MECHANISMS IN T H E G.

OF

EARTH'S I.

GENERATION

OF

ACOUSTOGRAVITY

WAVES

ATMOSPHERE*

Grigor'ev

and

V.

P.

Dokuchaev

UDC 621.371.24

The results of an analysis of observational data on gas motions at various heights in the e a r t h ' s a t m o s p h e r e a r e described. These data indicate the existence of acoustogravity waves in a large range of heights extending f r o m the e a r t h ' s surface to the top of the ionosphere. The m e c h a n i s m s of generation of these waves by various s o u r c e s a r e discussed. w Systematic observations of the state of the e a r t h ' s a t m o s p h e r e reveal its transient nature. In addition to secular, seasonal, and diurnal variations of the p a r a m e t e r s of the a t m o s p h e r e at different heights, wave motions of the gas a r e also recorded. Of p a r t i c u l a r interest a r e disturbances having periods of 1 0 2 s e c TO< 1 day, which a r e typical of a c o u s t o g r a v i t y waves (AGWs). The p r o p e r t i e s of the latter a r e strongly affected by the e a r t h ' s field of gravity. Before investigating the propagation c h a r a c t e r i s t i c s of these waves, we c o n s i d e r some of the observational data. The most complete s u r v e y of observations of these waves in the t r o p o s p h e r e a r e found in Gossard and Hook's book [1]. We focus our attention here p r i m a r i l y on studies of these waves at relatively large heights with the use of radiophysical m e a s u r e m e n t techniques, as well as the m e c h a n i s m of AGW generation in the upper a t m o s p h e r e . w M i c r o b a r a g r a p h s (MBGs) situated on the surface of the earth and having a sensitivity Ap ~ 1 d y n / r e c o r d both ordinary infrasonic waves with periods in the interval 1 0 - I s e c (" T O ,~ 102 sec and internal gravity waves with periods TO~ 10 min. A spatial MBG a r r a y is used to determine the wavelength )L and propagation velocity. A c c o r d i n g t o certain data [2] the indicated quantities a r e c h a r a c t e r i z e d by the following values, for example: amplitude AP0 ~ 5 to 100 dyn/cm2; TO ~ 10 min; ), ~ 20 km; Vp ~ 35 m / s e c . Radar probing of the cloudless a t m o s p h e r e [3] also indicates the p r e s e n c e of disturbances of the internal g r a v i t y wave type at heights z ~ 3 to 5 km in the troposphere. Airplane flights in the s t r a t o s p h e r e over mountain ranges a r e often accompanied b y s o - c a l l e d "buffeting." This effect is related to internal gravity waves f o r m e d by a i r flowing over i r r e g u l a r i t i e s of the e a r t h ' s surface [1, 4]. P h o t o m e t r i c and visual observations of noetilucent clouds in mesopause regions (z ~ 80 to 85 kin) disclose the presence of internal gravity waves with a v e r t i c a l displacement amplitude ~0 ~ 0.5to 4kin, wavelengths X ~ 5 to 50 kin, and phase velocities Vp ~ 1 0 to 20 m / s e c [5]. The r e c o r d i n g of n i g h t - s k y e m i s s i o n r e v e a l s pulsating inhomogeneities of the sunspot type, along with r i b b o n - s h a p e d inhomogeneities oriented predominantly along n o r t h - s o u t h lines. The lifetime of the pulsating inhomogeneities is AT ~ 1.5 to 2 h, and the oscillation period of the e m i s s i o n intensity v a r i e s in the interval 5 rain ~ - ~ 15 rain [6, 7]. Internal g r a v i t y waves also show up in r a d a r observations of the drift of ionized m e t e o r t r a i l s in the height range f r o m 85 to 100 km [8]. em 2

