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Ionosphere F-region as an indicator of the evolution of atmospheric gravity waves in horizontal shear flow
Phys. Chem. Earth (C), Vol.25, No. 1-2, pp. 97-100, 2000
0 1999 ElsevierScienceLtd
Pergamon
All rightsreserved 1464-1917/00/$ - see front matter PII: S1464-1917(99)00045-8
Ionosphere F-Region as an Indicator of the Evolution of Atmospheric Waves in Horizontal Shear Flow
Gravity
G. G. Didebulidze and A. D. Pataraya
Town Department of Abastumani Astrophysical Observatory, 380060 Tbilisi, Georgia Received 3 June 1998; revised 1 April 1999; accepted 20 April 1999
Abstract. The behavior of the electron density of the night ionosphere F2-layer influenced by the atmospheric gravity waves (AGW) evolving in the meridional wind with zonal shear is investigated. The height distribution of electron density in the ionosphere FZregion is obtained by presence of shear flow. The evolution of shear waves excited by the shear Aow in the night time FZlayer is demonstrated. 0 1999 Elsevier Science Ltd. All rights reserved. 1
shows the possibility of the formation of wavelike perturbation which corresponds to large scale TIDs with small period. The resulting characteristic periods of the FZlayer parameters after the certain time of the evolution of the gravity waves are close to 16 - 20min , which are in agreement to the observation given in (Oya et al. , 1982; Bowman, 1992). The shear wave which is due to the presence of horizontal shear flow, sometimes results in sufficient changes of the FZlayer.
Introduction
2
Many authors (Hines , 1960; Hocke and Schlegel , 1996) have considered travelling ionospheric disturbances (TID) as a result of atmospheric acoustic-gravity wave (AGW) propagation in the ionosphere F-region. The influence of the atmospheric gravity waves propagation on the behavior of the ionosphere FZlayer for different cases was considered by many authors (Porter and Tuan , 1974; Shibata , 1983; Didebulidze and Pataraya 1988). In the present consideration we develop the soiution of ambipolar diffusion equation of the ionosphere F2-region by using Green’s function (Porter and Tuan , 1974; Didebulidze and Pataraya , 1988). These investigations are based on the solution of ambipolar diffusion equation of the ionosphere F2-region, when the gravity waves propagation is taken into account. In present study, different from (Didebulidze and Pataraya , 1988), the presence of horizontal shear flow is taken into account. According to Didebulidze (1997), in the horizontal shear flow together with the acoustic and gravity waves the shear wave appears due to the presence of the shear flow. The height profile of the electron density obtained in the present paper allows us to investigate evolution of the gravity and shear waves in the ionosphere F2-region. The obtained night time profile of the electron density Correspondence
to:
Ambipolar diffusion equation in the F2-region
To obtain the height distribution of electron density N,(z,t) in the ionosphere F2-region in the nonstationary case the ambipolar diffusion equation is used. This ambipolar diffusion equation in the case of the existence of the atmospheric gravity waves and the neutral meridional wind in the mid-latitude night ionosphere has the following form (Porter and Tuan , 1974; Didebulidze and Pataraya , 1988):
(u + u~)sin&osf3N, + ztxos2~Ne] = -L,
(1)
where L is the loss rate; 2H is the scale heigt for ions; x axis is oriented along the meridian to the north and y axis to the west direction; z = h - ho is the difference between actual and some initial height ho; 8 is the angle between the magnetic field and the zenith, the angle between the horizontal component of magnetic field and x direction is considered to be the same; D, is the ambipolar diffusion coefficient and the following well known expression will be used: D,cos2f3 = Doeq($), and for the loss rate the following linear form is used: L = PiV,, P = Poezp(-2) ; Do, /?o - are the coefficients of the ambipolar diffusion and recombination at height h = ho , E is the gas mixing coefficient; 15e12.
