HAL Id: hal-01307127
https://hal.archives-ouvertes.fr/hal-01307127
Submitted on 28 Apr 2016
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished 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.
Effects of Long Waves on Wind-Generated Waves
Gang Chen, Stephan E. Belcher
To cite this version:
Gang Chen, Stephan E. Belcher. Effects of Long Waves on Wind-Generated Waves. Journal of Physical Oceanography, American Meteorological Society, 2000, 30 (9), pp.2246-2256. �10.1175/1520- 0485(2000)0302.0.CO;2�. �hal-01307127�
(*)&+-, .0/21+&3*4576 879:1;</&1<+>=@?BAC17DE7/&1<F
GIHKJMLONQPSRTHQUVPXWZY7[\H]P^H_WONZWO`aW_bdcfe2ghUjilkOHmNonpilPScqWrY7sXHoLutOilUvbOewsXH_LutdixUvbde2ghUjiSP^H_tIy2ixUvbvtuWOR
z|{}v~V"pfl "#ffxfv2 px'dM"l~~}MMIQ -dMM¢¡
£
p~}v¥¤X¦¢§VpxO}Iff}~M¨Q} ¦¢§ª©X|«¬M®¯°2«X¯ «Mv±¢²d³"MM²z|®M®®¢¡
´µ·¶]¶Q¸m¹Zºµ·»½¼¾¿»VÀ!ÁÂVÃĵ·¶Á¢¼¢¼¶Q¸m¹m¹fÅ
Æ
f«<ÇÈ}~¨ÊÉ7¦~
Ë
}½MQ}vpMlIÌZ~¢QQ}Ql~2-½ÍO}~j³VQMp "¦ÏÎf
É°&Ð2ÑÒÓ#~xfpx¯ÍÈÈS}{ÔÍf"xQpp}~Íf
É} :
Ë
l~¢§M³"É}pTM®¬
d¬¢vM{}pfxlxÈÉ7f]Õ
Ö
Q}~"f
×¥Ø
Ê}lKÙ¥m¦~ªÚI llVÕh«Ûl ¦v«Ü~"x
Ø
p«Û
ÝpÞßàÜápâQãáqä]å:âæ·ç^áß·è_áqåêé|äëìVâæväé|â]íKäîïé|áð¿ßfíKáé|âèZí|îÜäß·çÞ¥èMñáâ]ßdòOóhíKëäfç^ôuõjöáoé|á÷¥øhùúüû·ý]þwßuîïãáé|çKîÛíuñáÿdá àâ
ñápÿdîÜíKáoé|érâ]ßñáá÷Èâ]érçKáoîïàÜàïá÷uérâ]ßvè_á
ÊVfl-MlM ½f Q$Õ¯ l}l~0p¦Mfv}vplM~ Ê}qx~ pfp}XS}½MQ}·QMo§C]Õ¯ p
Ø
f~¢Q:Q¦}·&¦M:x~
Ø
¨f~Q}vpf7}OM-}pTp" ppf ¢§\}Qp}l~$¥lM~"¨Êm¦}~xO}xx§
Ø
¨M~fp}vQ7}OMf«< p¦xpfpx~¨ fm¦}~"lp l7pf ~pxl&7¨M~fp}vQxM~ÏQ¦"-p¦Mo:l~"
7}dfÏj§ :¦xm¦}O ¨MpQ¦l& "pM ½MplM~}QQ¦qx¯f}Q"pxf~¢:x~oQpp«2~fv
xwp¦-Ql~¢:x~\Qf2~f}Q¦È^}Èlpf¢§p¦ÈlM~¨7}OMvªp¦f~\Q¦È¦M
:l~"}OM} xxQ"h}~¦~f}xp!p¦qf~"fp¨v§l~p¦ p¦"M7}OMB}v-}¨Mxf~0pm¦Ïl
lfüQ¦}~Bl~Bp¦}"pf~"fxM~¨}OMv«j}~¢pxm}·Qx7¯"fjQ¦"lü pVfplwMqS}·Qf
QÕ"}l~:Q¦"&Q}·QlhQ¦2¨MpQ¦!Q}vpI}~Q¦#QQ}ªf~p¨§Ê~pZ§!:l~}OM:xp¦
}~:xp¦M"}$lM~"¨7}OMv:¦xm¦ lȦ:~QC}¨Mfpf}p~}§7l:xp¦ p¦S}½MQ}·QMo§
Õ¯ ½flf~¢Q«¦&¯"f½}l]Õ¯ S}x~:¦j§p¦l<p " pppxM~:x~7}OM¢§!}ÈM§ÊlM~¨
fxhx7~Mpf$l~!p¦IVff}~:¦f&Q¦"I! fQw"7lh~:l~#7}OM2}vpI]Õ¯ppÊx§
%$Êx#QÊpfO«IÌZ~p¦BVfKªp¦qfQxM~x~CQ¦"BQxf~¢&:x~0pppI¢§\Q¦lM~¨
7}dql:l}p¨M#M:pÊ}lv}xf:'(*),+.-z/:¦p0'(x#p¦T ¦}Bp ½f0'p¦TlM~¨17}d
}~2+.-Êxp¦pxQxM~ MlVfxZ§@&p¦ :x~ª¡]«23Ô¦~ p¦lQ}·Ql xl}p¨fqQ¦}~ }v M¯
z/:¦"lm¦xZ§¯ "lO}vüv'VfO}v~fx¿¡]½½p¦\p¦f"QxM~v¥Q¦"Tpp"lf~¢:l~Cppf&¢§Q¦"