Direct and indirect data now exist, indicating the p r e s e n c e of internal gravity waves it1 all regions of the ionosphere. Radiophysical methods a r e normally used to m e a s u r e the plasma p a r a m e t e r s . The inhomogeneities of the electron density Ne due to the propagation of internal gravity waves a r e c u s t o m a r i l y r e f e r r e d to as traveling ionospheric disturbances (TIDs). The latter a r e conditionally divided into two types [9]. L a r g e - s c a l e TIDs, with k ~ 103 km and T0 ~ 1 h, usually move with velocities Vp ~ 300 to 1000 k m / s e e . As a rule, they o c c u r a f t e r powerful magnetic s t o r m s and move in a broad front f r o m the poles toward the equator. The second type of TID is c h a r a c t e r i z e d by lower velocities Vp ~ 100 to 250 m / s e c , their wavelengths v a r y in the interval f r o m tens to hundreds of k i l o m e t e r s ' and they have periods T0 ~ 10 to 30 min. The magnitude of the variations of Ne fluctuates between the limits Ne/N 0 ~ 10 -3 to 10 -1. T h e r e i s also evidence of TIDs at heights above the F - l a y e r m a x i m u m [10] with amplitudes Ap ~ (0.1 to 0.2) P0. Thus, various methods of m e a s u r i n g the p a r a m e t e r s of the a t m o s p h e r e indicate the p r e s e n c e of AGWs in a l a r g e range of heights extending f r o m the t r o p o s p h e r e to z 0 ~ 500 km. * P r e s e n t e d at the All-Union Conference on Special Aspects of Radio-Wave Propagation in the Ionosphere and Outer Space, Gor'kii, September, 1976. S c i e n t i f i c - R e s e a r c h Institute of Radiophysics. T r a n s l a t e d f r o m Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 21, No. 7, pp. 945-950, July, 1978. Original a r t i c l e submitted March 3, 1977.

664

0033-8443/78/2107-0664507.50

9

Plenum Publishing C o r p o r a t i o n

w Aeoustogravity waves play a significant role in the interpretation of a g r e a t many physical p h e n o m ena in the t r o p o s p h e r e and in the dynamics of the ionospheric plasma. The disturbances c r e a t e d by them a r e governed, on the one hand, by the p r o p e r t i e s of the source and, on the Other, by the dispersion c h a r a c t e r i s t i c s of the medium. The latter have been studied in deta[i"for the model of an isothermal a t m o s p h e r e [11], as well as for m o r e realistic a t m o s p h e r e models [9]. It is deduced f r o m observations and appropriate calculations that P0werfuI explosions in the atmosphere, earthquakes, volcanic eruptions, j e t s t r e a m s and t h u n d e r s t o r m activity in the troposphere, and a u r o r a l and equatorial c u r r e n t s y s t e m s a r e highly efficient AGW s o u r c e s . Among some of the other possible generation m e c h a n i s m s we note the emission of AGWs during brilliant m e t e o r flights in the e a r t h ' s a t m o s p h e r e . The s y s t e m of initial equations for small perturbations of the p r e s s u r e p, density p, and velocity v in the p r e s e n c e of s o u r c e s of m a s s q, energy h, and m o m e n t u m f has the f o r m

Ov po ~ + v p - ~g =

f;

(1)

dp 0-7+ (vV)Po + Po div v = q;

OP 0-7 + (vV)po--c'[ OP 07 +

(vV)Po ] = (~ -

(2)

l)~0h

(3)

Here p0(z) and p0(z) a r e the mean values of the p r e s s u r e and density, g = (0, 0, - g ) is the acceleration due to gravity, c is the sound velocity, and 3' = ep/Cv is the specific-heat ratio. F r o m the s y s t e m of equations (1)-(3) we obtain the p r e s s u r e equation f o r an isothermal a t m o s p h e r e :

04P Tg 03P -

02

,

O~ g

(4)

in which Wg = (y - 1)l/2g/e is the B r u n t - Vffis~flff frequency, A = 02/0z 2 + A_L, and A• = 02/OX2 + 32/0y 2. We obtain the AGW dispersion relation f r o m (4) with the right-hand side set equal to zero, putting p ~ exp ( - i w t + ikR - z/2H). It may be written in ~he f o r m [11] ~o~ z = 0 ,

(5)

where wa = c/2H = 3,g/2c is the a c o u s t i c - w a v e cutoff frequency, k is the wave vector, k• is the projection of k onto the xy plane, and k = | k l . Equation (5) d e t e r m i n e s the phase velocity Vp

= w/k:

