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Title 潮流による海峡を通しての海水の交換及び混合の機構に関する数値実験的研究( Dissertation_全文 )
Author(s) 淡路, 敏之
Citation Kyoto University (京都大学)
Issue Date 1981-07-23
URL https://doi.org/10.14989/doctor.k2597
Right
Type Thesis or Dissertation
Textversion author
Kyoto University
罫
醐
学位申諦論 文
瑛 蹄 敏 乞
学 位 申請 論 文(Tkesls)
潮 流 によ葡 朧 遁 しての海水の交換 亙ぴ・
ラ箆!合一の機構 に関すろ数イ直実騨 ウ研 究
關轄
炎 略 敏 え
El :/~
1. 4
2. i~=T'')L'
2-1 ;1 ;MmittETilAz 7 t. Z
2-2 i)-St) ::-7u7
3. 5~4a)
3-i YTTI
3-2 VAJOV1z"R11-Ta "R11-4-414( ti*
4
5. rq %)k 91.;-7I< E1`
5-1. tl,zh IA. Li )-Sf10 a-11.4 -tA0 tit
5-2. , ri;, A' 7‘0A(.0)IQ] 01 t,
5-3. (n' K L 91- A2K t o ;14o`
7. % u;k.Iz lkoM iZ-21) Z
8. 4 LND
Arre"d1xI
- 1 -
- 5 -
-5-
- 6 -
- 9 -
-9-
- 10 •
- 13 -
- 15 -
- 15 -
18 -
- 21 -
23 -
-25-
- 27 -
- 28 -
-29-
-30-
- 32 -
1. T
A Itir.11;~~t`) Et. L 117-0 ; oT giAZ 7kt~ .i7-199
?v4'.~fr1:OR 6 7 I= a4 I g .`Ztot11J)Z 1,fato,
Z" 9 • i - i f;t4J I A a) t t~ L7 z t rc. -h' -1i' ,h I) E 1- i<,Za
VT- 1-207-7""3~~ -rt'~~2Ti9, 01*-A /x-2Z
Unt
^ ~~ ~~"'~ o~ 1 i~ . '4.i = li ry 411
Fa gfg=E . 01- tv- . fiJs ta o) 1
1 1"~ b'aW.6/9 -'7 l` n,1J ,ao 2, t M2411---46•
Zt1,6' 6/9Lr =2(vk-C-Va-)3'222. 07 7k1iz.
~v ^'r" ;C ~fi"'Mz 1 r~t=1,2a0k(LA t,ZT ~ t,Z T o
1_
こ鼠 まで のi麺ム天を免・し■の%レK交 換1二 閥、すそ〕石牙奴 は.穴 別 すうヒPナ ィラー的手活 にうヒっ・く
研 吹&び2)ラ ク"ラノヲン的 キ該 に もとつ冥 齎 貌 に分 ヴ5れ ろ。 前老 は才イう一的 茸棚 リ
に よリ得 られ る切 王鰻,老 ヒカ猟 、〈っガ の固定,点、に卸 乃 指 橡 物 唄`そ の多くば塩 劣)の搬
度 や その空 閻命布 風ド惣 妖 断 面 を血 魎 可うフラリクス量 をもとに した研 究 であ り・ 後 老 はレ'
タレ ・アイ寡 沙 の須 条レ物 を便 。た ラケランヲン衡 な観 狽・1㌍ノK理操 型 慶駿lo舌 ヴ彫 事勉 跡
り'5得 ら耽 ううチラングユ量 をもとに した窃 雲 であろ.後 石 の御 究 ば 最面 人工衛 星力'うの赤
外 宇真 アよとこの種 クの楕 報 をもイ更用 し砿ザ ラ進 め ら承 台々めてUる 斌 才イラー的 な餐見裂llにく
うペ ラ伊ラン方 的 π 観 刎 ザ 経 痛 的1託 技侑 的 に{.は るがに 困難 であ∂為、前 老の窃玖
に しび τ非 常 に 弊 いのガ現 オだで 励 ・
1)の オイラー匂つ手払rこよう石升郵 は、Pαψkere士α1、(n72)や 川不寸らdr75)1=よ フて1藍めらλた。
彼 引」宿峠 嘩ウ面 も臨 しての上ヅラ朝璃 ヒ下げ瑚 晒 で・の塩 窃1輪丞垂 の佐 に名 目し.兇れ力一老4美