G. G. Didebulidze 97
98
G. G. Didebulidze and A. D. Pataraya: Ionosphere F-Region as Indicator of Atmospheric Gravity Waves
In Eq.(l) velocities in tively. us which in the shear flow
u and w are the disturbed neutral gas meridional and vertical direction, respecis the neutral meridional wind’s velocity present case corresponds to the horizontal
[kzuk+ k,(t)Vk] - (ikz - E) w,,
(11)
where prime denotes derivatives in time; k. = k,(t = is the timevarying wavenumber; r.~is the component of the perturbed velocity in y direction; g’is the acceleration of gravity; H = ct/yg is the atmospheric (neutral gas) scale height; c,=(+$‘/~ is the velocity of sound, y is the ratio of specific heats; PO = pooexp (- ff ) , PO = Pooezp (- 5) are the unperturbed barometric height profile for the unperturbed pressure and density, respectively; pea and poo are the pressure and density at height z = 0, respectively; E = $jj is the isothermal E&art coefficient. cs , H and J are assumed to be constant with height. Equations (3)) (4) in the absence of shear flow, describe the atmospheric AGW (Hines , 1960; Hines and Reddy , 1967). The evolution of amplitudes qk in time At < t, , where 0) ; z(t) = i[k,, kar(t), k,]
(2)
‘1Lo= q/,
where a is the shear of the horizontal (meridional) wind. In Eq.(l) ionosphere is assumed to be isothermal and the condition of small changes of height profile of the electron density in the horizontal plane, & $$$ < &, e , is taken into account. 3
p; = -i PO04
Equation of Evolution zontal shear flow
of the AGW
in hori-
According to (Didebulidze, 1997; Pataraya , 1997) the amplitudes of the atmospheric acoustic-gravity waves (AGW) are changing in time. In these papers the amplification/damping of the AGW amplitudes is connected to the presence of horizontal shear flow. In the present consideration the disturbed neutral gas velocities ‘11 and w correspond to the atmospheric gravity and shear waves. These types of waves hereafter sometimes will be referred to as modified gravity waves. According to (Didebulidze, 1997) the perturbed values of pressure ( P 1, density ( P 1, and velocity components ( u, w, w ) of the isothermal atmosphere in horizontal shear flow may be described by the following transformation:
&=2-$
02)
2I
1
according to (Didebulidze, 1997) can be described using of the following transformation: qk (t)
=
q(t)
. exp
[-if+)]
(13)
,
where Real(d) corresponds to the characteristic frequencies of atmospheric waves and Im(f2’) are their amplitude amplification/damping rates, respectively. Using transformation (13) in the set of Eqs.(3)-(11) for the AGW gives the following characteristic frequencies (Didebulidze, 1997):
(4)
4(t) = k,a: + k&)y
+ k,z
(5)
k&) = lco- alc,t.
(6)
In these expressions the evolution of complex valued amplitudes, Qk(t) = {9, & , uk, vk, &} (t) , according to the equations of motion, continuity and adiabaticity when the dissipation is neglected, is described by the set of the following linearized equations (Didebulidze, 1997): POOU;,= -&h
-
(7)
apOOvk,
pooe = d(t)&,
EL- -i [k,Uk + ky(t)v,] PO0
(8)
- (’zk, -A)
Wkr
(10)
where
i(t) 2 = k;+k;(t)+k; I I
; “,b =
is the isothermal Brunt-Viidla frequency. In Eq.(14) high frequency, wa , corresponds to the acoustic waves and low frequency, ws , to the gravity waves, respectively. The amplification/damping rates ( Im(fl’) ) of the acoustic, wai , and gravity waves, wgi , respectively, are:
wai&)= 3
[,g(t)
_ W,2(t)]
Sign “-” at the beginning of the right-hand side of Eq.(15) corresponds to the acoustic waves and “+” to the gravity waves, respectively. Values wa,g(t) , (14), and wai,gi(t) , (15), are applied for describing the evolution of acoustic and gravity waves in the horizontal shear flow during time At < t, when condition ~2,~ > wii,gi is valid.