l~¨47}OMv}~M~5jf~¢px§!p¦&f"QxM~!x~Êp¦2pm}ª~f¨§f~xZ§Êp¦6:x~7}OMf
}qMfo§pÊ}x|7:¦"lm¦ Õ¯ S}vl~&:¦¢§p¦lI "¦f~Ê~M~ ¦}-~-§T½ff~ MfoMfM~0Q¦"
VfO}v~«
ѯMfp}-S}v Mp}vQ§*plz^«Û¨«I{\xQ"§¢}vp dM²M²È¤¦xlxl Ê}~ }~"~fdv±
Æ
M~S}~
dMM¡7¦}OMMpfp¦}v:¦f~}pQ}x~\v'l~¨fm¦}~"lO}vlx§
Ø
¨Mf~Q}vpf}OM-}TÊ}
Q M }¨M}vQx~ Q¦p}Ê"lpplM~}qp¦ :l~xql:x~¨'Q¦"f~Q¦$p¦"M
Ø
7}dfxf~¨p¦
:l~"
Ø
¨M~fp}vQ7}OMfI}pÈp" ppf«:&:Q¦"lM ½È¥p¦fm¦}~lf}7}dBx#x~fO}f
Q¦"fpBl2}!pplM~l~p¦B Qp}¥"f~xZ§Mh }plS}x§x~Cp¦qf~"fp¨v§M~¢m}x~l~¨ÊQ}~"¨M
}~ÊQ¦jp¦2pm}v½~f¨§f~"pxZ§Êp¦6:x~
Ø
¨Mf~Q}vpf#7}OMf«
Ö
M]Õ"}Ê "l :xp¦}TlM~¨
7}dXpxM v ( (½} "pOÕ¯lÊ}vQx§\®"«Ü®¢¯w{\xQ"§¢}vp zod²M²¢¡#f ½MI}pplM~x~Q¦"
Qvm}'~f¨§ f~"pxZ§ vp¦0:l~}OfBp\xfTp¦}~²M® <Q¦"v}x l~Q¦"!}"pf~"f
fm¦}~"lO}v }Off:¦lxqM ( (! ®"d®¢¯
Æ
~fl}~ zodMM¡#M~" p¦}vÈQ¦ pm}¥f~p¨§
~pZ§B"Q¦ :l~ 7}OM}¥pf"f j§B}2^}QMüª}v M¯X¯«ï¯« 3Ô¦}v}vpp¦7fm¦}~lÊ
pp ½M~lxÈQ¦x#oQ$#jl~¨ ¦"f~Mf~"M~&%&~:¦}v2lp¦xÊ "llf}vQxM~ÊQ¦T! fQ#
fxÏM~:l~ 7}df2M~\p¦È¯O}~%
ÌZ~ f 7}vQf:Q¦"!pf~¢QQ¦CMl"plM~*Ip¦$p5j~§ p ½fQ :l~"
7}df('-z)*,+-*,.¡]üxI¨MdMp~ ¢§p¦f~p¨§0}S}v~fq!j}vQxM~ z^fÏM-]Õ"}Ê "l0/ÈÊ~
2}K«dMv± \±1M¡Ù
2 '
2
.43 '65
2 '
2 + 879
3
7:<;
3
7>=@?A* zou¡
:¦pB)Êxwp¦XQ}"S}~7}d5jf~"§}~ '65'xwp¦X¨Mp Tfx¯xZ§M« ¦XQ¦f<pM"pfXQpf
79(7:<;<}~"C7>=@?pf "pff~¢OXfp ½fQMf§M'~f¨§l~ ¯M Q¦:l~¥~M~xl~f}Èf~p¨§
Qp}~of$Q}O]³ 7}OM0x~jpfp}plM~7}v~ ~f¨§*lpx }vQxM~ p 7}OM"pO}D#Vx~¨«
¦!}vMpÊ~¢Ql~f S}½Mp}vQMo§0O}pÊ~¢Q 7p!Ê}}\oQO}v"§ m}·QpCp¦}vÈQ¦"
p ½fQp}jf~xZ§}v}~¢§-pm¦q}~"p!jf~§Bxwpfpl~"fTf~¢Qxpf§-¢§ÈQ¦< :l~Ml"plM~
üQ¦pTpM"pfÈ~QxM~Tz/:¦"lm¦$Q¦Êfxf2}p-Qm¦\f ½f~"f~¢]¡] ~}vÊx§
'-zE)>*,+ ¡B GFIH
J
'IKL
5
zM79
3
7:N;
3
7>=O?¡P+-" z|M¡
¦TMff fplM~C :x~}OMIfl$Q¦pMpT -p¦fx#¥m¦}~¨M&f}p
¦}OM f~C "#M7}ph«
Ö
xppx§¤¦lxll "}~ }~~"fBzod·±j¡}vpppx"Q\p¦l: ¦"f~Mf~"M~
Q\f~"¦}~f 7}OMO}#jx~¨@z|«Û«ÏQ47>=O?p¡«Ê&fMp"l~¨$Q$Q¦xÈlf}"üp¦1:l~
Ø
pM~x¿
f"pp~¢&x#VS}·Qf¢§p¦xM~¨07}d :¦lm¦$Q¦"f~~¦}~"ff#Q¦ÈO}#jx~¨Êv'p¦"M:l~"
7}dfÈ}v#Q¦"Bffo-'p¦Bfm¦}v~lf} 7}OMv«2ff3px¨M¦¢Bzodv²¢¡:¦}&¦:~0Q¦}v#Q¦"
¤¦lxlx
Ø
}~~qfm¦}~"lp x QVO}D# }·Ê¦"l¨M¦0:l~*p ½f}~" Vf~ʦ}OM$Q¦"
fppXv}pl}vQxM~:xp¦0:l~p ½f«<ѯfM~§M¯{}pM~0zodM¬¢¡¦}v¨M¨MQÊp¦}vX~M~"ll~"O}
7}d]³ 7}OMx~jpfp}plM~Êz|«Û« 7:N;x¡-l¨¦jȽpp ½M~pxl M-p¦Êf"QxM~ l~ Q¦¨Mpp¦
