close

Вход

Забыли?

вход по аккаунту

1233584

код для вставки
Etude de quelques aspects du transport éolien des
matériaux granulaires: Processus de saltation et
formation des rides.
François Rioual
To cite this version:
François Rioual. Etude de quelques aspects du transport éolien des matériaux granulaires: Processus
de saltation et formation des rides.. Physique [physics]. Université Rennes 1, 2002. Français. �tel00199032�
HAL Id: tel-00199032
https://tel.archives-ouvertes.fr/tel-00199032
Submitted on 18 Dec 2007
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
N
Ordre : 2686
TH SE
pr sent e
DEVANT L'UNIVERSIT DE RENNES 1
pour obtenir
le grade de : DOCTEUR DE L'UNIVERSIT DE RENNES 1
Mention : Physique
PAR
Franois Rioual
quipe d'accueil : Groupe Matire Condens e et Mat riaux
cole Doctorale : Sciences de la matire
Composante universitaire : U.F.R. Structure et Propri t s de la Matire
TITRE DE LA THSE :
Etude de quelques aspects du transport olien : processus de
saltation et formation des rides
soutenue le 25 juin 2002 devant la commission d'examen
COMPOSITION DU JURY :
M. GUYON Etienne
M. BIDEAU Daniel
M. VALANCE Alexandre
M. CLEMENT Eric
M. COSTE Christophe
M. RASMUSSEN Keld Roemer
Professeur, Universit Paris XI
Professeur, Universit Rennes I
Charg de Recherche, Universit Rennes I
Professeur, Universit Paris VI
Ma tre de Conf rences, Universit Paris VII
Professeur, Universit d'Aarhus
Pr sident du jury
Directeur de thse
Co-directeur de thse
Rapporteur
Rapporteur
Examinateur
! "
# $ %
& ' & ( "
) & & * $ #"
) ! * # & % + , * & " - $ * #%
$ & # " . & * # " . # * # / & * $ 0 1 " # * /& 2%
* $ # 3 / " & " 0 , %
& $ * %"
* !& & 4 4 # #
$ * 5%
# 6 ( 7 & 3 / # + 8 * & & 6 ( & # " . # & # ." + " +* $ 6 ( 7 & 3 / & & % 3 / 6# 9::; * 8 ( %
& ,& / < < , # 2 # # # + "
- $ # & " # $ 0 & & $ = #
& * $ > "
4 # """ # 5 """ 7 # " 7 & "4
- '' 9?? @@A''' 9: @@@ 9?"
- # !& & B # C # " & $ 0 "
) . D # %
# E !& # , %
"
)$ $ A # & # %
& " F # 0 " '
!& & G# &" D & * # # $ # $ 0 * $"
) & "
) , # & * ," + -
# & * .""" " (
# $ " + - - " ) H 0 & * $ #"
. !& + $ 3 + / . 8 %
# & # ! $ # * ! $ "
+ # $ & 4$ # 4 "+"-"+"
& * ! $ # %
' ' B# & *0 C ' - ., + )% 7 "
) $% $%7 / I H D J & # , * & #
= 6 D $ "
* $ $ & , ( D . / - & E "
)%- . &
+ D + 4+ # 4 *%# "
) # %
E , %
+ " + * , & # & # &
E # * " ) 8 , 6 ( 7 & 3 / # " ) %
K $ B# C . + +* $ %
6 ( 7 & # 3 / " )
4 4 * ( %
. + + & 4 4 * ( . "
+ $ & + %
) + - + 3 / "
) # # # %
& " ! "
%
.
&
! " # $ $ ' ( ) % , - %
$ % ( ) %% ! %. / %& 0 10 .
2 # . /" 3 .% 4 .. , ' , , " 13 " 13 %
&
&
*
+
%
&
%
%.
%&
%+
%
..
..
.*
%
4 5 3 , 1 6 78 , % , 9: , , %
%
%%
%.
- " % % % % ' $; %
' ; 1 , < ! = , % ' ) 7 ) > ) = ) - ) $; 1 %%
' ; 1 , < ! = %% ' ) 7 ) > ) / ) = ) - ) - $; %.
' ; 1 ? ! %. ' ) 7 ) .*
.
&
&
&%
&&
&*
&
*
*
**
**
*
*
%
%
.
&
&
+
+.
+&
+
.
.
.
+
%
.
*
*
*
*
*
%&
%*
%
413 , " , .
.
.%
..
&.
*&
**
#
+
! " $ %
' /" 5 3 = = 3 *.
3 9 @A
*. 3 71 @21
5 3 1 *&
' 3 *& = *&% = @ , ' 3 / / &%
$; &% $; 1 &%% - , *
*
*%
*.
$ - " .
' ; 1 . ' ) 7 ) > ) > 1 : ) / " ) - , &
&
&%
%
+
+
.
*
#
%
%
%&
%&
%+
&
%
.
.
.*
.*
.+
&
&
&.
&*
&+
- B1 *%
/ 1 B1 *.
/ 1 *.
%
.
&
/ - C , ' ) ' ( *
*
##
*
D D E 3 " "
F -
;
, 1 1 3 1
D 1
)D F D F 1 D D 13 D D @
1 @
3 - D " ,"@ 1D D F ) "
D 3 , " E1 1 ,
! )
1 1 @
1 F D
" / D G1 D H F 3 1 =D D ; D 1 - D F D 3 D " 3 - 3 D 1 :
F E ' D 3 " 3 " D "
=D " ; 8 "
G
F 7 @4 B HD " 1 )F F F
"@
"
! 1 I G 1 3H GF 1D 3 B 3H 9 C 3D 1 F 1 3 0
B1 0 G H @
) D
D ) = F
1 )
! 1 5 D 3 D F D 3 D 1
3 I
- D @
3 1 , G " 3 7 B1 5 H G D H $ E D 1 1 = D 13
F 7 D D
@
13
1 7 3 J D 3
) , ) "
F
1
) )
1 3 3 1 /D @ GD D 5 H
C F 1
1
! 1
D 1 3 ) 1
3
1 " 1
D F "
- 1
1
3 13D D - 1
D 3 1 @
) , 3 -
1
F 1 3 1 7 D D
"
3 /D D
1
@
"
3 1 @
D 5 D , K C F D
=
/
3 / D D D F 3 C = 7 3 L =3 ,
@? D F E
D / ? 1 G D . H 1 ! D 1 D " = 5 ) D E D ' D
D 3D " D D D E D M D
=D I 0 D 1 ! D 0
$ D D ! 4 0(1 1 8 0D D " ) 1 3
' D 3 ! "@
3 3 5 N #D D
F 1 D D F D @
F ) 3 3
3 # D "
D 2 3
" = G= D H G= D H
- 1
D ! 2 @
2
? 1 1 D F 2 @
/ !D @
D 1 D ) ) 13 , 3 7 7 ! D D 1
D @
! "
, ) 1 3 2 F F 3HD F K F G @
3 - 1 1 D D D E
/
!D ? G
HD I
' H
F 1 G
G
H F @
D ? D 7 @4 B G GO D H
H - D I
K
; D
D
; - G H
G H
3 F D ? ) " I
G H
#
K
1 : D
1 : ' D : D ? F I
/ D I / D K
F " I
1 @
1 G' D %&HD D I
K G .H
? ' D - " G %H
> Q G .HD ' P F G
G &H
H / G &H I
G *H
Æ Æ ! K
$
D I
G H
D ' 3 D 2
1 J R
D D F ! I
+
, F F ; I
K
D
3 ? R
+
, F D
D < 6 G5
=" D H
D F G! H I
F ? G H
< , 1 3 @ D D E R
+
J ! 1 K
G +H
F ! 6 F %
Z
U(z)
Force de portance
Force de trainée
x
R ! !
0 I ! 5 0 00
F ) E F G H , " 7 ! E ) GA1 41:D H
( "
D "
? 1 G D . H $ D D
1 1 1 3 F
@ "
# - 1 D & '(
1 3 1 ) ' D
E ! 1
1 3 3 1 3 , @ F
1 S
2
; @
6 F 1 ; # F =
D ; J F 3 1
1 " ; J F 1 ;
' D 1 4 " D !
; 1 ' F ; ,
D 1D
@
F ! " # $ # % # # & ' ( I D D ! 1 : 4 1 : 1 1 D ! 1 D : 3 E ) 4 4 2 D " , / D I
@
@
H G
13
G
H
F 1 : 3 @
4 4
F D
, G
H
"
# D )F "@
& '(
Suspension
Saltation
direction du vent
Creep
Lit de sable
R ! ! I ( 4 D F
D
I F 1 D 1 < 2 D I
? F D
D
G H
I
; F " I
I
G G K
H 2 HD
G H
FL
FD
O
P
% R O F α
FD
P
O
. R O F G %H I
2 G H
I
; ! ' ! ! < G %H
[email protected]
? 3 "D & '(
= )
D "
F
D # - N1 1 D
F # ' : D N1 ) [email protected] F D D ) F 1 F ; 1 3 , " E
, "
6 ! '- ( # F , ! &
! / D " 1 /
@ 1D F 1 #
@ D F K ) " * + 10
VHXLOG LPSDFW9 9
1
H (cm.)