99
G. G. Didebulidze and A. D. Pataraya: Ionosphere F-Region as Indicator of Atmospheric Gravity Waves
s I
The set of Eqs.(S)-(11) also describe the evolution of shear wave, which has zero frequency and amplification/damping rate is determind by the following expression (Didebulidze, 1997):
2100= u&n&osf3,
V, =
V,O = Real { [uk(t)sin8
V,l =
00
e-b,,
(
z’,t
>
dz’,
f wk(t)cose] cOseei'} ,
+wT-zcos (0 + 41 + $2), * t’=t
According to the characteristic dispersion Eqs.( 14)-( 16) the acoustic wave frequency, us(t) , continuously increases during time t > t, , in the same time the gravity wave frequency, w,(t) , tends to the isothermal Brunt-V%isBla frequency wb. According to dispersion Eq.(14) in a long time t >> t, the meridional phase velocity of the gravity waves tends to the value of p. For the shear wave, which is due to the presence of t!he horizontal shear flow (Didebulidze, 1997), according to Eqs.(7)-(11), (13) and (16) changes of the amplitudes uk and vk (jukj , Ivk 1 > Iwk I) are essential at time these types of evolutional gravity t 5 t, . Henceforth and shear waves sometimes will be referred to as modified gravity waves. In the following for long time interval of both gravity and shear At > t, , when appearance waves is essential, we consider the evolution of these waves numerically using the initial condition in accordance to Eqs.( 13)-( 16). In the following we consider the behavior of the ionosphere FZ-layer which corresponds to the evolution of modified gravity waves. It is possible to describe these types of longperiod waves of neutral gas at the FZregion by Eq.(l).
4
Evolution of the gravity and shear waves in the F2-region
In Eq.( 1) values ‘u. and w correspond to the real parts of perturbed velocity of atmospheric waves which will be taken from Eq.(4). For solution of Eq.( 1) we use new variable C = n . ezp(-5) and we may obtain an equation in which Green’s function is the same as in (Didebulidze and Pataraya , 1988). Using this Green’s function we may obtain the following height profile of the F2-region electron density: N, = Nexp ;
[
{
v,1e-*
-Jqt
- to) - $
- &h(Y’t)]}
- ;e-+_
?
where x = 2vi + $L[&&$+;)
cx=IE+
K. =
uooH -,
gd
-I(l+;)]
Vd=$+,
A>
4 = 4Juaou~4~ono,
(17)
-c’Vn((‘,tl) + ~l=Jme 0 t’=to 2w
t s
[
Vno(<‘,t’)dt’
to
$1 = arctg
1
dC’,
1
42 =
a~ctg(&),
Im (Uksine + wkcos6) 1Real (uk sine + wk Case)I ’
Solution for N,(z, t) , (17), allows us to investigate analytically and numerically the evolution of the modified gravity waves in the horizontal shear Aow. According to solution (17) and Eqs.(S)-(11) we may use analytical as well as numerical results for describing the behavior of the electron density height profile, N,(z, t) , in the horizontal shear flow. According to Eq.(17) the influence of modified gravity waves on the behavior of the F2-layer electron density is more effective for the cases of k, = 0 , which are partially demonstrated in Figs. 1, 2. In these figures the evolution of’the maxima of electron density, NmF2(t) , their heights, h,F2(t) , for the atmospheric gravity and shear waves, are plotted, respectively. For all figures the mid-latitudes F2region and the wave parameters are choosen as follows: k, = 5.2 * 10-6m-1, ko = 2.7 . 10-6m-1, a = 1.16 . 10-4s-1 , to = O,sinBcosB N -0.4, E = 1.3, H = 6 . 104m, PO = 2 . 10-4s-1, DO = 9 . 105m2s-1, N = 106cme3, ho = 300km. In these figures the dark lines correspond to the case of the absence of the modified gravity waves (background F2-layer). t > t, According to the Fig. 1, in long times, (t, N 150min), the periods of gravity waves are weakly changed and are nearly 16 - 2Omin. This case corresponds to the formation of large scale TIDs with small period and phase velocity (2 p) in the meridional direction about 1000 - 1200m. s”. The period of nearly 17min is in agreement with observation of large scale TIDs by (Oya et al. , 1982;Bowman, 1992). According to cases demonstrated in Fig. 2, the evolution of shear wave gives different change of the background F2-layer on comparison to the case of the evolution of gravity waves. For the shear wave, sufficient changes of the FZlayer parameters h,F2(t) and N,F2 appear in times t 2 t,. Above applied method of N, solution may be generilised to develope the more realistic ionosphere where the values of H, P, Do and gravity waves linearly vary due to the nonisothermality and inhomogeniety in horizontal plane.