Q¦0:l~" 7}OMf«${}pM~ zodM¬¢¡&p¦" f ~"j}~¢pxm}·Qx fM }lM~:xp¦ }vm}"ü"
Q¦"\f}lS}·Ql~q p¦ p¦}vQ¦"\~"M~lx~O}v f~p¨§@pQ}~"f½ ff~ } xM~¨7}d0}~"
:l~"7}df-fO}fIp} l"x§:Q¦Cp¦Bp}vQx'Q¦"B ½O}#p!jf~§v'Q¦ :l~"}Of&p
Q¦"&l~¨47}OM&5j~§ :xp¦!~pl¨~xf}~¢7~f¨§Qp}~MXp}vQxM¨pO}·QfXQ¦}~}½M"
M«Ü²"«Ñ¯x~fqp¦ p5j~§ p}vQxl-¨MO}vpf-Q¦}~Q¦x-l~ }lüQ¦}vpff~¢plM~ S}½MQ}·QMo§
Õ¯ ½flf~¢QQ¦x#]Õ¯ S}~}vQxM~Vf:~:ff Vl}lv«
ÌZ~Q¦x7 } ½f-p"¨M¨MfoQ¦}·Q¦&p "pfpxM~$ :l~7}OMf:¢§}qxM~¨ 7}OMÈlIp
xpfÈfM" lx~¨$p¦lM~"¨}OM1:xp¦ p¦0:l~ z|«Û«79Ï¡]«3 Mxl }~ lf}$¨M¨Mpf
¢§${}D#Vx~#}K«z_dM¢¡}v~ÊpIff~¢Qx§!fxM $j§{}#jl~$}v~ /È"§M}djppz_dMMM¡
l~ Q¦lO}xfl}vQxM~ v-Q¦0"Q}¨@v-Q¦0O} ^}vf« #f~7p ½M0Q¦}vÊQ¦lM~¨
7}d\}ppqMf~¢Q">M>p¦#:x~} }0p}¨0M~@p¦xM~¨7}OM« É7M~fo}·Ql~
MÊ~¢Q Q¦"f~p¦" :Ip¦}v2Q¦x&p}¨lf}OMfI}!pÊ}lxfQ"pxf~¢-Mf~¢Q VÕ0x~CQ¦"
:l~"\p¨f~Q}vp 7}OMf :¦lm¦\Q¦ppÈfxM CM-pl:§M« fM xQ-"fppx "QxM~$
}j}v~jpxQ}vQMÊpql}vQxM~p¦lÊV| :¦lm¦@xlll}&Q\Q¦Êlf}Cppl½f "pl §
¢§ fxm¦f\}~" É7¦~ z_dMMM¡&xffl½fx~ ѯfQxM~ V«
Ö
"l|2}~ ~ Èj}~¢Qm}vpxM
fÊ }vplM~: Q¦È}vQ}:}pppl½fTl~ѯplM~T¬"«üÌZ~ѯfQl~T±" Xlfüp¦Xl lxO}vplM~"
#Q¦xq ¯fpM~ Q¦"! fpÊv&"7lM~ :x~ }OM!M~ p¦$¯O}~«
Ö
l~}vlx§}0p¦f
xpf"ppxM~\p¦T}p "QxM~:}~\f~fxpxM~#}p-¨xM~Cx~CѯfQl~V«
¦¯"fq¦ p¦l~¨7}d\}, hpqQ¦:x~
Ø
x~f ¨MQ¦:Q¦¦Mo}Of
lÈMlM ½f l~ Q¦fQ}¨Mf«
Ö
lpoQ§MQ¦"1:x~
Ø
l~"ff ¨M p¦ p}vQ<Q¦l~¨}O!l
QfÊx~fpx~¨fxpTM pVlMplf«CѯfM~"x§MüQ¦x¨pQ¦@p}vQQ¦ÊlM~¨
7}dxfCp pfÊx~IQ¦Ip}plM~vp¦-ppffªM!V"xv}l~¢Qx§Q¦"-ÊMf~¢p VÕh
O}vppxf\l~Q¦"4:x~\p¦}v#l#}"pM ¢§Q¦Tl~¨0}OMv«:ѯx~fÈQ¦ÈQvm}oQfp2l:f~Q}~¢
:xp¦¦fx¨M¦¢O Q¦j<}l-pfÊx~Q¦p}plM~ v½pp"l~jXoQfp<p!}vl~x~¨Il~qp¦:l~"
Q¦}vIx&}Ov}ll}xIQ¨M p¦Mo&:x~7}df«I m¦fÊ}vQxB¥Q¦qM~"¨Q}vplM~ :xp¦:l~"
x :x~¨dM:x~27}OM}~*l~¨}Off:}v~ Q¦MplO}v plf2f~jppx"QxM~qp
Q¦"qQQ}¥oQppÈl&p¦:~ l~
Ö
x¨«üM« ¦lx§Ï}~~}vlx§ p¦lIf"ff Q"pxf~¢-oQppÈl
f l~}!pql}M#Q¦qQm¦
Ø
lxÊQf\¨M p¦ :l~7}OMÈp¦}v-¦}I½ff~ Qpl~
f xplf}l§l~$ VlM"#l}½MQ}vpM§Êpxff«
Á ¾¿»½¼Z¾¿»½¼Âm¸p¼BÀ¶mµÃ¿Äµ-ÿĸlµ·»VÀ<Á¸
É7M~l}pQ}x~&xM~¨M~Vm¦M!}·QlvÊm¦}~xO}xx§
Ø
¨f~Q}vpf 7}df|«Û«<p¦
lµ·»VÀ
<Á¸
:¦"lm¦ x~ p¦}f~ vÊp¦ :l~h ¦} }~¨S}Cp5j~§ ) ( } lQ" (h
7}df~jq½f ( }~¦~f\}pxM ½ ( ( « ¦l xM~¨7}dC "pM }v¨¢}vQ l~@p¦$lfplM~
:Q¦":l~}~"*¨p::xp¦@Qm¦"Q0Q¦"$}plM~ :p¦#:l~"z^}qM"pfoM ¢§{C Ø
p¯§¢}}~"#M~}OM¢M¡]«¦:l~
Ø
l~"f¨Mpp¦\p}vQ&wQ¦-xM~¨ 7}OM (½"l7~"f
¢§
2
'(wz)w¡
2 .