2
k'
0.1
2
k
0.01
0
1
2
3
4
5
6
7
8
9
10
11
12
V (m/s)
& R ' D @ 1D @
G H G H
# ! / D #
F = 1 D F
#
F ) E F
' 6
F
#
F
#
1 F D F , F 6 !
. " J ) E
F
#D F 1 ,@ F 1 1 G *HD @
, E 3 4 #D & '(
"
Trajectoire
V1
W1
V2
Envol
W2
Impact
* R ( ) @ G 1 : H @
G Æ F Æ H
2 ) G *H , E F
3 4 $ D
%
1 %
- D 1 : F
G .H
1 : D
$
, " &
F I
G &H
< 4 I
$
4 1 : $ D D 1 3 F M &D
3 G *H
#
, " ) D 1
I
I
' G H
F @
% ' G +H
;" D I
J ;"
D - ( D " ( " D F I
G H
F " ( ' I
, F " / D
F G H
F 13 1 / " K
F 1 : D
2 D
$ ' '
' D
3
' K
"
D
G H
* '(
,
$
;" F ) ; / D = 1 #
(
D ; =
D / D F " ¼
@
1
13 ) ;" - 3 @
1 1 3 G D . H - D 13 "
' D F 13
G D . H N D
= ) D - 3 1 D %
E F D 7 D D 1 1 4 D "
< GD
HD
D 4 D F ! 1 , D "
D D
GA D +H < F ; GA D +H , ; E D
! D
@ 1 1 GQ D *H " E 1 G 7D *H
/ D < F
"
"
4 "D G D D
3D
H 3 G7BD ++H
D 3 D I E 2
D F " I
! G H
* '(
K
! R ! < D ? 3 , G H " $ F
!
! 3 3 G
" " ,1 $ G,1 D .&P $ A1D +P $ D +HH ? D ; #
9 '1 F 7 G' ) D H
= 3 D ,@
" < ) D 3 "
D ) D F I D D D ! ' " ) D " @
D D I
/ ) I
$
$
$ K
1 : D
$ /
I
2
6
$ 1 : G .H
@
1 D @
13 GH G ) : 3 1 K $
" 1
G %H
! C 1 H
GH F
GH /D 1 : G
=
1
)
H
13D 1 %D ) I
$
% $ $
$ )
$$
G &H
G *H
G H
* '(
$ $
' $
D
D " 3 I
$ $
3 $ $ $ $ $
D )
- 3
$D
F D 3 " G +H
1 3 1
- K
$ " I
$ % $ $$$
$ $ $$$
$
)
2 E " 3 F , " %
4 "D " )
"
Æ
$
G % H
D
= D ! < G %H
G H
! = G= 9 !D ++H
) - 3 1 D E F D 1 D )
F
D ) J 9 ! GJ 9 !D +H ) D ' D < GD F K
H : D D 5 D " 0 0 3
" "
" 4 D 0 0
3 ;" ' D ) C
D D " ! D D J ) G G(: D +H 1 D ! I 1H =D ( D "
@
" ;"D ) D " ! ! ) ) C , 1 9 ! GJ 9 !D +H
! 00
E
* I D F J ' D
* '(
0 10
)
3 G D ) H 7 D # $ D - K F #D @ , " < D D
) D F D 2
D F - D
D D D D 3 "
F I ;" 1 : F $ E ) D F
D I I $ 1 F D - D ) D , ! @
; ;" - " F ! @ D 2
! , D " K
F F
G D . H F 1 1D @ ) 28 G28D *.H 1 I
-! F G %%H
I
F D
HD ! " / G %H
G %H
K 1 " I
G
I
K E 3 G H ,
! D 3 GJ 9 !D +H G= 9 !D ++P AD P = 9 !D P 5/8 AD H @
J 9 !
GJ 9 !D +H D D
1 D D ! @ * '(
"
@ F
3 , " [email protected]
9 ! G= 9 !D ++P = 9 !D HD 5/8 A
G5/8 AD P 5/8 AD %H 4 G4 D H 3 G H )F , 3 E M I
R G 1H D
R ) R R
D
; D
D ) D
R 1D " ) D
R ) % ! D F D ;" , ;" 1D ;" " ! 3D F " 3 - 1 D 1 #
MODIFICATION
DU
PROFIL INITIALE
DE VITESSE
PROFIL DE VITESSE
DISTRIBUTION INITIALE
DES PARTICULES
RETROACTION
CALCUL
DES
SEUIL D’ENVOL
TRAJECTOIRES
FONCTION
SPLASH
7 D 3 D ;" 4 + R ' 3 2 D
D +H
(
'
D
G ' G %.H
4 G4 D H I
K " D
" D ( ' '
K
# " D
D
G %&H
I
, G? 5BBD P 4 D H [email protected]
( D @
;"
F ;" ++
$
1 G$ ?
D H , @
F 4 D H , " G D +P 4 D P
3 K G= D H
- D ! - ) ?:D +H D
) D - D 3 0 0 G(1 Q 8 D P
) E E ' E S
, @ - D 3 F
I F K 0 10 D ;" ! = D ? G? D +&H
3 D !D G "
- H
D "
D , # - " " " " %
! - ) , 3 G= 9 D +*P J 9 !D +HD
1 3 ,
E 2 1
I
R
#D GA1 41:D P A ?D +*P
A ?D ++P A ?D +P 5 /8 D P ? D &P
? D *P 7
R
"
D %HD
3 1 G51 D +*P
AD +HD
R
GA 9 !D ++P = 9 !D ++P = 9 !D H
7 " ! @
#
& 7 "
"
- "
# D 1 1 F " I ) 3 F @
F
L ( E
A1 41: D F
) @ F " D
D / ) ++
D D Æ
C @ Æ $ Æ Æ " " F +*H = 9 G= 9 D
A1 41:
, D ) D "
@
) I
D
C F G %*H
L A ? GA ?D +*H D
$
D D
;
D "
3 I 3 D
: G 1 D H
Æ $ 3 D Æ F Æ
" 1 "E $
1 ,( D Æ F Æ D
3
- . &
3 1 D ) $ ,( , M D F H G
3
GD H $ ( ) G K
HD 1 %
) ) 3 / ,( ,/ Æ $ ! ( / - D 3 ) 6 ) D Æ
1 3 E ; , GA ?D +HD
Æ Æ D
F " $ 1 ) , $
K F - . &
Æ
F 3 - E ,(
! D F D 1 , 3 $ D D ! ! G? D &H $ ) D F $ ( / ++
D ) ) F F ' D G?
D *H $ D F !D I E D " 1 3 " $ ( / F
@
6 6 ) I 3 8 D ' D # G7
D %H
( , Æ Æ D ( Æ Æ D ) 6 F D G D . H D 2 1 #
"
I
=
A1
41:
A
?
7
D 9
' ( > =
>
"
Æ
D.
"
Æ
Æ
=
Æ
Æ
Æ
'
) > ) = ) Æ
=
A ?
# $ '
7 D "
3D
= D " "D A GAD H 51 G51
D +*H
@
L A
1 3 GAD +H
1 GAD H $ 3 F )F Æ Æ "D
/ D - . & @
D
F $
,/ ( /D I @ , K
, 3 +
I
G %H
F ) + - "
"D
D @ @
D D ( / +
Æ F 1 G H @ 13 @
51 ++
)
G51 D +*H 3
D
D F
1 F
1 ) D
@
1 D
/
D 51 . &
1 F 3 I
- 6 / F Æ F F Æ ( / Æ - ) D D ! ) ) ! / 1 1 3 % # ( 7 7 F D F AD 9 ! = "
@
L 8
" GA 9 !D ++H
A 9 ! F " E 1 $ @ D "D 1 / D @
1 D I D D ) " @
8
G= 9 !D ++P = 9 !D H
1
= 9 !
1
G= 9 !D ++H $ -
@ G < H
1 $ )
E
D
H
Æ I
,( F )
. . .
( / 3
' D = F - . &
-
" , G <
- 3 D G %+H
! Æ D +
I
+ / /
- .
D ,/ I
!D
D
@
.
) F ++
"
R 1 "
= I
+ ) )
- D ,(
G , G=
! ,/ Æ $
) -
3 6 <
< ' D D Æ H
9 !D H 1
G %H
3 ) D !3 1 I
) . . G .H
#
)
K
D
/
.
-
I
D ) + / G / H -
' K
D 0
D
.
