# Faits saillants

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"Faits saillants"

```					Effects of atmospheric turbulence
on azimuths and grazing angles
estimation at the long distances
from explosions
Sergey Kulichkov
Igor Chunchuzov
Gregory Bush
Elena Kremenetskaya
Anatoly Barishnokov
Supported by RFBR, project No. 08-05-00445
OUTLINE
___________________________________________________________

     INTRODUCTION
     EXPERIMENTAL RESULTS
     THEORY
     high – frequency approximation of normal-mode code
(fine-layered structure of the atmosphere
     theory of anisotropic turbulence
     CONCLUSIONS
INTRODUCTION
   phase velocity Cphase = C0 / cos 0 ;
0 – grazing angle
   Cphase = C0 / cos 0  C0 (sound velocity at the
earth surface)
   sufficient variations of azimuths of infrasonic
arrivals and grazing angles are observed in
the experiments
   effects of fine atmospheric structure
   theory of anisotropic turbulence; normal
mode code
EXPERIMENTAL RESULTS
(tropospheric arrivals)
Finnish military explosions (31) during
August 16 – September16, 2007. R=303 km.
‫‏‬
Signals spectrum
Effective sound velocity
18.08.2007 (rocket data)
Acoustic field calculated by TDPE
code
Infrasonic signals
(theory- TDPE code; experiment)
TROPOSPHERIC
ARRIVALS
(azimutes and trace velocity)
Corr>0.8
Corr>0.9
STRATOSPHERIC
ARRIVALS
(azimutes and trace velocity)
EXPERIMENTAL RESULTS
(stratospheric arrivals)
EXPERIMENTAL RESULTS
AZIMUTHS
TRACE VELOCITY
Averaged azimuths of stratospheric
arrivals
(33 explosions, different time)
THEORY
normal mode code high-frequency approximation
______________________________________________________________________________________________________________________

coefficient of reflection
V = exp i{2 (z = h )+ /2 +  (h)}  exp {i};
phase of the coefficient of reflection
h( )                     m
 (z = h) =     kcos (z) dz =  (wl - wl-1) = k f;
0                      l 1
phase shift due to fine atmospheric structure
m
=              (-1)l { 1/(6wl) cos(2kl) (ql - ql+1)/ql+1 } ;
l 0

l =
2 l 1
        ( cos3 s +1- cos3 s )/qs+1;                         =900 – 0 ; ql  n2(z)/z ;
3 s 0

wi  (2/3) t 3/2 = cos3( i ) >1
(high- frequency approximation)
THEORY
normal mode code high-frequency approximation
__________________________________________________________________________

С phase = (Co / cos 0 ) =
(Co / cos o)[1+r (/ sin2) /( k  r/ sin2 ) ]
The value of phase velocity depends from the value of additional parameter

r (/ sin2) / ( k   r/ sin2 )
It`s possible that

С phase = (Сo / cos 0 ) < Co
THEORY
normal mode code high-frequency approximation
_____________________________________________________________________________
THEORY
anisotropic turbulence
_____________________________________________________________________________

tg= x1 t2/(y2t1)–x2/y2; (0,0), (x1,0) and (x2,y2) – positions of different microphones 1, 2 and 3
t1= t2–t1 и t2= t3–t1
The errors of azimuths calculation depends from the fluctuations of t2 and t1 ,
t2=t2 -<t2 >= (t3–t1) – (<t3 > - <t1 >)  3–1
 (tg)/ <tg>=t2/<t2 >+t1/<t1> 2 t2/<t2 >
{< [ (tg)]2>)/(<tg>)2 }1/22 [<(t2) 2>/<t2 >2]1/2
for tg  
[<( )2>]1/2/<> 2 [<(t2) 2>]1/2/ <t2 >
[<(t2) 2>]= < (3–1) 2>= D(z0=0, y0, T=0)
THEORY
anisotropic turbulence
_____________________________________________________________________________
Stratosphere
m* = N/(21/2) = 0.02 rad/s/ (21/2 5 m/s) = 0.0035 rad/m
L = 2/ m* ~ 1800 m – external scale;
N – Brent-Vaisala frequency
e0 = 0.026
e0m*2ym2<<1)
D(0, y0) 6<12> (e0 m*2ym2)
 = <vх2>)1/2 = 5m/s
< 2>s = 0.078 [sec2] (  0.1).
D(0, y0)  6<12> (e0 m*2ym2)  3.3510 -3 s2
(D)s1/2  0.057 s
<t2 > ~ 0.9 s
[<(t2)2>]1/2/<t2>= 0.06

[<( )2>]S1/2  8 0
THEORY
anisotropic turbulence
_____________________________________________________________________________

cos()={(c0t1/x1)2+[c0t2/y2- (c0t1x2)/(y2 x1)] 2]} 1/2
t22<<t12
cos()  c0t1/x1, sin()    [1-(c0t1/x1)2] 1/2.
  (c0/x1)2 t1 t1/[1- (c0t1/x1)2] 1/2  (c0/x1) t1/sin(),

(<2>)1/2 (c0/x1) (<t12>)1/2/<sin()>

[<(t2) 2>]= D(0, y0) 3.3510-3 s2
R= 300 km
(<2>)1/2(c0/x1)(<t12>)1/2/<sin()> =
(2.27) (0.057)/(0.57) ~ 0.227
 = 350
S ~ 130
EXPERIMENT
_____________________________________________________________________________
CONCLUSIONS
♦ The effect of the atmospheric fine structure on the azimuth and grazing angle of
infrasonic signals recorded at long distances from surface explosions is studied
both theoretically and experimentally.
♦ The data on infrasonic signals corresponded to tropospheric and stratospheric
infrasound propagation from explosions are analyzed.
♦ The experiments were carried out during different seasons.
♦ Variations in the azimuths and grazing angles of infrasonic signals are revealed for
both the experiments carried out within one series and carried out during different
seasons.
♦ It is shown that, due to the presence of atmospheric fine-layered inhomogeneities,
fluctuations in the phase of infrasonic waves mainly affect the errors in
determining the azimuths and grazing angles of infrasonic signals.

 ~ 50 ;  ~ 100
due to effects of anisotropic turbulence
THANK YOU
FOR ATTENTION

```
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