('(hz)w¡A* zK¬¢¡
:¦p '(zE)w¡lQ¦"T pQ}Ï~pZ§$üQ¦Èl~¨}O«
Ð#f~j&7f}#jx§
Ø
~~lx~O}#}~}x§Vp& :l~Cuf}OMzv}~
Æ
l~ dMM² flm¦"fBOMM¢¡
(
9
3 (
(
+.-
'(
) (
9
+7-
'(
) (* z^±j¡
:¦p'(Bxp¦ ¦}p ½fÊvQ¦xM~¨&7}OMv
(
x¥Q¦}vpS}v~fªQ¦xM~¨&7}OMv :¦"lm¦ l
L
(
}v7Qm¦ + + J
}~ 90}pI}l}~7}vQ~pQlff QMx§M +7-l7p¦&pxplM~
MlVfZ§ÏQ¦:l~!}~
x<p¦-}o§¯Ql: fpp-¯ $fl~¢Èzm}xlXp lm¦
dM¢¡«6¦q~Ml~}vpM#l~ z±j¡ ~}f§ 3 ( (
hxI}O}D#V§ Ø
~M~"ll~"O}#fMpQxM~p
Q¦" }O ¨MpQ¦p}vQv7:¦xm¦ }pxpI O}"pqQ¦"Bl~¨#7}d}Mp&ÊMf~¢p pM Q¦"
:l~"Q¦"fp¢§qlf}O¯x~¨-}&f"ffxM"pp"l~j :l~ oQpp~f}¥p¦p"^}7QI¨f~Q}vp
xÈ¢§p¦Ê~"M~
Ø
f }vQ}vpf ¦fQpl~"¨\fm¦}~l z lm¦dMM¢¡]«
Ö
l~}xx§hQ¦¨MQ¦ p}vQ
fV!$lf~¢f
<}q"~ x~ z^±j¡-v}pxf :Q¦@Q¦"Q}vpl'( ),+.- } p¦" :~x~
Ö
l¨«¥¯:¦xm¦
fÊ }vpf#¯l\v}xf:xp¦}vQ}"«¦pS}vplM~¦l $½ f~ }v~
x2xÊf"S}vpfx§
pf~\pM z^±j¡]«
Á¶]ÃK¾¿Ã^¾|µ·» ¸Ã7¸m¸»<Á¸ Z¾¿»½¼Âm¸p¼q¹ÃK¶Q¸m¹m¹BÁ»½¼ÊÃ^¯¶  l¸»Ã ¾¿»½¼¹Ã^¶Q¸m¹m¹
ÌZ~Cp¦T ppf~"fq¥po^}f4}Off½Q¦4:l~$MlVfZ§$O}~C TfM MfCl~¢QQ¦fT }oQf
+ +
3 + 3
+Sw~}vÊx§}pl
Ø
}OfQ}v¨Mf }~ p }vQl}l§ Ø
}OMfp}¨MÊf}~ :x~ +Ïü}}OM
Ø
l~"f Êf}~ :l~"
+ÏX}~}Cpp"l~j0:x~ "Q}vQxM~+ «¦~ Q¦!pm}voQppl~
Q¦" :x~}OfQ}v¨Mf\dMf#}7}dfxf~¨p¦wp¦}OMfolp¦-p'}qpp"lf~¢:oQpp
B
+
! "#
}~ }#7}d
Ø
l~"ffppff$!(4
+
%#
:¦"fp
#
ppIp$}dfp}¨Ml~"¨
dM}&7}OMlf~"¨Q¦½lM~"¨&}Off« #f~:p¦Q"pxf~¢Xppp<}pxp'pM MQxO}¯QQ}v~p ½M
h¦Mp'&fM~¢Q}ªÊMf~¢p ¢§Q¦:Qxf~¢l7}v~Êp¦67}OM
Ø
l~"fQf}lp<M
MplO}vQQ}v~p ½M:v¥¦p(&M~¢m}hÊMf~¢p¢§Q¦" 7}OM
Ø
l~"f È«
3Ô¦f~0p¦ :x~0}v~7}dfÈ}B½Q¦CQ}vQxM~}o§$l~CplT}~0MlM 0~x§f§Cpx:x§
:xp¦qpm¦z|«Û«¢}~¢§qm¦}~¨M: Q¦qQm¦}pdfÊ}~¢§ 7}dfxf~¨p¦XªQ¦ }OMm¡]Vp¦f~ Q¦"
O}~ÊÊ~jp 5j}·Ql~ʦ:7Q¦}·<p¦2pm}vQflXf~Q}~¢:xp¦Ê¦"fl¨¦jIzü:~p~
- 3
!( f~Q}~¢
+ - " z|M¡
°2Èp¦È¨Mf~Q}vplM~$ 7}df#¢§ :l~$l"Qpl~$j§p¦IQ"pxf~¢:l~$oQpp2}vQ¦"
7}vQÊ^}« ü O}xfl}vQp¦\pp"l~j:l~" oQpp _l~ Q¦\ fp~fC&p¦\lM~¨
7}dVQ¦}O
Ø
x~foQpp7}p¯S}vpf:Q¦Q¦#l~¨}OMv !( Vlpfpl~"f«¦"
7}d
Ø
l~"ff$oQpp}·p¦Ip"^}&l<5j}v QTQ¦2Q}vp&m¦}~¨M&Q¦"&MÊ~¢Q x~ÊQ¦"
7}d½¦f~"fÈMQ¦ÈxM~¨7}d
!( F J
2 (Ïz)w¡
2 .