D
%
D ,/ 3 ! I
0 %
G . H
G H ) I
D ) F "
#
F F @
) D F ; 1
## , ! "D 3 G H ) F
E
3 ! D 3 " I 3 D Æ / ) D F ) ) 3 1 , E F M D 1 $ 3 @
GA 9 !D ++P = 9 !D ++P = 9 !D
) 0 $
111
000
000
111
000
111
grain réfléchi
en saltation
Vr ~ 0,5 Vi
grain incident
en saltation
θ r = 30°-40°
grains éjectés
111
000
000
111
000
111
Vej < 0,1 Vi
θ ej
Vi
θi
= 60°
= 10°-15°
LIT DE GRAINS
R 413 1
H " "
" " F -
1 F
G= 9 !D H J "
"
3 /
1 1
@
D ; @
) 1 Æ , " "
) C "
; 13
) , "
D 3 D ; 1 ) , 1 @
%
#D 3 "
1 3 D
3 3 @
3 F /D D
F D 1
, F 1
1 3 F , E
D @
, 13
7 1 1 1 D D " 3 / D ) C 3 C 4 D
D D !D 1D "
3
C D 3
" F "
F D D F
D D 1 I D @
: 6 " " D
1 : : 3 D
" " 3 4 3 1 :
' (
D F D G D G D . P
D P D &HHD 1 D 2 D D D
) 0 F I 1
D F D
D @
* F 3 F F "
- ED 3 1 3 3 1 3 1
1 D ) F ,
I 1 G4 D H , E F 3 GQ D H 2 D D E 1 ! 04 10 I / @
@
1 3 " / @
- 1 " D 3 1 " - "3
1 D E F G HD F
G @ H F @
1 , D D D - 1 " D 3
) C -
D D D F " " - " D F 7 D
1 3 1 6 1
D
! 1 " ' "
( (b)
(a)
F
δ
O
F
R G H I " D
G H I " Æ
" I 3 78 G078 "
0H 3 " / G D +H /D @
D
D 1 @
, "
1
- "
%
! " )' D 1 1 @
/ " / D G 12 H 2 )
" < ,3(
1 F @
< ' F " - " D 6 F D 4 Æ
" 13 D 4 @
" D 12 I
1
2I
Æ2 / 1
1 D I
G H
13 13 2
1 3 D
1 Æ
1 2
1
: I
, D 1 4 G9:D +*HD
Æ 2 I
GH
G%H
12 Æ
( D F D " 3D 1 D
D I
K
1 1 1 Æ
1 Æ Æ G.H
G&H
1
G*H
1 1 D 2 " 1 Æ
" 1D Æ Æ
Æ I
H I
G+H
/ D GH
G
1 I
( Æ
Æ
F " GH
1
I
G H
1 ' " :D # 1 2 4 D " F I Æ )'
/
- 1 D 1 1 D 1 ) 1 9: 1 J ! " ) 1 / D 3 2 1
1 @
< -
"
I
- G
H
K
"
" 1 K
-
F K
-
3
, < 1 ' D < " D D /
@
@ /" ! 1 @
BC # &$
, / F "
, ; J "
E 3 $ 3 9: F " @ J " < E
K
- GQ8
@
- G H
BC .* &
- ) 6D D D D ) Q D +H I
@
! @ = 1
F D D : T 1 GT 1 D +&H
" . - @
#
I
( 3
1 G %H
D 3 " 13
1 U 1 < " 13 I
1 1 1 2 D " D D K
D "
1 < I
- G? D +P O 1D
*H
@
BC * &
- 1 9:D F
F G? D +&P - -8D &H I @
B#C * # G$ < G F 3 D 3 H D < 2 D !D 13 @
< 1 4 D 4 G1 V GVD
;" . HH
B#C $ W F F $
M 1 D D !0
$
3 < %
) "
D K < 1 ! @ D 7 "
3 5 8 G5 8 D *HH " 13D "
3 G D .H G 3 " 5 8 " "
I
@
D " 13 1 @ ' D 3
@
3 F "
@ - D F I
-
- @ - ( @ - & =
3D 3 3 D
F 13
3 1 1 7 3 I "@ " # - " " / 0
)%
K
" )
5 5
( 5 5 G .H
G &H
) 1 ¼
) 13 5 D 3 1 5 - 1 GD HD 3
I
G *H
GD HD I
5 - 5
"
- - H 2
3 G D
5 5
G H
" 5 , 5 G H
F 3 "
! - D ! 3
" G H ;" ' 5 5 - 6 1 "
, " "
- 1 " D
3 @
" 3 1 , )
ψ2
: courbe theorique
2
: courbe theorique
modele de Maw, Barber, et Fawcett
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
ψ1
-0.5
-1
Regime
sans
glissement
Regime de glissement
5
R , 1 HD 3 5 8 G H
5 I 3 G )
1111111
0000000
0000000
1111111
0000000
1111111
0000000
1111111
Vo
0000000
1111111
0000000
1111111
0000000
1111111
0000000
1111111
0000000
1111111
0000000
1111111
0000000
1111111
0000000
1111111
0000000
1111111
% R /"
) (N-1)
(N)
1 6 78 ' )
J (N-2)
(2)
(1)
( 1 3D ! 3 13
, " 01 6 78 0 7 1 F @
) C 1 F ! 3 1 = 3 1 6 78 D " 3
F - I )* +, 1 6 78 G 078 0 H
"
1 1 6 / D F " F , "
1 6D "
F ' < 1 6D 1 @ D 1 6 3
" D " D D
3
' )
3D " 1 6 2 F - F D F 1 ( D 1 6 F K 1 6 F ' D 4 @T D H "
1 6D D 3 13 13 91 G91 78 D 1 1 6 " 3 "
D 1D F
F
! F 1 G H 1 =D D 1 E 1 6 G9 4:D +H
2 3 D 1 1 +
"
2 F 1 : 5 :1 G 5 :1D H @
1 G D .H
3 F
$ < !
+
3 13 3
I
G +H
)
( h
(1)
Vo
do
(2)
(3)
(N-1)
(N)
O
. R ,
+
3 -" 4
+ D
+ K H F G
+
< !
3 F 1 ' 4
+ D F 1 D E 1 6 1 6 - D < ! 1 @ 3 , ! D +H $
@ 1
"
1 "
3 / G D ! [email protected]
))
13 G D .H 4 3 @
@ " I
GD
#Æ
G H
@ Æ Æ H F !
# # #Æ
# #Æ
F I
@ GH
= @
F 6 !
- K
D 13 ! 1 I 0 0 6 D F G D H
2
3 ! D @ 4 D "
1 : G &H = 1 6 78 D ) C 7 F E D 1 6 13
D ! 1 D ; 1
1 : )
( 1111111
0000000
0000000
1111111
0000000
1111111
0000000
1111111
0000000
1111111
0000000
1111111
0000000
1111111
Vo
0000000
1111111
0000000
1111111
0000000
1111111
0000000
1111111
0000000
1111111
h
(1)
(2)
(N-1)
(N)
O
& R ,
1 2 11D D F 6 < !
2 F %
D
1 2 @
D 3 @ @
" I
#Æ . Æ
Æ
K # # . D
1 . G H
< F < -
2 D
3 D ! @
1 ) ; 1 )F )"
0.7
N = 10
N = 50
N =200
0.6
0.5
Vi
f
0.4
0.3
0.2
0.1
0.0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
o
n de la bille
* R >
= 3 D @
3 1 G +
H
A 4 *D 3 D 2
D +
=
6 1 1 G D
+H
@
+
1 1
1 I
)#
( 1.0
0.9
0.8
Etot
0.7
0.6
0.5
0.4
0.3
0.2
0
20
40
60
80
100
N
R X @
1
+
+
+
- 2 * + <
GD
GH H GH )F H
+
3 I
3 D F P
) D ; 1
3 P
GH @ !
G
)$
1.0
0.8
eeff
0.6
0.4
0.2
0.0
0
20
40
60
80
100
120
140
160
180
200
N
+ R ,
+
< !
< !
G
H +
6 , < I
D !D + )F ; 1
K
E
1 "
+ +
I
++
K
/D < ! +
F 1 , D GH
%
$
1 2
4 ! 9:D F 1 @
%
( 1.0
0.9
Loi d'interaction linéaire
Loi d'interaction de Hertz
0.8
0.7
0.5
Vi
f
0.6
0.4
0.3
0.2
0.1
0.0
0
1
2
3
4
5
6
7
8
9
10
0
N de la bille
R >
3 D GÆH 9:
+
G¾H D " "
2 ! G H %
3 1 9:
E F 1 3 - 1
1 2 3 - D D
D ! D +
- 6 3 D < ! +
+
/ +
! 3 1
D 1 "
@
7 1 D ; 1 ! 4 D 1 , 2
-
1 D D 1 " ) 1 3 1
5 ! - - F / !D D
D 1 G ) F - " F -H ) ' D " F - ! 7 " D
F -
- J D
D D D U F D G9 9 D H
" -
¾ 1
?
-
3
Æ Æ = ) D D F 1
F ( D 1 3
7
2 F D 7 1 " J
3 I
1 C D F
1 D 3 1 F
7 G% H
, % R , E - "
3 3
1 % 1 2
) D
3 " 3
) ! < ' " ) D " 3 D
J F " 1 ) - 3
1D 1 )
D
1 3
D F
D @
) = D " I F " G D F =
D 3 D H @
G Æ HD F
$ 1 ) D 1 ED F K
G ) ! - $ @
G D +%HH
- D " )
D , D D G- D HH @
F "
" F
3 F ) G "D
3 "3 D ; " D !D G " GT D HH I - D F F $ 3 ! @ ) C
) , 1
D
1
&
3 1 , D - " - "
, ;
1
E
F ! F J ) D " "
3 GA ?D +*P 51 D +*P A 9 !D ++H
7 D D
"
) 1
+
#
"
; 3
D 1
!
% 1 3
1 4
,
"D +
" " '>,D 1 F D F = ' J " 1 "
D ) 7 1 D
D F I
R J F - " ! # ) ) * & "
Cellule
Vanne 1
sous Pression
Cellule sous vide
Vanne 3
Canon
Azote liquide
Vanne 2
Bille incidente
Billes
ejectees
Pompe
a vide
1111111111111111111111111111111
0000000000000000000000000000000
1111111111111111111111111111111
0000000000000000000000000000000
Stroboscope
Timer
PC
Camera
% R 41
"
R 1 J 1 D D G H 1 F F G H D 1 R , F 1 G G H %H / : 1 1 J 1 ,,- 1 : #
, %% R /"
I G 1H @
) ) H 1 " G
1 3
3 " 1 D G
) G
H 7 1 4 = D D H @
1 D
@
1 N1 D ) ) < " D 1 ) , ) D ! I ) 3
G %%H
1
GH D 3
" D D ! - D 1 E - "3 D G H D 1 1 * & $
: :D F G42HD D 1
:D D
D 5 D " D @D E1 7 1 " D 3
$ $$H 3 $$D
3
"
3 "H -
G $ 1 E @
E F
- D @
3 G D .H " D D
@
1 G/ D H , "
) %. ( D @
"
1 D F
< " 1 G 3 F
7 @
1
D @
< ' $D
$$D -
H
- !
=
1 1
G %%HD " G 3 H ) 1 ! !2 342 ! 3 # " 0 # "%
, 55
billes de type I
billes de type II
50
45
40
35
30
25
20
15
10
5
0
5.75
5.80
5.85
5.90
5.95
d (mm.)