100
G. G. Didebulidze and A. D. Pataraya: Ionosphere F-Region as Indicator of Atmospheric Gravity Waves
5
Conclusion
The night time height profile of electron density N, (z, t) has been obtained which allows us to investigate the evolution of the gravity and shear waves in horizontal shear flow. The evolution of the meridional and vertical components of the velocity of the gravity and shear waves and their influence on the behavior of the FZ-region electron density is demonstrated. The essential changes of the F2-layer parameters N&72(t) and h,F2(t) appear for the shear waves in times t 5 t, . For atmospheric gravity waves in times t > t, values /472(t) change essentially and the frequency of their oscillations tends to the ishothermal Brunt-V%;il;i frequency. For the scale height of the F2-region neutral gas H = 60km the characteristic periods of variation of &$2(t) and N,F2(t) due to the evolution of the gravity wave in the horizontal shear flow at great time t > t, are close to 16-20min.
400
References
Fig. 1. The behavior of N,F2(t) influence of the evolving atmospheric
"0
5350 $
pp
E300 .,,,,,.., 250’ 0
200
100
.........f
.
:. ,,...,..: : 100
and &$2(t) gravity waves
400
300
j . . . . . . . . . ... . . .,...,....:
; 200 Time, min
under the
.
. ..
..
I 400
; 300
Fig. 2. The behavior of NmF2(t) , (a), and under the influence of the shear waves.
h,FP(t)
, (b),
Bowman, G. G. Some aspects of large-scale travelling ionospheric disturbances, Planet. Space Sci., 40, 829-845, 1992. Didebulidze, G. G. Amplification/damping processes of atmospheric acoustic-gravity waves in horizontal winds with linear shear,Physics Letters A, 235, 65-70, 1997. Didebulidze, G. G. and Pataraya, A. D. Reaction of the ionospheric F-layer on oblique propagation of the inner gravitational waves in the presence of a local wind. Bulletin Abastumani Astrophys. Obs.,66, 223-232, 1988. Hines, C. 0. Internal atmospheric gravity waves at ionospheric heights. Can. J. Phys., 38, 1441-1481, 1960. Hines, C. 0. and Reddy C. A. On the propagation of atmospheric gravity through regions of wind shear. J. Geophys. Res., 72, 1015, 1967. Hocke K. and Schlegel K. A review of atmospheric gravity waves and traveling ionospheric disturbances:1982-1995, Ann. Geophysicae, 12, 917-940, 1996. Oya, H., Takahashi, T., Morioka, A. and Miyaoka, H., Wavy patterns of ionospheric electron density profiles tfiggered by TIDobservation results of the electron density by Taiyo Satellite J. Geomagn. Geoelectr., 34, 509-525, 1982.. Pataraya, A. D., Pataraya, T. A. An excitement of the gravitational and acoustic waves in the solar atmosphere caused by inhomogeneous flow, Astron. Astrophys. Tmnsc., 13, 121-126, 1997. Porter, H. S. and Tuan, T. F. On the behaviour of the F-layer under the influence of gravity waves, J. Atmos. Tew.Phys. 36, 135-157, 1974. Shibata, T. A numerical calculation of the ionospheric response to atmospheric gravity waves in the F2-region, J. Atmosph. Terr. Phys., 45, 797-809, 1983.
