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

(tropospheric arrivals) EXPERIMENTAL RESULTS (tropospheric arrivals)

Finnish military explosions (31) during August 16 – September16, 2007 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)

(stratospheric arrivals) EXPERIMENTAL RESULTS (stratospheric arrivals)

EXPERIMENTAL RESULTS

AZIMUTHS

TRACE VELOCITY

Averaged azimuths of stratospheric arrivals (33 explosions, different time)

normal mode code high-frequency approximation 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  (z = h) = kcos (z) dz = (wl - wl-1) = k f; phase shift due to fine atmospheric structure  = (-1)l { 1/(6wl) cos(2kl) (ql - ql+1)/ql+1 } ; l = ( cos3 s +1- cos3 s )/qs+1;  =900 – 0 ; ql  n2(z)/z ; wi  (2/3) t 3/2 = cos3( i ) >1 (high- frequency approximation)

THEORY С phase = (Co / cos 0 ) = 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

normal mode code high-frequency approximation 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 [<( )2>]S1/2  8 0 Stratosphere _____________________________________________________________________________ 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 _____________________________________________________________________________

due to effects of anisotropic turbulence 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

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