P)>* zK²¢¡
:¦p (Ïz)Ï¡ÈxÈp¦!Mf~¢Q" f~xZ§ Q¦ÊlM~¨7}d:¦xm¦ x~@¢§ zp¥M
Õ"} x¤¦xllx &O¯ \±¢®¢¡
(ÏzE)w¡( 9) ('(z)w¡A" z M¡
ѯ"QQ"pl~¨*zMM¡Bl~¢p*zK²¢¡B}v~px~¨Q¦:x~
Ø
x~f¨M p¦Q}vp ("~ x~ zK¬¢¡|
§Vllp¦-Mlx :x~¨q]Õ" "pfpxM~CM !(hÙ
5( 9 F J ( ) ('(ÏzE)w¡OP)" zK¢¡
×
j}vQxM~z^±j¡BM Q¦" :x~
Ø
x~f*¨Mpp¦ Q}·Q\&p¦$lM~¨7}dCp¦f~ p¦:Êp¦}vQ¦"
ppp#l~"ff\¢§Q¦ÈxM~¨7}dB½fMÊ
5(
3
(
( ( ( * zK¢¡
Ó2~"f:}BoQO}v"§#:x~¯p¦-} xxQ"2vÏQ¦-xM~¨ 7}OMÈMfxM :Q¦!Qm¦z|{CQ"§¢}
}~#M~}CdM¢M¡]}~"pM p¦qppQI"fppx }v dMQ¦qfl}vQMB"f ½f~~ff}~
:pppf~
(
(
zE+ ¡ )D
(
zE+
J
¡( Ôz
( ( (*
* ) -N* - -]¡ * zod®¢¡
:¦pCp¦$Qm¦ f ½f~"f~Mf 7}vQ7}OMl0:pppf~ x~ "lf~lM~xfqMp }
Mxl:
Õ¯
(
'(
zE+ + J
¡ ]Õ"
9
3 L
z ( ("¡
(
)- z- -]¡ " zoMu¡
-
xÊ~pxM~lpÈpm¦ lÈQ¦}fflQ}vplM~Q0¨Mp}O¯Z§M +xp¦ÊQm¦}~ + J
!}O§
f~pxffQB &p¦Il~xq Qm¦$}v :¦lm¦p¦6:x~½f¨Mx~pql~ f~&Q¦"IlM~"¨ 7}d
z|{\xQ"§¢}vp@}v~ #M~}d¢M¡«0¦"l-pS}vpxq}vpS}v~fv :¦"lm¦ l-¨MO}vpf-Q¦}v~ "~xZ§0È}
½MpQx}vl jxpfpl~"fxQQ}vpxfx§M<}T¨xM~Ê"lf~lM~xf }Q}vÊQff
( (½ ) -&}~ - -O«
¦fM M~C"pl~"¨zKM¡:}v~ z_d®¢¡p¦p}vQx¥p¦oQfp&l~"ffC¢§\p¦TlM~¨17}dp
Q¦"Èpm}vppf2x¨Mxf~\¢§
5(
L
zM ( ("¡
(
3 L
zM ( ("¡
( * zouM¡
:¦xm¦M:}lM~¨7}OMTpÊ}llM ½}~$Mp¦pm¦x:} dÕ¯x!}vpf§ L
z ( (¡ «
¦:Ql~¢ :x~Qf}vp¦ }vpf<po^}fv_ :¦lm¦l<}Ov}ll}xQȨM~fp}vQ:l~"
7}dfl<M"Q}l~ÊM z|M¡X}~ÊO}~! #v}x}vQ!l~¨zou¡MXQ¦"2oQppx~f¢§Q¦"
l~¨}OQ¨M M
!(
3 L
zM ( ("¡
( " zod¬¢¡
°2vQQ¦}·} ½MpQM Q¦"\p}vQx ) &llp Q¦}·Ê"~xZ§ "" M"~f l ¢§
&fp#}ÊxÊp¦l ½«
×
j}·Ql~ zod¬M¡¦:Q¦pp0¦Q¦"l~¨ 7}OMpfQ¦"
Q"pxf~¢ :l~"Qf2}·Q¦&pO} ^}«<°2È}vffpx~¨qQqp¦-~M~
Ø
p }Q}·Qf¦fQpl~"¨
fm¦}~"lp\Q¦:x~¨Mf~"fQ}·Qf07}OMfÊl~ M ½MplM~ pQ¦pp"lf~¢ppp}vp"^}
z flm¦"fÊ}~ #~¢OMM¬" fxm¦f\dMMM¡q}~ ¦"f~CQ¦" :x~27}OM#:lx $pf l~
Q¦" ff~@qp¦xM~¨ }O«ÌZ~ }"xplM~ Q¦"l\5j}vplM~p¦:Cp¦}v\Q¦p}p M
xÊ~pxM~lpT }p}ÊQpp¦}vpfÊx~Êp¦!Ê}¨M~ Q"Ê7Q¦Ê! ffÙ Q¦Êl~QS}v'pxM
XQ¦" lM~¨7}OMv ( (ÏQ¦"}§VÊQpxq fpp¯ $Êl~jf :¦"lm¦ lIfl}vQ0QQ¦"