0 1999 ElsevierScienceLtd
Pergamon
All rightsreserved 1464-1917/00/$ - see front matter PII: S1464-1917(99)00045-8
Ionosphere F-Region as an Indicator of the Evolution of Atmospheric Waves in Horizontal Shear Flow
Gravity
G. G. Didebulidze and A. D. Pataraya
Town Department of Abastumani Astrophysical Observatory, 380060 Tbilisi, Georgia Received 3 June 1998; revised 1 April 1999; accepted 20 April 1999
Abstract. The behavior of the electron density of the night ionosphere F2-layer influenced by the atmospheric gravity waves (AGW) evolving in the meridional wind with zonal shear is investigated. The height distribution of electron density in the ionosphere FZregion is obtained by presence of shear flow. The evolution of shear waves excited by the shear Aow in the night time FZlayer is demonstrated. 0 1999 Elsevier Science Ltd. All rights reserved. 1
shows the possibility of the formation of wavelike perturbation which corresponds to large scale TIDs with small period. The resulting characteristic periods of the FZlayer parameters after the certain time of the evolution of the gravity waves are close to 16 - 20min , which are in agreement to the observation given in (Oya et al. , 1982; Bowman, 1992). The shear wave which is due to the presence of horizontal shear flow, sometimes results in sufficient changes of the FZlayer.
Introduction
2
Many authors (Hines , 1960; Hocke and Schlegel , 1996) have considered travelling ionospheric disturbances (TID) as a result of atmospheric acoustic-gravity wave (AGW) propagation in the ionosphere F-region. The influence of the atmospheric gravity waves propagation on the behavior of the ionosphere FZlayer for different cases was considered by many authors (Porter and Tuan , 1974; Shibata , 1983; Didebulidze and Pataraya 1988). In the present consideration we develop the soiution of ambipolar diffusion equation of the ionosphere F2-region by using Green’s function (Porter and Tuan , 1974; Didebulidze and Pataraya , 1988). These investigations are based on the solution of ambipolar diffusion equation of the ionosphere F2-region, when the gravity waves propagation is taken into account. In present study, different from (Didebulidze and Pataraya , 1988), the presence of horizontal shear flow is taken into account. According to Didebulidze (1997), in the horizontal shear flow together with the acoustic and gravity waves the shear wave appears due to the presence of the shear flow. The height profile of the electron density obtained in the present paper allows us to investigate evolution of the gravity and shear waves in the ionosphere F2-region. The obtained night time profile of the electron density Correspondence
to:
Ambipolar diffusion equation in the F2-region
To obtain the height distribution of electron density N,(z,t) in the ionosphere F2-region in the nonstationary case the ambipolar diffusion equation is used. This ambipolar diffusion equation in the case of the existence of the atmospheric gravity waves and the neutral meridional wind in the mid-latitude night ionosphere has the following form (Porter and Tuan , 1974; Didebulidze and Pataraya , 1988):
(u + u~)sin&osf3N, + ztxos2~Ne] = -L,
(1)
where L is the loss rate; 2H is the scale heigt for ions; x axis is oriented along the meridian to the north and y axis to the west direction; z = h - ho is the difference between actual and some initial height ho; 8 is the angle between the magnetic field and the zenith, the angle between the horizontal component of magnetic field and x direction is considered to be the same; D, is the ambipolar diffusion coefficient and the following well known expression will be used: D,cos2f3 = Doeq($), and for the loss rate the following linear form is used: L = PiV,, P = Poezp(-2) ; Do, /?o - are the coefficients of the ambipolar diffusion and recombination at height h = ho , E is the gas mixing coefficient; 15e12.