%. R -
' " 1 D D D ) E
) ) ) =
) 7 % F %
D
/ D F 1 ' G1 " " HD D
D ) 3 D F F - D ! 3
"
1 ) ) D F
1 , ) D " "
) 3 ' F
56 , "
D D F D , W K 3 " D @ ' D ! = 1 D G " D ! D 1 D F 3 G ) H ,1 F %& " F $% &
,
F ; 1D D
' D F 7 D ) D , @
)F "
D D F G51 D +*HD
) ) 2
! ) ! ) ' 1 D , " D D H E1 D ) "
, 16
14
12
Nej
10
8
6
4
2
0
0
1
2
3
4
5
6
7
8
9
10
(Vej/Vi)*100
%& R -
) , F 7 , "
1 F
+
H " F Æ - ' D D $
1 " G 1 " )
-
F 1
D .) 1 D D E G H /
1 1 1 " 7 D
D < G H 7 D ! D
< @
1 : 56 , "
1.0
e
ex
ey
0.9
0.8
0.7
e
0.6
0.5
0.4
0.3
0.2
0.1
0.0
8
10
12
14
16
18
20
22
Vi (m/s)
%* R ,
D < ! D
3 1 3 3 1 F <
1 E F 2 F , +
" H 4
D ! G %*H < < G F @
3 % , D "
, θr
40
20
0
8
10
12
14
16
18
20
22
Vi (m/s)
% R =
, Æ " Æ J 1 ! J ; E G "3 H G "
H F " F 3 2 " G " ) H ,
/D F )F " D
D G %+H : D F 3 < ! " @ 3 56 , ")
%+ R $
" 1 ' C D D D 3 D - 7 " ) 3 ! ; 1
) 1 ' D ) G D G 5
2
2 ) E $ D
" ) ) 0 0HD
) ) 0 30HD
) +
% , ) F 3 ' D "
, 7
6
Nej
5
4
3
2
1
0
8
10
12
14
16
18
20
22
Vi ( m/s )
% R /
"
) @ , = D ) + 2 D
D 2
I
G%H
) 3
F 3 ) ) 3
I
) 3 3 + <
) D % ) +
+ ! I
+ + 2 D
G%%H
56 , ""
6
Nej+
Nej-
5
4
Nej
3
2
1
0
8
10
12
14
16
18
20
22
Vi (m/s)
%
R / ) + 3
+ + 2 3 I D D 2 D 2
) ) 3 G%.H
) , ) @
0 10 = < ' D "
<
-
H " @
3 GAD +P A ?D +*H < / " , < G= 9 !D ++H $ F G D
D ) - "
D
) 1 " D "#
, - D 1 ) ) 6 " ' , " ) ,
D ) D ! * 9 9 ! GJ 9 !D +H
7 ) , D
3 F " D ) / !D
B K 1 : D @ C @
1 : 1 D @
1 , " ) D F K 6
) , @
1 / D
) < 7 1 ) 1 %
) 2
) F 1 " , 1 % %D + %D
% %% % % %D ) F I
% ++ %
G%&H
% ) 5 # 56 , "$
Vi = 10-12 m/s
Vi = 14-16 m/s
Vi = 18-20 m/s
P ej(h) dh *100
h/d
%
R - ) ! K
+ ) G
7 %
! %
7 3 ,
1 /
) D %%
' 1 %
D + %%H
K %
"
' ) 1 % HD
D
) 1 % I 1 F
,
) F F 1 +
) 2 ) %
% D
) D
E ) D 3 G GD
#%
, P ej(h) dh *100
20
15
10
5
0
1
2
3
4
5
6
7
8
h/d
% R - ) ) " G H
% %
H 2 "
%
K
%
I
%%
% %
3 % G%*H
D&
% % ! &
*
D&
I
D.%
% F G% 2 2 HD C F G H = % " < I
% 2 8 2 8 ?
= G= 9 !D ++P = 9 !D HD F
-D "
) 4 1 %
56 , #
) D I
% %
% , )
D %
) / G=
G%+H
/!
G%H
# ) D
D + "
@ F
3
+ %9 3
G= D HD
, "
+ %9 3 "
# GA1 41:D H , 2
9 !D ++H I
= 9 G= 9 D +*H
$ D
)
K
/D = "
G%H
G= D H I
%
K
%% %
F %
K
( D
) ) ) 3 G % % % .H 2 @
) 3 F 1 2
!
) !
! !
) G % &H ) F 1 : ) 1 : G
F H 1 @
#
, 50
45
40
Vi=10-12 m/s
Vi=14-16 m/s
Vi=18-20 m/s
P ej+ (h) dh *100
35
30
25
20
15
10
5
0
0
2
4
6
8
10
12
14
16
18
20
h/d
%
% R - ) ) ! 65
60
55
Vi=10-12 m/s
Vi=14-16 m/s
Vi=18-20 m/s
P ej- (h) dh *100
50
45
40
35
30
25
20
15
10
5
0
0
2
4
6
8
10
12
14
16
h/d
% . R - ) ) 3
! Vej / (gd)
1/2
56 , 3.6
3.4
3.2
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
#
Vej,x
Vej,y
8
10
12
14
16
18
20
22
Vi (m/s)
% & R > ) 1 : ! !
(Etot /(1/2*m* Vi ²)) * 100
Vi (m/s)
%
* R / ) #
, 4 ; !
D F ) /D 1 " ) 1 )F 1 D
G % *H
D 2 F
2
!
D " D < 1 ) I
1 + 2 % %% + % + 4 D /D " ) 3D
3 4
?
@
D " 7 ) 2 ) Æ
G %
) Æ
H
) 3
= ) F Æ Æ G= 9 !D ++H 7 ) / !D 1 " =D ) F 1 56 , #)
110
100
90
θej
80
70
60
50
8
10
12
14
16
18
20
22
Vi (m/s)
%
R = ) ) ) 3 " 2
,
) ! D G %
) +H ' C 3 ) , D D ) " 1 ) ) ) ) ) ) ) 3 E
3 #
, 0.7
Vi=10-12 m/s
Vi=14-16 m/s
Vi=18-20 m/s
0.6
0.5
0.4
N ej(dej) d(dej )
0.3
0.2
0.1
0.0
-10
-8
-6
-4
-2
0
2
4
6
8
10
dej/d
%
+ R - ) ! , ) , 7 )@
) 3 G % H
@ D ) , E ) F : D
D
P
G
%H , 3 " ! ) "
J
D D D R , 7 - - D
F ) ) ) " ) ) 2
!D
D ) 56 , #"
dej / d
Vi (m/s)
%
R - ) % R J "
! ) ##
, 6
dej/d
4
2
0
0
1
2
3
4
5
6
7
8
9
10
h/d
% R , ) 1 %
3 % G
) D ' D % 1 H ) F F 1 % G % H = " D @
F D D ' D 1 : ) R , ) ) ) 6 ) Æ
) G %H
) Æ
) , ) E 3 ) Æ
Æ
) ) ) ) 56 , #$
120
100
80
θej
60
Vi = 10-12 m/s
Vi = 14-16 m/s
Vi = 18-20 m/s
40
20
0
-8
-6
-4
-2
0
2
4
6
8
10
12
dej
% R =
2
) , ) , ) D ! / !D F ) 3 - D ) F 1 Æ 3 1 ++P > ? D H 4 %%D ! Y
F / D
G= 9 !D
@
@
@
) ) 3
3 D " ) F 1 I
1 ) D
$%
, 35
Vi = 10-12 m/s
Vi = 14-16 m/s
Vi = 18-20 m/s
30
Pej(lR) dlR
25
20
15
10
5
0
-14 -12 -10 -8
-6 -4
-2
0
2
4
6
8
10 12 14 16 18 20 22 24
lR/d
%% R -
! ) "
" G%.H I
" 3 G
7 F K
) " " F +
D+&
) #
£
G% H
) 3 ) H I
&
.%
D%
*&
D
H
G "
= G= 9 D +*H 4 G4 D H "
$ ) 56 , $
15
14
13
12
11
10
9
Pej(lR)dlR
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
lR/d
%. R -
"
G H ) ) 7 )@
) / !D 1 : ) )@
) F , ) ?
Æ
D +
Æ )F ) D $% & 1
3 D = D
F D " ) - F
) ; 1 G= 9 !D H
7 1 1 7 $
, 16
14
12
10
8
6
4
2
0
50
60
70
80
90
100
110
120
θej
%& R -
) @ ; 1 1 ) - 3 .) , +
1 ! G D H
2 " ! 1 + ' + D < D ' + D < + / D 1D %* < ! 1 ; < $ G %H ) 1 "
+
56 , $
1.0
Vi = 10-12 m/s
Vi = 12-14 m/s
Vi = 14-16 m/s
0.9
0.8
0.7
0.6
e
0.5
0.4
0.3
0.2
0.1
0.0
0
6
12
18
24
30
36
Nc
%* R /
"
< 2
+ 2
D +
- 2
!