¨M p¦ Q}vp fV!$fxf~¢O
w}-~f l~*z±j¡ Ïp¦ lf~"pl~lpIxM~¨7}d5j~§) -<
}~p¦È! fpxT"lf~lM~xf7pm¦ #- #-f« ¦"Èpp"l~j :x~$ppf2xpf0}
Q¦"fp# }p}QpXl~"fpf}pv :xQ¦Ê}- }oQlS}v'p~pQxVZ§qQTl~pf}px~¨-Q¦:pxM ½hp¦:lM~¨
7}d-}Xl¨M¦¢< #Õ¯ ½fQfh«
×
j}vplM~zoO¬¢¡ :ll" #pl~Q¦"2p!jf~¢#}~}vx§Vpx<v¦
¸ õÈÃĸlµ·»VÀ<Á¸Bµ·» ¼V¸ ¸ lµmº!¸»Ãµ ¾¿»½¼ <Á¸m¹
Mpx~jfoQl¨M}vQx~¨0Q¦$ hQ#Q¦"\xM~¨7}OM\M~ :l~
Ø
l~"f*¨pQ¦#Q¦$¦M
7}df7Bpff}lwMÊTf xplf}ÏpS}vplM~":#p¦BMlM f~¢& :x~7}OMfz:xp¦
~$l~¨ }OMO¡È"~fÈoQO}v"§:l~h«Ñ¯l~07}qQ\fM }qQ¦¯:Q¦ S}½MQ}·QMo§
}vQ}" 7<pXQ¦"XQm¦pfl}vQxM~Ïm}vlxp¦¢§{CQp¯§¢} }~Ð##jll¦z_dM¡hl~TS}½MQ}·QMo§
O}pÊ~jp: :x~V³ 7}OMTfl Ê~¢O*:¦xm¦\§Vll
- )
G "ܱ¢
+
-
K
J
* zoO±j¡
MMlM f~¢:xp¦\Qm¦\üQ¦Èp ½fQp}Ï f}#p!jf~§M&)
ª}~
9 -
±"Û±¢ d® K +
-
L
* zouM¡
MMlM f~¢:xp¦\Qm¦\üQ¦Èf~"fp¨v§$f~xZ§vp¦:l~}Off
9 «
°2 7-Q"p~Q p¦IMfxM f~¢#wQ¦6:l~
Ø
}Of#l~!p¦- pp~fTwQ¦-xM~¨ 7}OMv«
&~"¦f7-Ê}#I}Bffl}}p "plM~V~}f§Q¦}v7Q¦I~x§! f:ÏQ¦"-lM~¨4}OT~
Q¦"fl Ê~¢XQ¦:x~7}df<l¥pIm¦}~"¨MQ¦7pp"l~j:x~ pppf_j}v¥p¦7}vQ
p"^}«#f~BQ¦Tpm¦S} :&jpf }½dMvÏ}~:¦"lm¦f M"m}vl~l~\Q¦q}p~fB
}xM~¨}OMv<}p!}pÊ@QC¦Ml p¦ :Q¦ }~" :xp¦M"B}l~¨7}OM«¦fM'Q¦"
pxplM~ MlVfxZ§
-f'x~ z_O±j¡È}~Ôz_uM¡-l}pl¨M~"fp¦Êv}xQ¦"!lVO}v'Ql~¢ :l~"
pppfQ¦}v
-I z )
¡
L
+.-4:Q¦@~"l~¨7}OM$}~
- >z )
¡
L
:xp¦Q¦"
l~¨}O«
¦f~"fül~¨ z_O±j¡2}v~ zouM¡]hQ¦"qfxM f~¢ :xQ¦0Qm¦ XQ¦"q f}#C5j~§ }~"
Qvm} :x~
Ø
7}OM~f¨§}p<M"Q}l~"f :xQ¦B}~4:xQ¦"M"üQ¦<lM~"¨7}OM«¦"7MfxM f~¢
Q¦"fp j}~¢pxQxf: Q¦\}~:Q¦"Q¦"TxM~¨ 7}OMÈO}v~\½-fÊ }vpf$l x§M~ff¨M~xplM~
Q¦}v% ¦}-Q¦"p}q}vl0:xp¦ }~:xQ¦"M"-Q¦"xM~¨ 7}d«¦lÈxIQp"½ff}¥¢§
l~ }Com}vplM~}v§ p¦lTQ}v¨}l}~fp¦ ppp"p¨Mp}l~¢Tp¦}vMpfp¦1:l~ zQ¦"
§V~ "Qx# "pfp2¨Q}xf~¢XdMXp¦:¯O}~M'p¦ ppp2¨MQ}"lf~¢X:~Q¦p~~l~qQ¦"
S}v Mp}vQ§"¡«¦I fpp-¨Q}xf~¢Q7q7 #Q¦&Q}2Mp~pxl2fM }lp~ :Q¦}~"
:xp¦M":p¦BxM~¨0}Ofz:¦lm¦0x~\p¦TS}½MQ}·QMo§l xlfQ¦TQ}È^}~ fª¡#}~\¦f~