G. G. Didebulidze 97
98
G. G. Didebulidze and A. D. Pataraya: Ionosphere F-Region as Indicator of Atmospheric Gravity Waves
In Eq.(l) velocities in tively. us which in the shear flow
u and w are the disturbed neutral gas meridional and vertical direction, respecis the neutral meridional wind’s velocity present case corresponds to the horizontal
[kzuk+ k,(t)Vk] - (ikz - E) w,,
(11)
where prime denotes derivatives in time; k. = k,(t = is the timevarying wavenumber; r.~is the component of the perturbed velocity in y direction; g’is the acceleration of gravity; H = ct/yg is the atmospheric (neutral gas) scale height; c,=(+$‘/~ is the velocity of sound, y is the ratio of specific heats; PO = pooexp (- ff ) , PO = Pooezp (- 5) are the unperturbed barometric height profile for the unperturbed pressure and density, respectively; pea and poo are the pressure and density at height z = 0, respectively; E = $jj is the isothermal E&art coefficient. cs , H and J are assumed to be constant with height. Equations (3)) (4) in the absence of shear flow, describe the atmospheric AGW (Hines , 1960; Hines and Reddy , 1967). The evolution of amplitudes qk in time At < t, , where 0) ; z(t) = i[k,, kar(t), k,]
(2)
‘1Lo= q/,
where a is the shear of the horizontal (meridional) wind. In Eq.(l) ionosphere is assumed to be isothermal and the condition of small changes of height profile of the electron density in the horizontal plane, & $$$ < &, e , is taken into account. 3
p; = -i PO04
Equation of Evolution zontal shear flow
of the AGW
in hori-
According to (Didebulidze, 1997; Pataraya , 1997) the amplitudes of the atmospheric acoustic-gravity waves (AGW) are changing in time. In these papers the amplification/damping of the AGW amplitudes is connected to the presence of horizontal shear flow. In the present consideration the disturbed neutral gas velocities ‘11 and w correspond to the atmospheric gravity and shear waves. These types of waves hereafter sometimes will be referred to as modified gravity waves. According to (Didebulidze, 1997) the perturbed values of pressure ( P 1, density ( P 1, and velocity components ( u, w, w ) of the isothermal atmosphere in horizontal shear flow may be described by the following transformation:
&=2-$
02)
2I
1
according to (Didebulidze, 1997) can be described using of the following transformation: qk (t)
=
q(t)
. exp
[-if+)]
(13)
,
where Real(d) corresponds to the characteristic frequencies of atmospheric waves and Im(f2’) are their amplitude amplification/damping rates, respectively. Using transformation (13) in the set of Eqs.(3)-(11) for the AGW gives the following characteristic frequencies (Didebulidze, 1997):
(4)
4(t) = k,a: + k&)y
+ k,z
(5)
k&) = lco- alc,t.
(6)
In these expressions the evolution of complex valued amplitudes, Qk(t) = {9, & , uk, vk, &} (t) , according to the equations of motion, continuity and adiabaticity when the dissipation is neglected, is described by the set of the following linearized equations (Didebulidze, 1997): POOU;,= -&h
-
(7)
apOOvk,
pooe = d(t)&,
EL- -i [k,Uk + ky(t)v,] PO0
(8)
- (’zk, -A)
Wkr
(10)
where
i(t) 2 = k;+k;(t)+k; I I
; “,b =
is the isothermal Brunt-Viidla frequency. In Eq.(14) high frequency, wa , corresponds to the acoustic waves and low frequency, ws , to the gravity waves, respectively. The amplification/damping rates ( Im(fl’) ) of the acoustic, wai , and gravity waves, wgi , respectively, are:
wai&)= 3
[,g(t)
_ W,2(t)]
Sign “-” at the beginning of the right-hand side of Eq.(15) corresponds to the acoustic waves and “+” to the gravity waves, respectively. Values wa,g(t) , (14), and wai,gi(t) , (15), are applied for describing the evolution of acoustic and gravity waves in the horizontal shear flow during time At < t, when condition ~2,~ > wii,gi is valid.