++
+
"
! <
1
I
F
- G -
HD <
6 +
F 2 E ' D - " D D ) @
/ F 3 ;" 1 1 @
6 - Ý + / " 7
$
, D F F ) / < 1 4
; +
+ D , - Æ ) G %+H
+ ;3 6 1 ! I
+
5
" 1 ; ) " + 2
1
' Æ
1 G Æ H + , 7 ' D 1 @
) % )@
D
) +
G
D ) D ! +
H
' 1 - ) 3 G %%HD ! 1 F 56 , $)
1.0
0.9
Vi = 10-12 m/s
Vi = 12-14 m/s
Vi = 14-16 m/s
0.8
0.7
ey
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
6
12
18
24
30
36
Nc
% R /
1
< +
Vi = 10-12 m/s
Vi = 12-14 m/s
Vi = 14-16 m/s
1,0
0,9
0,8
0,7
ex
0,6
0,5
0,4
0,3
0,2
0,1
0,0
0
6
12
18
24
30
36
Nc
%+ R /
1
+
< 1 : $
, 10
9
6 couches
12 couches
36 couches
8
7
Nej+
6
5
4
3
2
1
0
8
10
12
14
16
18
20
22
Vi (m/s)
+
% R 7 ) ! 1 +
10
9
6 couches
12 couches
36 couches
8
7
Nej-
6
5
4
3
2
1
0
8
10
12
14
16
18
20
22
Vi (m/s)
+
%% R 7 ) 3 1 ! +
56 , $"
Vi=10-12 m/s
Vi=14-16 m/s
Vi=18-20 m/s
7
6
Nej+
5
4
3
2
1
0
5
10
15
20
25
30
35
40
Nc
%% R 7 ) ! + 1
+
+
Vi=10-12 m/s
Vi =14-16 m/s
Vi = 18-20 m/s
4
Nej-
3
2
1
0
5
10
15
20
25
30
35
40
Nc
%% R 7 ) 3
! +
1
$#
, 7 @ + + G % %%H ' ) D F D ) 1
' D F D ) 1 ' D 3 ' " ) 2
D E +
D ) 3
, D 3 I ) + )
1 D ; 1 F
< ) E
/ D 1
+
6 6D 3 ;" D D
1 D D
) D E
1 = D F @
< ) 1 = D 3 ;" D ) F , 1
F
1 F ' "
+ D 1 < 1 - D F GD
H
! 1 6 " 7 ) F G
H G ) F 1 %
! 1 @
%%.H 56 , $$
1.1
1.0
Nc = 6 couches
Nc = 12 couches
Nc = 36 couches
0.9
0.8
0.7
dNej
+
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18
h/d
%%% R -
1
+
) ! 30
Pej(h)dh * 100
25
Nc = 6 couches
Nc = 36 couches
20
15
10
5
0
0
1
2
3
4
5
6
7
8
9
10
11
12
h/d
%%. R -
) ! 1 @
%%
, ) ) @
1 !
F
%H 2
F 1 D D "
GD
I
D ) % %
G
HD )
G%
% +
3 +
% %%
% ' %
1 D D *
D*
H
I
%*
D&
6 3 1
%
$ < 1D 6
' D ) ) 1
G
G
!
!
+ H , %
6H ' D 3 G
F +
! D 1 ' D 1 : I ; " ' ) !
F 1D 1 : ) ) 3 H F
6 3 1
1 : ) +
GD
HD "
,@ + 6 1
' GD
+
HD
56 , 1.8
%
Nc = 6 couches
Nc = 36 couches
1.6
1.4
1.2
Et
1.0
0.8
0.6
0.4
0.2
0.0
-8
-6
-4
-2
0
2
4
6
8
10
dej/d
%%& R -
1
) ) 1 "
) 1 F %%& F 1
F J
+
F F ! 1
1
+
1 ; 1
F , F ) 4
" 1
+
) F I Æ
) 3
1 , ) "
+
F Æ Æ
, 2
Etot/(1/2*m*Vi )*100
%
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Nc = 6 couches
Nc = 36 couches
8
10
12
14
16
18
20
22
Vi (m/s)
%%* R / D
" ) 1
110
100
θej
90
80
70
60
50
0
6
12
18
24
30
36
Nc
,
%% R / ) 1
+
56 , %
1,6
6 couches
12 couches
36 couches
Nej(dej ) d(d ej )
1,4
1,2
1,0
0,8
0,6
0,4
0,2
0,0
-10
-8
-6
-4
-2
0
2
4
6
8
10
dej/d
%%+ R -
) 1
" ) 7
! 1 D F
D %%+ @
) + F E "
) ' 1 D ) E 2
) 1 2
) 1 I " ) F ) 3
+
+
+
,
) 3
" F
@
D @ D " ) G 1 H ! ;" F @
%
, (B)
11
00
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
000
111
000
111
000
111
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
000
111
000
111
000
111
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
000
111
000
111
000
111
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
(A)
11
00
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
000
111
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
000
111
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
000
111
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
00
11
%% R ?
0 Z0 @
I G=H 1D GH 1 D 1 GÆ H 1 "
" " D D " D ) @
3 ; 1 3 F ) 1
D 1
) D " I + G %%H 2
I
1
" D F
"
& @
F 2 "
) @
F 1 ) 3 )F ) I
+
D @ ) +
! 1 @
%% F
3 ) ,
3 F 56 , %)
3.0
2.5
Nc = 6 couches
Nc = 12 couches
Nc = 36 couches
Nej/Ns
2.0
1.5
1.0
0.5
0.0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Lrep/d
%. R -
D ) +
1
+
' +
+
F
D " 3 2
) ! F ; 1 D ) F
) F
F 1 ) F 3 D D ) 3 7 1 Æ =D D
@
2 ) 2
1
F 3 %
, $% 7 G H !3 3 < < "
) 3 H ! ?
-
-
" G 3 < $ $$ 7 "
1 1 #
- 7 2
.) , ( %. < !
I " 2 <
! 3 D G < , 3 H
D ; # - 5
" ! ) D ) 2 !
) 3 G %.H 2
2 )
/ + 8 " 9 " ) 56 %"
0.40
billes de type I
billes de type II
0.35
0.30
0.25
ey
0.20
0.15
0.10
0.05
0.00
8
10
12
14
16
18
Vi (m/s)
%.
R , < ! " D
) < I
+
D G% H
$D D $$
I
O $
$$
) 1 ! ! 2 " ) G H
G HD ) ) / D ) C %#
, 20
billes de type I
billes de type II
18
16
14
Nej
12
10
8
6
4
2
0
8
10
12
14
16
18
Vi (m/s)
%. R /
+
) ) ! ) D 3 '( , "
1 @ @
) 6 1
H
@
-
@ G
G H 4 I <
H ' D +
D @ 3 G
) 7! %$
3 "
) ) [email protected]
D D 1 )
6 3 G
H F ; 1 , H I
%
)
%
E
: 3 ; G% %H
" ) , % ) / D D %%
D + " % 2 ) 1 ' D + % +
K
) ) ) F 1 "
D J F
) ) F 1 G
) F [email protected] 1 G
HD 1 @
6D ) , ) 3
;" D ) , )@
1 ) ; )@
%
, J < 6 3
) G H ) ) )
! # , E ! " )@
1 4 1 3 , @
- "
D D ) D " ) F 1 , E E 7 D
"
D
- D D F D 4 D ) J < "
2 D
D
F " 1 , D D 4 ; G
M " HD ) /
D ) F 3 1 E , ) F 1 ,
! @ , /
D 2 "
%
I
F :I
) F , : :
: %
F 1 ) ) D 2 2 3 )
1 : : : ! ) ) "
E
"
: G% .H
D F ) I
+ % + % % % G% &H
) 1 : % + % :
: % G% *H
I
+ % :%
G% H
, 7 D D 6 G
1
D
E D
"
D
H
, *
! , "
F -
G Æ H 6 3 D G F Æ H - D
, "
D "
"
4 1 1
@
1 1 F D E " "
J 1
"@
N1 3 F " "
D
) "
)
3
) 3 1 4 1
6 3 "
3 F ) I
< D ) , "
1
F
1 1 $
1
1
; D D ; @
E - 1
C ) D ) " D
ED 3 1 3 E G . H I
R
R
& I F I 6
" 3 R
I D D D
F ! " , / ( 8 ( , 9 , : & , , * (3)
(2)
(1)
.
R ! G H I P GH I P G%H I . R $
" 1 J 1 "
1 D " 1 3 /
G .H , "
1 3 1 6 D 3 @
F D 1 6 "
1 G( D ++HD 1 @
GT7? "D P ?
) D *H ,
@
G .%H I
@ G H @ GH @
5 )
F
3
1
2
.% R ! I G H D GH @ D G%H @ G%H ,
< G 1 D
H
! D "
" D F D @
3 D F , 3 )F " D
" D
F G-! 5 D &H 4 9:D "
1 G9 D +P O
D H
, F D "
D - " GO , D H 1 3 D F ! G F
" H , E
! 3 1 F @
F 2 1 7 "@
, * ! ! , !
;
"
' @
D 1
3
,
F @ ) '>, 1 D = ! D 2
F K
! 3 @
J E ! 1 "
! D , < F 3
1 G 6 !D *H
7 11 "
3 C D
' "
D ! I
7 1
G $ $$H
D F ! 1
@ J F 1 G
"
" F "
3 !3 H " - D , 1 E " M D ! 3D " 5 "
< ! G $ -
-
$$H 2D D
1
%D ; < ) $ 3 1 ! @ J F , F
E D F
D 1 @
/ !D ; F ; G 3 G?T D
E ! 3 D
H $
6 F %H 5 D 1
@ D = D 1 F G D +%H 1
3
D : 1 F
D M F " D
D
M D
D
D 3 )F ) " @
G D +%H , 1
D F D F L ) ! G 13 H @ < ,
" 7 D
1
D I GH GH "
#
, * .. R $ 1 #
F
3 1 G 1 " H 13
F "
1 7 @
1 3 G ..H @
G F E 1H
#
- .) .& < ! / I
/ D D E D
$ E
" ; 3 2
* & (
$
ordre
désordre
0.8
0.7
0.6
ex
ex, ey
0.5
0.4
0.3
0.2
ey
0.1
0.0
6
8
10
12
14
16
18
20
22
Vi (m/s)
.& R ,
< ! @
D # - 5
" - D ) = @
G .*H
D ) 1 2
) <D +
GF H I
G. H
D
) D
%
, * 20
ordre
désordre
18
16
14
Nej
12
10
8
6
4
2
0
6
8
10
12
14
16
18
20
22
Vi (m/s)
+
.* R 7
) 6 ( ) D D 1D H ,
2 D
!
