Документ взят из кэша поисковой машины. Адрес оригинального документа : http://acoustics.phys.msu.su/teachers/gusev_files/rao24-1.pdf
Дата изменения: Wed Nov 7 11:25:28 2012
Дата индексирования: Sat Feb 2 23:12:58 2013
Кодировка:
XXIV ,







. . , . , 0.1 - , = 0.2 .

. 5 . 6. ( 09_02_01239 11_02_00774), " - 20092013"( . 02.740.11.0565), ( 3700.2010.2).
1. Handbook of Acoustics, Edited by Malcolm J. Crocker, John Wiley & Sons, INC, 1998,1461 p. 2. Witham G.B. Linear and Nonlinear Waves. N.Y.- Sydney-London-Toronto: Wiley, 1974. 3. .., .. c , // .. 2004. . 174. 9. . 973­989. 4. Lili Ganjehi, Regis Marchiano, Francois Coulouvrat, Jean-Louis Thomas, Evidence of wave front folding of sonic booms by a laboratory -scale deterministic experiment of shock waves in a heterogeneous medium , J. Acoust. Soc. Am., V. 124(1), 2008, pp. 57-71. 5. Michael S. Canney et al., Acoustic characterization of high intensity focused ultrasound fields: A combined measurement and modeling approach, J. Acoust. Soc. Am., V. 124(4), 2008, pp. 2406-2420. 6. Bajram Zegiri and Antony D. Bond, The influence of waveform distortion on hydrophone spatial-averaging corrections ­ Theory and measurement, J. Acoust. Soc. Am., V. 92(4), 1991, pp. 1809-1821.

534.222

.., .. -
. .., , , 119991, , .: (495) 939-2943; E-mail: vgusev@bk.ru
. , ­ , , N-. .

161


XXIV ,





. .

. , . «» ; . , . . , , , . , , ­ . ­ . , , . = b 2c0u0 . , << 1 , . (., , [1,2]). ­ -, , , . . , . , , , . . , . , , - , , . . , , , ­ S ( z ) [3]:

V V 2V (1) -V = S ( z ) 2 , z V , z - , . S 1 (1) . (1) . , (2) (3): 1 2 (2) + ( ) = (x, y, z ) , x 2 u b 2u . 1 u u (3) + = + u + + - 2u 2 c 3 T 2 2 x x c0 T 0 - , - , - , - . (3) , b . , (3)

162


XXIV ,







u -2 x c0
. V = u ,

u

b 2u , u u d (4) + ln = 3 T 2 dx 2 c0 T 2

z=



x

0

dx



(4) (1),

S ( z ) = ( x( z )) .

, , . , (1) , . , - (1) . [4-6] , (1) S ( z ) = 1 + z z0 . (4) . , , (1) S ( z ) = (1 + z z 0 )a , a - . , , ( a = 0 ), , . (1) S (z ) = 1 + z z0 , [6] , . : A 8 , (5) ( , z ) = A th 1 + 1 + 2 A z0 1 + z z0 4 A - . , . (5) , N- [6,7]; , . S (z ) . . * = , , [3,8]: V 2Vint, 0 D* . (6) = 0 , Vint,0 = D th Vint, 0 int, 0 + 2 2 * * , D . , , . : (6) ,

2 (5) . : 2V0 V S V0 (7) + V 0 + * =0. 2 * * z * dS dz , (7) (6), . , (5). , (7)
0

1 + 1 + 8 A2 z

(

)

163


XXIV ,







(5) [6,7], : A 8 dS . (8) 1 + 1 + 2 V0 (x ) = A th A dz 4S , , , . . 2 < z < 2 . , , , , ­ , z 2 . z > 2 . , . (8) ­ . ( S = 1 + z , A = (1 + z )-1 ) zlin ~ 1.5 . , , (1). , . . , , . , , . ( ) , . , (1) V z . : -2 2 1 . (8) - S ( z ) + V = S ( z ) V V V V 2 z , Vmin , ­ Vmax . , . , , . (8) V Vmin Vmax . V . V + Vmax . (9) = - min z 2 , , . (9) , . , ­ . , , , . Vmin = 0 . , N-, A , . S = 1 + z . , A ~ (1 + z )-1 2 , ~ (1 + z )3 2 ~ 1 + z . ~ (1 + z ) 1 z ~ 1 , .. 164


XXIV ,







( z ~ 1 ). , . N- , ~ , .. N- . [2] Re = A S ( z ) , ­

. . S ( z ) A , .

. , , : 1) , 2) , 3) . . ­ . , . . . (1), . . . , , ( Re >> 1 , ), (1) ( Re 0 , ). ( -4590.2010.2) ( 09-02-00925-).
1. 2. 3. 4. 5. 6. 7. 8. .., .. . .: , 1975. .., .., .. . .: , 2008. Enflo B.O., Rudenko O.V. To the theory of generalized Burgers' equation // Acta acustica, 2002. V. 88. P. 155-162. .., .. // . . 1968. .4. 2. .. // . . 1970. .6. 2. .., .. , // . .1. . .: , 2010. .., .. , // XXII . .1. .200-204. .: , 2010. Gusev V.A., Sobissevitch A.L. On a problem of propagation of shock waves generated by explosive volcanic eruptions // Nonlinear Acoustics ­ Fundamentals and Applications. International Symposium on Nonlinear Acoustics ISNA-18, 2008, Stockholm, Sweden, pp 397-400.

532.529.6 .. , ..

,
«- », , 603950 , . ., . 25/12, . (831) 436-72-94; (831) 436-99-02, -mail: rf@nirfi.sci-nnov.ru, .
, , .

, . .1 , 165