99
G. G. Didebulidze and A. D. Pataraya: Ionosphere F-Region as Indicator of Atmospheric Gravity Waves
s I
The set of Eqs.(S)-(11) also describe the evolution of shear wave, which has zero frequency and amplification/damping rate is determind by the following expression (Didebulidze, 1997):
2100= u&n&osf3,
V, =
V,O = Real { [uk(t)sin8
V,l =
00
e-b,,
(
z’,t
>
dz’,
f wk(t)cose] cOseei'} ,
+wT-zcos (0 + 41 + $2), * t’=t
According to the characteristic dispersion Eqs.( 14)-( 16) the acoustic wave frequency, us(t) , continuously increases during time t > t, , in the same time the gravity wave frequency, w,(t) , tends to the isothermal Brunt-V%isBla frequency wb. According to dispersion Eq.(14) in a long time t >> t, the meridional phase velocity of the gravity waves tends to the value of p. For the shear wave, which is due to the presence of t!he horizontal shear flow (Didebulidze, 1997), according to Eqs.(7)-(11), (13) and (16) changes of the amplitudes uk and vk (jukj , Ivk 1 > Iwk I) are essential at time these types of evolutional gravity t 5 t, . Henceforth and shear waves sometimes will be referred to as modified gravity waves. In the following for long time interval of both gravity and shear At > t, , when appearance waves is essential, we consider the evolution of these waves numerically using the initial condition in accordance to Eqs.( 13)-( 16). In the following we consider the behavior of the ionosphere FZ-layer which corresponds to the evolution of modified gravity waves. It is possible to describe these types of longperiod waves of neutral gas at the FZregion by Eq.(l).
4
Evolution of the gravity and shear waves in the F2-region
In Eq.( 1) values ‘u. and w correspond to the real parts of perturbed velocity of atmospheric waves which will be taken from Eq.(4). For solution of Eq.( 1) we use new variable C = n . ezp(-5) and we may obtain an equation in which Green’s function is the same as in (Didebulidze and Pataraya , 1988). Using this Green’s function we may obtain the following height profile of the F2-region electron density: N, = Nexp ;
[
{
v,1e-*
-Jqt
- to) - $
- &h(Y’t)]}
- ;e-+_
?
where x = 2vi + $L[&&$+;)
cx=IE+
K. =
uooH -,
gd
-I(l+;)]
Vd=$+,
A>
4 = 4Juaou~4~ono,
(17)
-c’Vn((‘,tl) + ~l=Jme 0 t’=to 2w
t s
[
Vno(<‘,t’)dt’
to
$1 = arctg
1
dC’,
1
42 =
a~ctg(&),
Im (Uksine + wkcos6) 1Real (uk sine + wk Case)I ’
Solution for N,(z, t) , (17), allows us to investigate analytically and numerically the evolution of the modified gravity waves in the horizontal shear Aow. According to solution (17) and Eqs.(S)-(11) we may use analytical as well as numerical results for describing the behavior of the electron density height profile, N,(z, t) , in the horizontal shear flow. According to Eq.(17) the influence of modified gravity waves on the behavior of the F2-layer electron density is more effective for the cases of k, = 0 , which are partially demonstrated in Figs. 1, 2. In these figures the evolution of’the maxima of electron density, NmF2(t) , their heights, h,F2(t) , for the atmospheric gravity and shear waves, are plotted, respectively. For all figures the mid-latitudes F2region and the wave parameters are choosen as follows: k, = 5.2 * 10-6m-1, ko = 2.7 . 10-6m-1, a = 1.16 . 10-4s-1 , to = O,sinBcosB N -0.4, E = 1.3, H = 6 . 104m, PO = 2 . 10-4s-1, DO = 9 . 105m2s-1, N = 106cme3, ho = 300km. In these figures the dark lines correspond to the case of the absence of the modified gravity waves (background F2-layer). t > t, According to the Fig. 1, in long times, (t, N 150min), the periods of gravity waves are weakly changed and are nearly 16 - 2Omin. This case corresponds to the formation of large scale TIDs with small period and phase velocity (2 p) in the meridional direction about 1000 - 1200m. s”. The period of nearly 17min is in agreement with observation of large scale TIDs by (Oya et al. , 1982;Bowman, 1992). According to cases demonstrated in Fig. 2, the evolution of shear wave gives different change of the background F2-layer on comparison to the case of the evolution of gravity waves. For the shear wave, sufficient changes of the FZlayer parameters h,F2(t) and N,F2 appear in times t 2 t,. Above applied method of N, solution may be generilised to develope the more realistic ionosphere where the values of H, P, Do and gravity waves linearly vary due to the nonisothermality and inhomogeniety in horizontal plane.