%
% GF @
" D
K
! ) 3 ' G .H 1 ) D
" ) % D
!
' D ) 3 " G .+H
* & (
14
Pej(h)dh * 100
12
ordre
désordre
10
8
6
4
2
0
0
1
2
3
4
5
6
7
8
9
10
11
12
h/d
. R -
) F D
4.5
ordre
désordre
4.0
Vej,y/(gd)
1/2
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
6
8
10
12
14
16
18
20
22
Vi (m/s)
.+ R > D
) @
, * ordre
désordre
2.0
1.5
Vej,x/(gd)
1/2
1.0
0.5
0.0
-0.5
-1.0
6
8
10
12
14
16
18
20
22
Vi (m/s)
. R
> 1 : ) 6 2
" 7 ) ) 3 / )@
D 1 : ) 3 G .H ' D D ) 3D ! . H ' ' 6 " " ) " ) G D " ) F ,
7 " ) * & (
4.0
ordre
désordre
3.5
Etot/((1/2)m(Vi)^2)*100
3.0
2.5
2.0
1.5
1.0
0.5
0.0
8
10
12
14
16
18
20
22
Vi (m/s)
.
R / " ) ) 7 G.
H
D D ' F " ) - H 3 - "
G
" ) " ) 1D
, F 1 G !D
1
% ! 1 E " 1 1 G
G 1H
1D ! 1 - D " ) HD " D
D D ) 3
H / 1D
, 3 "
D
, * Ordre, Nc = 6 couches
Ordre, Nc = 36 couches
Désordre, Nc = 6 couches
5
4
E
3
2
1
0
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
d ej/d
.
R - " ) ) 1D 1
= " "
1 3 @
D ; F F - D 6 I 2 7 5
"
-
G
! @
D 3 D 1 3
D F @
" 1 D " ! -
H $ 7 D 1 * ( )
!
) 7 D
D 7 D H 1 4 . D E
) 6 1
"
F %H , D 6 D
HD "
H 3 G
J H 7
1
H 2 ) D G
"
H
"
D C
13
5 1D F GD
"
G
GD
G
) ) G F "
" F 1
,@ $D ! 2 ) "
"
D
1 ' D 1 ) D ! 7 1
; , @
D ) 1 F @ F 1 ' @
, * 9
0%
27 %
50 %
8
7
6
Nej
5
4
3
2
1
0
8
10
12
14
16
18
20
22
Vi (m/s)
+
.
R 7 ) "
D @
6 F 1 ' D @ @
1 2 D D ! 1
& D F
"
1 7 3 1 D ! - 1
D
D ! ! )@
! D 3 @
' D ) I
@ ) @ ) @ " ) !
" # , 1
F D 3 D D F , 3 D
3
G,
@
1D *P , D +H
) D
) , " D ) 3D 3 D "
"D 1 ; 3 F @
" ; ) (
F 1" " - 3D 1 ' @
! - 7 " #
) ; ,/ (i,j+1)
(i+1,j+1)
qE
rE
(i-1,j)
(i,j)
(i+1,j)
rE
E
(i-1,j-1)
&
(i,j-1)
R ? D ;
H ' G
;
F D F ;
2 3 11
3 F F < 2 6 = D
F = 1 D " 4D D 6 < D 6 <
M D (
6 < 7 " " 6 < 6 < G & H , 3D 1 ( 7 (
7 - D (
7 - D -! D E1 ? F " KD D 6 <
) $
M 6 <
6
<
6<
" " "
" 6 < 4 D D 6
D <
4 " D ' D 3 H F 3 D
- D 6 < ,
G , 3 3 G 1 H
F
D F D " 1 D ( D
3 ) D
1
E ) G
M D
4 H 1 9 " 1 ; 1 7 " " D F - 1 D 3 "
+ 7 D F
3D " 1 F GD
"
F K
;
D
@
H 7 1 F " F
@
%
) ; ,/ 0.10
Nc = 5
Nc = 10
Nc = 60
0.08
E
0.06
0.04
0.02
0.00
-50
-40
-30
-20
-10
0
10
20
30
40
50
dej/d
1
& R -
G
;
H ! 1 F F 4 &D 1 G 4
7
) G 1 H , ) 7 !
3
6 F 1 =
@ ! 2
D H F " F "
) D 6 1
I
! ! ) + $
!
D
) D / G &%H G& H
!
F E ) "
@
) 0.04
A - Ainf
0.03
0.02
0.01
0
10
20
30
40
50
60
70
80
Nc
!
&% R /
1
G H G H
2 "D D @
1 "
) ?
D "
+
3 G F
+
F F
2 D
D H 1 3 ) ) H
G
G 1 2
1
"
=
+
H
1 F "
,
) ' D 3D ! D E1
) ) ; ,/ p=0%
p= 20 %
p= 30 %
p= 40 %
0.10
0.08
E
0.06
0.04
0.02
0.00
-10 -9 -8
-7
-6
-5 -4
-3
-2 -1
0
1
2
3
4
5
6
7
8
9
10
d
1
&. R -
F ! + 7 ! D 7 1 ) %
. 7 D
! F GD
;
F @
G &.H 2 F D
) ) G F H G &&H ' HD F
1 G &&H 1 G &*H
1
F 1 D ) 0.10
0.08
A
0.06
0.04
0.02
0.00
-5
0
5
10
15
20
25
30
35
40
45
50
55
p
&& R =
! 0.50
0.45
0.40
0.35
0.30
Et
0.25
0.20
0.15
0.10
0.05
0.00
0
10
20
30
40
50
p
&* R / 1 ) ; ,/ 0,14
p=0%
p = 30%
0,12
0,10
0,08
E
0,06
0,04
0,02
0,00
-10
-8
-6
-4
-2
0
2
4
6
8
10
d
& R /
F 1 D -" D G
H G
H
, 3 D H 1 D 1 6 D G
" 1 1 1 3 GO / D
) D D ) , F
6 D ) "
D
J ! ) F @
D ' HD D @
' 3 @
G &H
! H ' F "
G "
D
D ) )
) 2 " / !
) "
"
D F ) F
% . ) 7 1 ! 7 F 1 2 D D "
! !
G & H I
! + +
! + < D + 2 + I + ' D +
D +
2 + G K
D
/"
H
D % / D D 3 3 ! "
5 D ! 1 ! ) # - ) ) ; ,/ 0.25
p
p
p
p
A/Ainf - 1
0.20
0.15
=
=
=
=
10
20
30
40
%
%
%
%
0.10
0.05
0.00
6
12
18
24
30
36
Nc
&+ R =
1
& R '1
3 +
1 1 D
G HD 1 G &H - D ! D
)F 1
2
D
F D F 2
@
" F 2 ! F
G- D H
) "
d d’ S
R
R
&
R 1 ! , 0 3 G & H 4 13D
13 1 : 2 D 3 D < = 1 @
: % F % I = % % % % $D %
% / % % D % % % % D F < I = % % 3
"D @ED F 0
$ ¼
1 : 3 @
D 1 : 0 0 I
0 I 0 % 0 % =D
0 = 0 >0
K <
> > % H 2 $ I
%
> N1 GD H 2 >
2 < GD
#
) ; ,/ >
2 =D F 3 @
! 3 "E ) D - " 1 3D E 7 3 " G ) H ' D 3 D D 1 J 1 E 2
3 ,
@
E D
D !D D $
% & )
" H F 1 G D @
"3 "
4 G D . HD D
D @
3 F D F @
D G D . H
- D 3 - D =
3 1
D D
,
1 3
W GD
H " F D D ; %
*! *
D "
1 @ $ 2
R '1 D D !
?
3 " @
G D . H ' D 3 ' D = G= D +H F - 3D D
D F D " @
' D G71 21D %P 9 A
3 < D P (: D +P > ? D
P ' :1D H
7 "
F 3 3 " @
@ " " ) "
'(
B
C
A
* R 2
)
+# 4 D W F ;" @ ;" D D ;" =D "
6D ;" - D ;" M ;" "
;" D "
) D !' " ' D D D ! ;" "
D F F ,
) ;" )
F ' D "
G *H $ ) ( &- 7 3 = G= D +H @
*! h
θ
α
h(x,t)
x
*% R J "
3 = 3
$
- D 2 3 - "3 1
13
D < E 3
1 ) D D ! 1 *%H 4 K
A ;" % E , D F
G
I
G* H
1 : F , ;" 1 : E
D F " I
A A A"
A ;"
"
@% @A
@ @
K
D ;" D A" ;"
G*H
- ; ,< 3D F 1 3 " , A 2 F Æ - " + ) ! ) 2 A / ) " + ¼
A ¼
D G*%H
I
@% + + "
@
G*.H
$ ) ;" @
= ) +
I
+ + 1 + K
F ) E
4
1 : D ) , + D "
F
I
+ , + , K
G*&H
,
)
G**H
1 : G*.HD G*&HD G**H
3 3
F 2 F ; F
; ' D 11 % % G#
*! Taux de croissance ω
2
1
0
−1
0
2
4
6
Nombre d’onde k/lR
B
*. R ?
C " " G H
H 1 3 + 2 #
" 2 ' G*H
*.
,1 "
D " "
D 1
= " 3 I
B 6# ) K
10
#2 ' 4 G H 4 K G H 8
D I
@ % " " " D 3 D = " -
"" " + + ""
G*+H
; ,< J )
D
D I
B 6# ) #
G*H
K # " - 3 " " 1D " D " I
" " " G* H
"
"
O I
" K
" "
"
" "
G*
- "
I
B 6# ) 2 " 6#"
#" D G* H
! " ) *.H , O D I
B 6# ) , ?
7 6#" # " #
G* %H
#
F
" D " 2 F D
D
: G *.H ' D F / !D " @
G 1 H
$ *! )
- 0#
(
' 123
3 9 A
G9 A
D H " = 1 ! !