V

~=~-- r176sin2 ~

(6)

where $ is the angle between the v e c t o r s k and - g . Two wave modes can propagate in a given direction ~: 1) low-frequency (w < wgsin $), or internal gravity waves; 2) AGWs (co > Wa), which go over to sound waves in the limit g ~ 0 (Vp ~ c). It is expected that for the real a t m o s p h e r e with a smooth profile T(z) t h e AGW d i s p e r s i o n c h a r a c t e r i s t i c s will be the same in the f i r s t approximation as in the case T = eonst. Numerical computations c a r r i e d out by Dikii [12] for a standard a t m o s p h e r e confirm this conclusion. The main difference is that guided-wave modes can o c c u r under real atmospheric conditions. The dispersion c h a r a c t e r i s t i c s of such guided waves a r e analyzed in [9, 12]. Various models of the a t m o s p h e r e a r e used in these papers. Some of the models allow for dissipation due to viscosity and t h e r m a l conduction. w The perturbations in Eqs. (1)-(3) a r e p r e s u m e d to be c r e a t e d by force s o u r c e s f, m a s s s o u r c e s q, and e n e r g y s o u r c e s h. Any specific generation m e c h a n i s m is described by one of these s o u r c e s or a combination thereof. The emission of AGWs by monochromatic, impulsive, and r e c t i l i n e a r l y moving s o u r c e s has been investigated in the literature. F o r a t i m e - h a r m o n i c m a s s s o u r c e [13] q = Qo e~'t ~ (x) ~ (y) ~ (z)

(7)

665

the solution of the inhomogeneous wave equation (4) has the f o r m l~Qo P--4~R

foil -- =,11-----g-exp

z

+ lo)t--

iR

V r

w --~,

2--o~7 g

where R 2 = x 2 + y2 + z z, ojc = ~gCOS#, cos ~ = z / R . s o u r c e s have an analogous form.

The perturbations for sinusoidal f o r c e (f) and e n e r g y (h)

It follows f r o m the solution (8) that emission takes place in two frequency ranges: (1)

% ~< o~ -.< ~og,

(If)

~0 ~ r

(9)

The f i r s t interval c o r r e s p o n d s to internal gravity waves, and the Second to infrasonic waves. In the f i r s t interval, i.e., for w < Wg, resonance growth of the disturbance field takes place on a biconical surface: (o

Oj;es_= a r c c o s - - .

(I0)

O)g

Outside the biconical surface with c e n t e r at the source (for Aces -< ~ -< ~ - Aces) the disturbances have a wave c h a r a c t e r ; and inside this surface they a r e exponentially small at large distances f r o m the origin (7). The d i s turbances produced by harmonic f o r c e s o u r c e s and energy s o u r c e s behave s i m i l a r l y [14, 15]. Observations have shown that low-frequency TIDs a r e strongly excited in the a u r o r a l zone. Calculations have indicated that the main s o u r c e of wave emission in this case is the action of the ponderomotive f o r c e f = (1/C)[JstH0] on the s u r r o u n d i n g gas [14, 16], where j is the c u r r e n t in the polar electrojet, H0 is the magnetic field, and C is the velocity of light. Two AGW generation m e c h a n i s m s o p e r a t e efficiently in this connection: 1) quasiperiodic e l e c t r i c a l c u r r e n t pulsations [14]; 2) supersonic motion of individual segments of the a u r o r a l a r c s [16]. E l e c t r i c a l d i s c h a r g e s in the troposphere, the flight and burnout of brilliant m e t e o r s in the upper l a y e r s of the e a r t h ' s a t m o s p h e r e , earthquakes, and both chemical and nuclear explosions c o m p r i s e impulsive s o u r c e s of low-frequency waves. In determining the disturbanc e fields in this c a s e it is n e c e s s a r y to int.egrate e x p r e s sions of the type (8) with r e s p e c t to the frequency w. Such calculations have been c a r r i e d out [n s e v e r l papers (see, e , g . , [17-.20]), At large distances f r o m !~pulsive s o u r c e s two signal s a r e generated. One of them is caused bY the generation and propagation of internal gravity waves at frequencies w -< Wg. The s p e c t r u m of the i n f r a s o n i c signal includes frequencies above wa:We have made a detailed study [15] of the generation of a low-frequency pulse in connection with the flight of a m e t e o r in the e a r t h ' s a t m o s p h e r e . In this case the disturbance s o u r c e was taken in the f o r m h--