pQV l _«
Ð#B§!}~\Ç-ldv}~}~¨flz_dMM¢¡X pdVl"IÕ¯ ½fpxÊ~¢m} Vl~f-x~p" wp¦lfM~
Ø
fxpxM~«2~Mx j-xM~¨7}d :xp¦\lM ½ ( ( ®Cz^ "p:l~7}dfQ¡ ®"«ï®"ª®"«O±M:®"«ï
7}2¨f~Q}vpf:Q¦C} }x-Q¦}v# M }¨M}vQ}v2¬¢q¨Mpf#QQ¦ÈO}~:l~\xpfQxM~«
¦Q}vpl'( ),+.-Tp}~¨M-pM ¬¯«xCzM ( ( ®"ïM¡2p²"«ï zM ( ( ®"Ü®M¢¡]«ÌZ~ O}vm¦ O}vpwQ¦"
7}dfxf~¨p¦Q¦xM~¨ }OM 7}qÕQlfTQ¦}OMl~¨Q¦p¦p¦"M:x~ 7}OMf}v
Q¦"p ½fQp}: f}#ª« ¦"§ Êf}pf*Q¦\QQ}:Qf!l~¨ p¦ p¦x~foQS}v
Ø
"lpl }·Ql~
Q¦"¯ }~f¯§
Ø
fMpS}vplM~ Q¦"¯«ÌZ~
Ö
l¨"«Ï¬" 7 x-Q¦v}l"fÈ<Q¦QQ}'oQpp
)
hO}pj§Ð:fB§}~ Ç-ldv}~}v~¨Mfx<zodM¢¡2}v¨¢}l~"2pl Q¦lM~"¨7}d« ü
Q¦"-}fQ}v§Ïp¦-O}pÊ~jp7Q¦"IQQ} oQfp:x7fxO}x§Ê~}, fQ\¢§ÊQ¦IxM~¨ 7}OMv
}#}¨MfC}½dM«
2~fv'pM z_O±j¡x6)
J
xTp¦Ê5j~§p¦! Qp}< f}# :l~" }Of l~ Q¦"
}f~v¥xM~¨0}OQ¦~
)
) J
K
J
L
* zod²¢¡
:¦xm¦ l lxf-Q¦}·BQ¦"p ½fQQ}v f}# p5j~§ ¦}q¦"l¨M¦v}xf :¦"f~}0l~¨7}OMl
}"f Q:l~" 7}OMf7x~ j}lm}vpx}¨Mfff~¢0:Q¦ S}v Mp}vQ§ Mfv}vplM~"\z
Æ
M~S}~
dMM¡«
¦B h&X}ÊxM~¨1}OqM~¨pQ¦C:l~"7}dfIx6j}v~jpx0¢§\l~¢MQx¨¢}vpl~¨ Q¦"
Q}·QlBwQ¦:x~
Ø
7}OM-¨MQ¦$Q}vpf:}v7Q¦I5jf~"§$wQ¦"Ip ½fQQ}vÏ f}#ʽp¦:Q¦$}~"
:xp¦M"l~¨7}OM~}Êx§¥z)
¡T}~ J z)
J
¡Tfp ½fQMf§M«¦lTQ}vplCO}~@½M"m}vl~
¥z)
¡
J z)
J ¡ )
) J
* zoM¡
:¦xm¦pM zod²¢¡]½ffÊ
¥zE)
¡
J zE)
J ¡
J
L " zod¢¡
2p72pÊp¦#^}v<Q¦}v
v}l<~x§ l:x§ :xQ¦ ) -Iz^f
Ö
l¨"«VM¡}~¦f~&x<~"O}x§
Q¦"Tp}:xQ¦C}~ :Q¦M¯Q¦Èl~¨0}OMv«
Ö
l~}l§MV5j}vplM~zodM¡7p¦::Q¦}·Q¦ÈQ}·QlB¥~f¨§$~pZ§ :l~ 7}df:xQ¦\}~"
:xp¦M":xM~¨7}OMBx
J
L
* zod¢¡
:¦xm¦CxQ¦ppÈppM~¨x§$}, fQC¢§p¦ÈlM~¨07}OM«
q¦MTpm¦¥p¦!p}vQxMÈQ¦"Ê ½O}#5jf~"§M¨pQ¦Q}vp}~f~p¨§ ~pZ§
:l~"7}OM:Q¦\}~ :xp¦M"lM~¨7}OMÈ ~ lÊ}pxx§ ~$p¦-l~¨}OlM ½ ( (
}~ÊQ¦&}§VÊQpx: ppp"pI¯ $Êl~jf
«üq!}D#&M2x~xpS}M¨M¦ÊfoQlÊ}vpf<Q¦"
! flM~¨ 7}dfM~Q¦p6V}~¢Qxplf 7&} dÕ¯x!}vpqz_d¬¢¡¥Qpm}x~!M~§qQ¦"&ppM~"¨Mfo
~f~"§M½~}f§
3 L
zM ( ("¡
" z|®¢¡
©<}S}vplM~Êl~ p¦ Q}vplMfxpl~¨@M p¦l$}v pOÕ¯lÊ}vplM~ }vp xppf l~
Ö
x¨«<± }v$}