2
3
! ) C D !D F D D
D ! D - " D D G9 D +H
' ! D ) ;" AI
K
+ G* .H
A + ,
G* &H
$ D D I
A
A A A" A
7 ,
I
K
7
+ D @A
"
@ % @A
@ @
G* *H
- G F HD E
1 @%
@+ D @
@
I
@% @ " @
)@% @ %
@ %
@ %
G* H
< K
"
+ +
7 J
%
F
F I
@ % 0 @%
0 " ) 2 ) ?
) ! H
;" )
G
H 7 D
3D G 3 = HD 3 1 D 9 A
3D ;" / D ! ;" G 0 J ;"
D G* +H
' ! $ 3 D " D )
3 ED / ) !D 9 A
: D F 1 3 1 / D : G41 D *%H G Æ
Æ
@
"
HD F F " Æ ) #
*! 0# ' + ) 2&)
3 71 @21 G71 21D %H "
@ !3 $ @
;" 1 3 $ 3 K
I
3D D A ¼
G* H
3 @ 4 1
+ 8% E I
K
13D ;" + ¼
& ¼
G*H
¼
D ' D G K
H I
A @%
@
< " " @%
@
- H I
I
@ A A
@
G*H
@D + D + @
D @% 8+ @% @ @ + G* H
@%
@
F ¼
@% @ G*%H
G G*.H
E 2 "
# B 8 + 6#
¼
I
#
G*&H
< $
Taux de croissance w
5
l 0> l
C
0
−5
l 0 < lC
−10
−15
0
2.5
5
7.5
10
nombre d’onde k/l0
12.5
15
*& R ?
3 71 @21 ' " I @ G H @ G H
2 F F 8+ -
? I
?
- G**H
3D D 3 = F
3 71 @21
, E -
" "
@
D ) - D D # ) )%
*! )
,
0%
( - '
3 1 3 3
1 1 3 0,?/0 G 1 D .H
1 ,
1 3 D +H E , 1
1 G(: 3 = D 3
3 7 ! 3 1 ( D 1 = D D F 1 " D ) F
7 1 G(: D +HD D ) " "
D " " P F " D
G 4 1 3 3 1 F D - E = D " 3
"
7 D 3 D 7 M 1
3
" /D 3 6 , - ) * ) ; ! ! = H 3 0,?/0D D F 1 - 1
)
% " 1 GF GF D % @
F F G*H
G*+H
! "
1 H
I
@ @ ! %
@ % ! %
, " $ F D @
3 1 G(: D +HD , !
)D F D 1 2 " D !
1 F
1 D
D D ) ! I
!
7 @89 " , G*H
" ) !
" " !
1
D ) $ 1 ;" , ;" D D D F 3 = " ) W F !
K
+
+
G*%H
;" ) 3 = )
*! ! < ) / !D F " F =D E K
" I
D G*% H
2
D D F " " ) I
"+
+ D
/ " ** - % / G
G*%H
I
+ " !
% )%
% %
%
G*%%H
HD + D )
) )
"D )
D
D )
1D ) )@ % )@ % ) )% )@ % E %
!
)
) "
!
K
" ) /"
I
G*%.H
! " I
R ) ;" ) D F D 1 : D
R F
@ %
F
I " ) G ;" "
R ; @ %
H
; I < " E
R " @ ;" ) ; ! ! )
@89 " - 3D ( I ;" , 3 G= D H D 6
" G*%&H
I
!
K <
. 2
. . [email protected] % [email protected] %
<
.
G*%*H
E , E E
" . D
K
1 : @
4 D "
! ! .H 7
*%* " " 6 / @%
! " I
( D F ! E 2 @89
D !D G"
HD G
3 9 @A
G9 A
D HD
D 4 D =D "
"
G
)
*! .H /D "
3 3
*%* , - D ) . ! " E
*D *+D *%&
@% F
F F 0% 4 7 " # '
@
3
" D F D 6
- D " 1 ! I
!
- D !
! -3 < ) K
G G*%H
G
)
!
) HD 3 D
- ;" HD
D
B . ) . ) " # " # 6." #
K
" . ' / " ' E1 E
" I
?
- ) " '. G*%+H
1 : 6 3 I
F ) G*%H
) ; ! ! ))
1.0
Re(Ω)
0.5
0.0
-0.5
-1.0
-1.5
0.0
0.5
1.0
Nombre d’onde k/kc
1.5
** R ? K ' " I @ G
P H
@ G
P H
-
-
K
- ) G @
" ' 3 = H #
, 6
D " D D 1 ! " I
!
' I
K
- !
!
D ) .
G*.H
@ / !D " B .) -" # 6' " # ' " # ) . ' '
# G*. H
) . )
*! - GD ) . H G **H 2 )
) ) @ HD
)G
K " / D "
#
2 I
'- "
?
G*.H
2 " ' 0% 4 2 ' J
? D H - K D @ @ 1
@ D G> %
I
@% 0 @ % 0 @ % 0 @ % 0 @ % G*.%H
@ K 0 . "
) .-D 0 ." ' D 0 ." ' 0 .." ' 2 @ % 7 - K 1 D @ I
@% 0 @ % 0 @ % 0 @ % 0 @ % 0 @ % G*..H
@ K 0 ) " -D 0 ) " ' 0 " ) . - D 0 ) " ) 0 ) " ) )" .' @ % F @ % 7 6 " $ 2 :;;<
) ; ! ! )"
7 " I
% %
% G 3 H F % % % %
G*.&H
K 3 @ < % " D 3 1 $
6 W I G *H , W
"
? ! 2 !? I , D D D @ K
=" D F % G / 1 D F 2 @
*.&HD F - D ? ! !? W E 2
" ' D 6 ,
F
% )#
*! * R ?
%D
D /
,
D @
@ D D 3
D F D @ G " *.& @ H " D D ! WD
3 D @ 1 J , " F , 1
3D ))
=
! .H G
3 1 3 0,?/0 G 1 D
1HD @
)$
! 1 6 ! G! 1H ! F " W G H
1 3 6 '
= 1
D 3 1
D F @
3
7 3
- D D F D F 1 D F
D F - !D
1 1 1 1 D 1 F " B1 H , #
3 B1 I
G H
G Æ Æ HD 1 G Æ Æ H ' E
H 3 G
3 ) D D
G 4 D @
1 3 F
) " R B1 B 3 G 7 B1 F ? D 4 5 H
GH GH "
"
1 D F 1 D
F ; J
B1 3 1 3
/ 5 D < 7 @/H # D 3
B1 1 G
G H - ED ) D ; 1
7 7 1 "3 D C D B1 - D 1 F
3 = "
3 B1 3
" *! 2
B1 *
" . F
G $
D D F 1 "H E1 B1 ) F 3 /" @ F
B1 S , "
G4 D P = , D H 1
F ( F 1 9 9 G4 D H 3 ! 1 GH @
3 I
G H %
7 "
3
B1 D
D GT B 9D &HD F
1
G%H , ;" I
3 " ;" ( F ;" D F G H
2 ;" @
3 D
@ D @
" F
"
;" ;"
G.H (
I
@ ( ( (
@
" 3 I ( I
K
GH
@% @(
@ ( @
G%H
/ D 1 Æ D
D
*
E /
1 F 3 "
( D 1 B1 1 D ! C @
B1 @
) F + /
" . 5
$ )! 7 1 =B) ) 5 , 3
: B1 1 3D
! B1 G 3 1 H ,
G H 7 B1 C
B1 @
1 1 D
" ( ( 2
35
30
25
20
15
10
−10
−5
R -C
0
5
B1 10
15
1 )
" W (m)
20
18
16
14
12
10
8
6
% R 1
1.2
$
1.4
1.6
H (m)
1.8
2
B1 1 4
26
L (m)
24
22
20
18
16
14
. R 1
1.2
1.4
1.6
H (m)
1.8
2
B1 1 4
" ( ( 2
7 < 1 G %H I
2%
8% 1 4 .H I
2
8
< G G&H
, < $
G.H
2 4 8
2 8 $ 2% 4 8%
- ED 4 "
F <
5 $ ! - 1 B1 D =B) )D F % B 7 7 B1 ' F : # F 4 @7 : #
4 @/ , " I 1 @
7 @/ 4 @2D 6 )@
CD
W /D D
[email protected]/ 7 @2
3 B1 @
3 D ! 1 7 @/ 4 @2
) F . %
H D B1 1 D F
! B1 1 7 /
2 : 2 4 1 @ I
B1 D B1 G 6 3 F 1 F ! #
" 4
3
2
1
3
2
6 5
1
7
7
& R J D
"
[
1 B1 ! D 1 - 3D - "3 3D 3 D " 3 " 1 4
$
% 2 1 1 , D "
D 3 D F F 1 D "
1 "
F
F F
F B1 , " F H D "D 4 4 G 1HD F
D G D 1 I =D E
) F 3 , F
J ) )F
"3 3 K ! D E D F " *! = $
T= 0mn
T= 20 mn
T=40 mn
* R /
*
C 0 "
7 C )F 1 3 =
D C ! 1D
'
1 D B1 " 1
G 1 *H
D "
" "H = F @
" C 1 ! G
D C "%
" 1,0
Cone 1
Cone 2
0,9
0,8
0,7
h/h0
0,6
0,5
0,4
0,3
0,2
0,1
0,0
0
10
20
30
40
50
60
70
80
90
t (mn)
R /
G 1 C CH N F 1 3 C 2
1 C 2 1 %
I
%
%
1 G*H
, D WD F
)D F D @
1 2
"
C
)F #
, = G= D H , D F "
D B1 6
@
@ - D C 1 : 3 D D
6D " " *
"
! - 1
"
D " 5 C F 7 3 - F ) 1 ' 1 1 1
B1 J 1
1 ) D 1
F ! , @
1D F 1 : 3 G 3H , 1
E F @ J @ D B1 ' " D
D F D *
7 1 1
D
1 / / 5 D 1
D 1 7 B1 G D H 2 , ) D 2
& "
1 6
D F D F
D < ! " I D
"
" + R $
@ 1 @
D D 1 1 C D D E "
1 1 3 )F 1 1 1 ! !