$~ exp ~;~ a=L

(., r,) L=

(11)

a= '

where $0 is the total e n e r g y r e l e a s e d in burnout, a is the radius of the m e t e o r trail, L is its length, and 6(t) is the pulse time function. The radiated e n e r g y in this case is $ = SA + Sg, (T - - 1)'~o $A = 2(2=)31~PooC=a=L ,

(T -- !)'%~ $g---- 2(2~:)a/2pooc2a= L

Here SA is the infrasonic radiated energy, $g is the e n e r g y radiated by internal and P00 is the density of the a t m o s p h e r e at the point of maximum vaporization of f r o m (11) and (12) that in the case of a point s o u r c e (a, L--~O) h--)-g~(t)~(R)'the: bound. Numerical e s t i m a t e s based on attendant calculations show that about 1% ated in AGWs in the a t m o s p h e r e of earth.

(12)

waves f r o m the s o u r c e (11), the meteor. It is evident radiated energy grows without of the total energy $0 is r a d i -

The m o s t detailed experimental studies have been c a r r i e d out f o r AGWs generated by s t r o n g earthquakes and nuclear explosions in the a t m o s p h e r e [21, 22]. Ground MBG a r r a y s were used to r e c o r d and analyze infrasonic pulses and pulses of internal gravity waves a s s o c i a t e d with such explosions. F o r example, it was noted that the oscillation period of the p r e s s u r e in the pulse i n c r e a s e s linearly with the distance of the observation point f r o m the detonation site, On the other hand, a simple e x p r e s s i o n for this period is obtained f r o m theory: 2~:r '=D = --for >> hO, ~og ho where h 0 is the height of the detonation c e n t e r above the e a r t h ' s surface.

666

Segments of a r c s moving at s u p e r s o n i c speeds a r e often o b s e r v e d visually and optically in the polar regions during well-developed a u r o r a l activity. At that t i m e g r o u n d - b a s e d MBGs c l e a r l y r e c o r d p r e s s u r e pulses c o r r e s p o n d i n g to the s o - c a l l e d " s o n i c - b o o m " effect, s i m i l a r to those a s s o c i a t e d with supersonic flight. L e s s attention has been given to p r o b l e m s of AGW generation by j e t s t r e a m s in the t r o p o s p h e r e and s t r a t o s p h e r e , although a c o r r e l a t i o n is o b s e r v e d between the frequency of o c c u r r e n c e of internal g r a v i t y waves and the inception and disintegration of such s t r e a m s . G r i g o r ' e v [23] has e s t i m a t e d the efficiency of generation of internal g r a v i t y waves and t h e i r a s s o c i a t e d T I D ' s during w a r m i n g of the ionosphere by powerful radio t r a n s m i t t e r s . The f o r m a t i o n of a p p r e c i a b l e e l e c t r o n - d e n s i t y inhomogenelties in the ionosphere is possible in connection with the pulsed operation of t r a n s m i t t e r s with power W ~ 2 MW. The possibility of TID generation af the t e r m i n a t o r and during s o l a r e c l i p s e s is confirmed by e x p e r i m e n tal data and c o r r e s p o n d i n g calculations [24-26]. In both c a s e s the s a m e generating m e c h a n i s m is operative, namely, s u p e r s o n i c motion of the boundary between w a r m e d and "cold" regions of the a t m o s p h e r e . Thus, the theory of propagation of a c o u s t o g r a v i t y waves in an i s o t h e r m a l a t m o s p h e r e and in m o r e r e a listic models accounting for dissipation p r o c e s s e s and nonisothermicity has been developed in f a i r detail to date. Aspects of the generation of these waves have not been investigated as carefully, although [n the s c i e n tific l i t e r a t u r e c o n s i d e r a b l e attention has been given o v e r to the a n a l y s i s of various AGW e m i s s i o n m e c h a n i s m s . LITERATURE 1.

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.. 26.

CITED

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