100
G. G. Didebulidze and A. D. Pataraya: Ionosphere F-Region as Indicator of Atmospheric Gravity Waves
5
Conclusion
The night time height profile of electron density N, (z, t) has been obtained which allows us to investigate the evolution of the gravity and shear waves in horizontal shear flow. The evolution of the meridional and vertical components of the velocity of the gravity and shear waves and their influence on the behavior of the FZ-region electron density is demonstrated. The essential changes of the F2-layer parameters N&72(t) and h,F2(t) appear for the shear waves in times t 5 t, . For atmospheric gravity waves in times t > t, values /472(t) change essentially and the frequency of their oscillations tends to the ishothermal Brunt-V%;il;i frequency. For the scale height of the F2-region neutral gas H = 60km the characteristic periods of variation of &$2(t) and N,F2(t) due to the evolution of the gravity wave in the horizontal shear flow at great time t > t, are close to 16-20min.
400
References
Fig. 1. The behavior of N,F2(t) influence of the evolving atmospheric
"0
5350 $
pp
E300 .,,,,,.., 250’ 0
200
100
.........f
.
:. ,,...,..: : 100
and &$2(t) gravity waves
400
300
j . . . . . . . . . ... . . .,...,....:
; 200 Time, min
under the
.
. ..
..
I 400
; 300
Fig. 2. The behavior of NmF2(t) , (a), and under the influence of the shear waves.
h,FP(t)
, (b),
Bowman, G. G. Some aspects of large-scale travelling ionospheric disturbances, Planet. Space Sci., 40, 829-845, 1992. Didebulidze, G. G. Amplification/damping processes of atmospheric acoustic-gravity waves in horizontal winds with linear shear,Physics Letters A, 235, 65-70, 1997. Didebulidze, G. G. and Pataraya, A. D. Reaction of the ionospheric F-layer on oblique propagation of the inner gravitational waves in the presence of a local wind. Bulletin Abastumani Astrophys. Obs.,66, 223-232, 1988. Hines, C. 0. Internal atmospheric gravity waves at ionospheric heights. Can. J. Phys., 38, 1441-1481, 1960. Hines, C. 0. and Reddy C. A. On the propagation of atmospheric gravity through regions of wind shear. J. Geophys. Res., 72, 1015, 1967. Hocke K. and Schlegel K. A review of atmospheric gravity waves and traveling ionospheric disturbances:1982-1995, Ann. Geophysicae, 12, 917-940, 1996. Oya, H., Takahashi, T., Morioka, A. and Miyaoka, H., Wavy patterns of ionospheric electron density profiles tfiggered by TIDobservation results of the electron density by Taiyo Satellite J. Geomagn. Geoelectr., 34, 509-525, 1982.. Pataraya, A. D., Pataraya, T. A. An excitement of the gravitational and acoustic waves in the solar atmosphere caused by inhomogeneous flow, Astron. Astrophys. Tmnsc., 13, 121-126, 1997. Porter, H. S. and Tuan, T. F. On the behaviour of the F-layer under the influence of gravity waves, J. Atmos. Tew.Phys. 36, 135-157, 1974. Shibata, T. A numerical calculation of the ionospheric response to atmospheric gravity waves in the F2-region, J. Atmosph. Terr. Phys., 45, 797-809, 1983.