D 1 5 @
F 3 1 F G
@ D " D " H F D 1 @
1 J
C D 1
" 1 G H
, < " $ ") 0 , R (1
3 D D 1 D D D
- 5 5D @ 4 1D D 4 1 @ 1 @" G @" H F 1 D 3 F " / 5 D 1
/ !D
1 ' "
D F F 1D E1
, G H
F
"
" R (1 " 1
"
") 0 , ")
J D M D ! [email protected]
F
3 ( )
) D D D ) , ) = 13
"
@
3 - ) 1 ) 04 10 ,@ ) " F 1 F 1 7 D /
3
3 D D D 4 1 F ) @
' D D ) 3 " , 3 D E " D Æ D
1 "
Æ Æ - D
= ) $ D "#
" ) < $ D ) ' D ! ) 1 : D G H "
" 4 1 " 7 1 ) 3 1 ) D ! " D
3 D 4 1 D F D D D D ) D J " 1 3 ' D 2
D
J
D F D 1 ) "
F @
1 <
1 ) )@
D 13 3
F 7 1 3 WD F @
' D 1 11 7 @
) @
D G D
F H 1 ") 0 , D
"$
D 2 "D
D
7 1 F D )
D ) 3 F
D ) 1D 3
1 C D 1 1
/ D
< 1
* = D ? G +H = 1 ( ,D D
.%R&*
= D ? G H = " @ : 1 %( " #"D &D R*
= D ? 4 9 !D ' Q G ++H 4 ( D D
+R+%
= D ? 4 9 !D ' Q G H A " + "D :/ ;<D R&
= D ? 4 9 D G +*H 4 8 I ( 8 " ( "" D"D &#D &%R&%&
= D ? 4D 4 D 5D AD G H = 8 " + "D :/ ;<D R
= D , D ' G H 4 1 I =
8 @ ( " ")"D"
= D D - D 4D , D ' G H 4 1 1 I - D 8 " ")"D"
D ? = G . H 7 , * M ,1 9 6D ? !D ' G *H 13 I
= " 13
M 7 ,D D D D 5 :1D ? G H 2 8 )" , ""D D &.&R&&.
D T O G +%H ? B 1 1 B , " #" D
#= D &%R * D - G +%H $ %
& & 13 @
D J ? $
D 7D Q G *H 5 -" )" ( ( "D
D + R+*
1 D [email protected]'D , D 5D ' B 1D TD / 8 D 4 G .H = 1 )" "6"'"D D %+%
,1 D A G .&H - 8 I ( ( "D >D
%R. , D 'D 1 D T 'D , D 5 /D AD T ' G +H 5 ; , " #" D #D ... D..&
#
'( 1D / G *H 5 ; B , " #" D D
.*%D.*+&
, 1 BD VD 5 1D ,D ? D D > D = G +H - " , " )" D D R+*
- D 4 -8D 9 = G &H / 8 )"
+ " , " ( D D *R -!D T 5 D ? G &H [email protected] )" " + "D D &+&R&%
- D T G H ( / / D , GH / ( $ D / G H - * 8 E 13 D
J $D , D /D 1D ,D D 4D , D , G +H , @ 81 8 " , " )" DD &D R % D 4D D 5D ,1 D 9D = D Q G .H 5 @
1 , " 6 D D %%
OD , D , G H 7 M
9::;D %D *
O
D T G H 7 8 " ," ( " D >D &D % O 1D A G *H ' D = O D /D 9D T 'D 'D G H 8,
,& , & 4 =
/-' 4 \,7?4 / O D /D ? "D 4D 9 D =D D -D (
D T 'D ,
D 9 G H 7 @
@ 1 1 I
"
" , "D D %%R. 9 D / 9 D 9 T G H 41 B @
1 81 9D ,D =D 5 =D , D =D $
D $D - D 4D D O OD D
- G +H / 1 , " #" D #=D ..%R.&
9 D 4:D 5 G +H 9 8 1 1 8 B1 B @
1 81 " )" , "D >= D R+ 9 D 9D 4 !D -D ? "D 4 G +H > @
, ""D D *&R*+
9:D 9 G +*H 2 1 + + %
D ;D .*R +%
91D / T 4 @T D 4 G H (1 " " ( " " B;NNNCD D % R%
9 D ? A
D = G H = , " #"D
D *+* R*+*+
$D T -D OD ?D 5 1 D T ?D ' BD T G +H = 11 I 1 ! ( ,D D *R*
$D T - ? D Q ? G H (1 ! 8 ( ,D D %R% ,
'( $D T - A1D ? G +H 4 11 1D ( ,D &D R T B D ' 4 9D T , G &H = 11 I 1 ! F" )" " + " ( "D >D T D ]D , D ,D >BD G H , " #" "D *D +*%R +**
T7? " G H , B I = M T 1 D Q G +&H - + , J '
QD 4 TD ? D A ,D 41 D A ,D ? D = G *H (1 )"6 + "D >D . R%
Q D QD 4 D OD 9 D 9 T GH 5 , " #" "D **D &.% Q8
D O Q D Q G +H ? < 8 8 1
)" )" * " , "D D %R %%
D 7 G &H , * ? D D Q D 9 9 G +H $ M D 5 D A D 4D ,D /D ? )1 1D TD - D T G .H = @
I (1 1 ! , " #"
"D >D . %R. 5 /8 D $ QD AD D ?D 5 = G H (1 \ 8 ( ,D &D R + 5 8D 7D D T ?D 8D T 7 G *H (1 1
L D *D 5/8 D $ Q AD G H 7 1 "
+ "D :/ ;<D &%R**
5/8 D $ Q AD G %H =
1 @ 8 1
)" 6 + "D D R &
51 D 4D ( D 5 D AD (D 9 !D ' Q G +*H (1 \ " + "D D *%D *
5 D 4 = =" D = T G H = ) 8
1 ; 8 )"6 + "D D %R+
7
D 'D 9D T ,D D , G %H 4 ; )"
6 + "D D ** R*+&
7BD A O G ++H (1 8 ( ,D D
.R& 71 D 9 21D 7 G %H 8 @ 8
, " #" "D #D 28D ' ? G *.H 4 )" 6 + "D >D &R.
' ) D G H $ , # 13 D J 7 ' G %&H D %
' :1D G H 7 , " #" D >D #
#
'( 'D Q ( D 9 G H J8 9 D ? ) D D T D 5D 5 D TD ? "D 4 G *H 8 @
, " #" "D ##D .R
? D , G +H (1 1 1 , " #"D
D ..R..
? D Q ? 5BBD 9 / G H A " + "D :/ ;<D %&R ..
? D T G +&H / 8 )" , " .D *D %R%%
?:D T = G +H 7 )" 8, " .#" (-D
>D %&R % ?D 5 =D AD D 5/8 D $ Q G *H 2 81 [email protected] @ ( ,D D R% ?D 5 =D AD D 5/8 D $ Q G &H = " @: ) 81 ; ( %
,D D *&R*
?TD 5 BD 'D ' 1D = G %H 0 81 B0 ? D - = G +&H 4 I : ( %
,D D *
4 D OD Q D QD 9 D 9 T G H = , " #" D D % %&
41 D ? ' G *%H A )" "D #D * 4 D 5 G H = 8
8 " + "D
:/ ;<D *R+ (: D 2D , D 'D 1 D [email protected]' G +H = " , " )" DD D %
( D (D =D 5D D -D O D =D T D (
D TD 5 D T
G ++H 7 ) , &D *D
%.
(1 D U Q 8 D U G H ,1 8 " - - *" (-D D * R *&
J D T 9 !D ' Q G +H 4 ( ,D D +
> D = ? D G H = "
, " )" DD >D &.%
> D = ? D G H = "
, ")"DD >D &.%R&.+
AD ( G +H 13 D , $ (1 AD ( G H = @ 8 @ 8 ) *
,D &*D R AD ( 9 !D ' Q G ++H (1 I 8 @
( ,D D +
A1D ? 41:D T , G H 5 ! )" 6 + "D *= D
. R & '( AD ?D 5 = G +*H , " + "D D
&&R*&
AD ?D 5 = G ++H ' ; 8 ( *"
" 6 D D R+
AD ?D 5 = G +H , : 81 I 1
; ( *"
" 6 D D R%
A D T G +H = 11 ( *"
" 6 D D R%
VD , G . H (1 , " #"D &D **R*%
#)
7 13 %
D E ) ,
) F " 3 E J D D 1 D -
) ' D ) "E I
D ) /D
3 1 D F D 1 ,
3 " " ) 3 13
I 7 3 @ 3 3 " ) @
" 7 D D 1 3 W I D " ! + ( D D " D D
D D
4 (1 1 1 81 1 A
1 811 1 1 ; 8 4 ) 1 = 1 81 1 D ) (1 ) 1 1 1 1 " 8 8 @ B (1 1 D D 1 1 D 1 B 11D 1 1 1 B - 8 ) 1 1 1 D 8 1 1 8
1 1 ) " 1 1
B I $ 1
BD ) = D 8 1 1 1 1 B
8 1 B
(1 1 1 81 I 8 811 1 @ 1 ' 1 B 1 ) 8 " A 1 8D D 1 1 D 811 " ? [email protected] / D D D D
D D
1/--страниц
Пожаловаться на содержимое документа