~QxM~$¥xM~¨07}dlM ½IMp¦pT" fp~¢#v}xf:
«
Ö
pM p¦fʨM"pfxTlTfxO}-p¦}vB}Ql~ v:}CxM~¨}OM! pM }¨¢}vpl~¨$l~ Q¦":l~"
xpfQxM~ O}"pfÊ}0pQl~ x~@Q¦~f¨§f~"pxZ§@:l~ 7}df}~ Q¦}v Q¦x ! f
½ffÊl Mom}~¢7}7p¦-lM~"¨ }OTlM ½Ixl~pf}p«
Ö
M}ql~¨ 7}dÈpl Ivü®"«x¯Q¦"
f~"fp¨v§f~"pxZ§0 :x~}OfBx-pf¢§ p\±M® <Q¦"q}vl:Q¦M¯ÈlM~¨7}OMv
"<Q¦"&¨M p¦Q}·Q2}v7 ½O}D#qp5j~§!lXM~§pf¢§Ê" ÊQq® hQ¦#}vl :xp¦M"
l~¨47}OMv« ¦"&ppM~"¨B! fhQ¦#pplM~Êl~Q¦#f~p¨§~pZ§:l~"7}dfx<M
Q¦"T]Õ¯ M~"f~¢Ix~ z_d¢¡]*:¦lm¦\l:S}vp¨MQ¦}~$Q¦"T]Õ¯ M~"f~¢&x~@z_d¢¡]« ¦" h2¥xM~¨07}d
7}d&lM ½f}Xp¦:~x~
Ö
l¨«±¢}}v~! Ql~Cz_d²¢¡«
Ö
l~om}~jM<}TxM~¨7}d&lM ½
( ( ®"x"Q¦È Qp}Ï ½O}#!5j~§$xl~pO}vpf\¢§M~§«¦pTppQp Q¦"
¯X}¨MfV}lm}vpxMx§ :xp¦l} Q}vpM§Êf}pff~¢Q«$°2]Õ¯TQ¦"ʯ"flÈMÊ }p
j}~¢Qm}vpxfx§:xp¦\]Õ¯lpl~¨l} Q}vpM§Ê}vQ}"«
0 N (& & 1
üqfM }2p¦&¯"f½pfxp :Q¦l} Q}vpM§}·m}" 7&~fQ #j~ÔQ¦&pfxv}~¢7v}xf
M$lf~"pl~lp }p}QpI~}f§ ( (½ ) -}~ - -O« °2M~"TQ¦"
S}v Mp}vQ§\}vQ} pdVl}vlI M&XQ¦ ¨MQ¦Q}·Q fV!$lf~¢f
«Ç-xf~ }S}vp¨M
pf}vppf
f ½Mpf!x~p¦&xxpfQ}·Q¢x<x7}Q}vlx§q}Tppl #¢§jfoQxM~!¦ Qm¦¯pI}v~
} "pM S}vp-}vlÈ M
«I:Qp}vQ¨§\l#}Mxl:f«ÇÈMf~$Q¦}v:Q¦TQ}vpl'( ),+.-:M
Q¦"l} Q}vpM§!Õ¯ pxÊ~jp&x#x~\p¦Bp}~¨MT'¬Q!¯ Bq}pl~"¨Ml-v}l" ®Êl~
Q¦"B¯|«3ÈQ¦~0O}xfl}vQ-p¦BMpfp ½M~"l~¨}vl2
}~
( }~\~}xx§m¦ #
O}vlf"S}vpf
v}xf#}-l~Q¦"Tp}~¨M-v¥}·m} fMxS}vpf¢§\¤S}~¢z_dM¢M¡}:p¦:~\l~
Ö
l¨"«¯
~}f§
¬±d²"«XÐ:ff}l Q¦}v TO}xfl}vQ
pM f
×
½«üz±j¡
3 L
zM ( (¡
( " z|¯u¡
{CQp¯§¢}}~"#M~}\z_dM¢M¡<Êf}pf$§VoQfÊ}vplO}vlx§¦x¨M¦}vl
:¦xm¦$p¨M¨fp
Q7pBI}BfS}·Qx2¦"l¨M¦<v}x#
«'ÌZ~f}TfM }lM~!hQ¦2ÊVfªfp"xQ :xp¦
{CQp¯§¢}Ü zodM²²¢¡Õ¯ pxÊ~j&p¦:&p¦}v&}ʽQf2}¨MfÊ~j&l:M"Q}l~"fC
d²M®"
"#}v¨¢}l~Q¦-f M~"l~¨qv}xfv
}Il~p¦-Q}v~¨MIf ½Mpf$¢§${CQp¯§¢}C}v~ 2M~}
zoOM¢M¡]«\ѯ
M®\¦}T f~@f x~ p¦!MÊ }pxpM~ :xp¦p¦ÊfxpB:¤¦xlxl È}~"
}~"~f zodv±j¡}~
Æ
M~fl}~ zodM¡« p¦
M® }v~ d²®*¦}O ½ff~pl~ÔQ¦"
fÊ }vplM~:xp¦0{\xQ"§¢}vpÛqz_dM²M²M¡}vQ}"«