variability in gravity wave variances. Altogether, gravity wave variances of AIRS and HIRDLS are complementary to each other. Large parts of the gravity wave spectrum are covered by joint observations. This opens up fascinating vistas for future gravity wave research.

Propagation of electromagnetic waves in a warm plasma-filled cylindrical waveguide in the presence of an external magnetic field

1983 ◽  
Vol 29 (3) ◽  
pp. 383-392 ◽  
Author(s):  
Sanjay Kumar Ghosh ◽  
S. P. Pal
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Electromagnetic Waves ◽  
Transverse Magnetic ◽  
Cylindrical Waveguide ◽  
Small Magnetic Field ◽  
Warm Plasma ◽  
Plasma Theory ◽  
The Waves ◽  
Constant External Magnetic Field

The propagation of electromagnetic waves in a plasma-filled cylindrical waveguide in the presence of a constant external magnetic field is investigated using warm plasma theory. It is found that the waves cannot be separated into transverse magnetic and transverse electric modes; only hybrid modes are propagated. Dispersion relations are derived for zero, finite and infinite magnetic fields. Frequency shifts for the wave propagation in the case of a small magnetic field are calculated.

Random waves and dynamo action

1975 ◽  
Vol 69 (1) ◽  
pp. 145-177 ◽  
Author(s):  
A. M. Soward
Keyword(s):  
Magnetic Field ◽  
Wave Energy ◽  
Dynamo Model ◽  
Length Scale ◽  
Kinetic Energy Density ◽  
Random Waves ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
The Waves ◽  
Upper Boundary

The propagation of waves in an inviscid, electrically conducting fluid is considered. The fluid rotates with angular velocity Ω* and is permeated by a magnetic field b* which varies on the length scale L = Ql, where Q = Ω*l2/λ (l is the length scale of the waves, λ is the magnetic diffusivity) is assumed large (Q [Gt ] 1). A linearized theory is readily justified in the limit of zero Rossby number R0 (= U0/Ω*l, where U0 is a typical fluid velocity) and for this case it is shown that the total wave energy of a wave train is conserved and transported at the group velocity except for that which is lost by ohmic dissipation. The analysis is extended to encompass the propagation of a sea of random waves.A hydromagnetic dynamo model is considered in which the fluid is confined between two horizontal planes perpendicular to the rotation axis a distance L0(=O(L)) apart. Waves of given low frequency Ω*0 (= O(R0Q½Ω*)) and horizontal wavenumber l−1 but random orientation are excited at the lower boundary, where the kinetic energy density is 2πρU20. The waves are absorbed perfectly at the upper boundary, so that there is no reflexion. The linear wave energy equation remains valid in the double limit 1 [Gt ] R0Q½[Gt ]Q−½, for which it is shown that dynamo action is possible provided $\Delta = L_0U^2_0/l^3\omega_0^{*2} > 1 $. When dynamo action maintains a weak magnetic field (Δ −1 [Lt ] 1) which only slightly modifies the inertial waves analytic solutions are obtained. In the case of a strong magnetic field (Δ [Gt ] 1) for which Coriolis and Lorentz forces are comparable solutions are obtained numerically. The latter class includes the more realistic case (Δ → ∞) in which the upper boundary is absent.

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.

scholarly journals Alternative derivations for the fields inside a waveguide

2021 ◽  
Vol 72 (2) ◽  
pp. 129-131
Author(s):  
Raghavendra G. Kulkarni
Keyword(s):  
Magnetic Field ◽  
Wave Equation ◽  
Electric Field ◽  
Longitudinal Magnetic Field ◽  
Transverse Electric ◽  
Transverse Magnetic ◽  
Longitudinal Electric Field ◽  
Microwave Engineering ◽  
Introductory Textbooks ◽  
Helmholtz Wave Equation

Abstract Generally, the longitudinal magnetic field of the transverse electric (TE) wave inside a waveguide is obtained by solving the corresponding Helmholtz wave equation, which further leads to the derivation of the remaining fields. In this paper, we provide an alternative way to obtain this longitudinal magnetic field by making use of one of the Maxwell’s equations instead of directly relying on the Helmholtz wave equation. The longitudinal electric field of the transverse magnetic (TM) wave inside a waveguide can also be derived in a similar fashion. These derivations, which are different from those found in the introductory textbooks on microwave engineering, make the study of waveguides more interesting.

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.

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