を孟 し匂 吻 ・k嫁 換 に あ ヱ生 匠 ・、ろ ヒして 瀞 蕗 し研 ∫ケ 量 力・5勉 糠 襖 砿 誕 蛎
す/、。ラメー9一ひ あ る誕 換考…を誹 価 し乏 。 循豚」霊 拓ゾkeゾ 凌 へし1葱」=、ア姻 時 に痢 考 へ…義
入可る・全塩 末.のうち新7と に 流)◎ う外 湾 フKの劇 含 と、‡長 川耕 引3上 ザ 姻 踊 に 閃 秀 へ流
λ3る 晦 未 のうち下げ襯 鮪 に 丙角 氷 ヒと吻 隼呈彦 メれガノりるのガ ヒuラ 劇 ・合{弘 そ・k宮ソt女
僻 ヒして磁 し、琳 嫌 彩 嫌 。 纏 嘱 齋 ・種1砥 懲 のた換 は 和 看
メ(が 霧 内♪㍑ 動 疎 馳 ・の あ ろ頷 域 で・霰 合 筋 二とに よ。マ 取 り残 猟 急と吻 教 が あ
も。 中田 と平野([r76)は 一歩伽Z数 丁固のフワ〆トの 動 丘から 簸 合すうと恩 わ 》Kろ範 嗣(鍍
らは これ を規 合唇猿 ヒ・肌 で 幡)乏 購 り、 初 殻 合容狽 肉 で 鋤 氷碗 全鵬 勿"古・誘
とイ夏日巳して 歩訪 フラッ7ス と二廟7kの 麦換 量 ~しの関 係 式 を導出 し7三。 以 ムの差うに・Dの 巧イう一
鱈 殉 誌 じフ・く厨 曳 ほ 磨 的pl3晦 欲 周 逸 のあ樋 域 囚 働 揚 勅 宛盆 彪 合蔦 ・て
庄 じ るヒ いう老 乞 に 立脚 レてqる 。 し勾'レ ユフの狛1kは ひのあ1ヲ♪で・沙のめ な 爵1=・と》)
さうに して 菱しいりなう0)カ'iさ.よくゲ カ㌧てい7寡 、)のが覧手昆窓(で・1めb・
徽.狛 峡 を孟 して0噸 絞 換 機 梅 も解 明 レ な 換 貌 正 しく評 価 鮪 肋1鳳
上1ず鋼 爵 に紀 入してくろ勉 太か'肉 尭7Kと ラ&台 筋 劾 固乞正碓 に托 纏 すうこヒカ蛍 薯 であう・
=^i. 1/07~~-AcTiL "' •mr;)1-:_-&-00-730t' *Kii 0 _a)-tab)
4ellit''• _1r6tA1 iraa L--b‘ Lis If'''. fitij21—ia'77 jrd;tIo)m --Ath. 2)a)
~t7ft0 <. o9n5)it't-5 01976)
G.13`"Sd172 It Ts 0 1.-7'1,• 2-k.-, ZtiPkik/d4-4(•
A• is t _~ v .' o A'I,,-n` P.,ke' et QI. -'
l ~ t6 ' 9, t r OLD h a 4 TI- ::**%- . hfi, 5 .
t . 2_4,=r, ..-131':_)rt=7--0).to)aio=t t~~ a z~a
61T—c-c. zc.)4c)t0 Z(NIo
C. Cr) c-ra ;Z,o~^ Z, 1.t~*z•'t<ka'77)11.7t,7a —
(= E 97b CStok.s, i 4 z) E_ 13 L. *it-eggel - .dCfi°'4 4 5
t' I-L-r= .t=L R '1 ta1 s ~~T~sr ^~ h~ ~, ~~ ~
:. iir 0 SS ; AL -)2'"/A-apt-la'. :. as Vr~~ifl^a r;1114(00)/
' . Fq.1 ^- l: t7j e'k(C') F1_11 tz_4- -5WI:;A(L.
<t„Ai,,641( 4,47K~~~..,~~, 417Z10 T-(F4.1.010%),~ ,Z
t)a' Izl,'t)z11 It '1 A-0° _194. r.$669
1 >~1 ~~ ^_ ~, l=rd ~~''~; ~1~;7~-c,' ~-%; n h z-T05"744-7a°
- 3 -
75 km
\i,STRAIT
41)km
I
INNER
BASIN
4km
1I
5km
OUTER
BASIN
OPEN BOUNDARY
n r
Y
>x
35 km----------- f------------------- CO KM------
Fig. 1, Schematic view of the model basin
tiaZ L, -to') :I crizli ,ril1s c 'I*'4 7-xA KTI6-WT TT 4-?I 4-
>~~ r la . 1,1 5-€1 :&-r4 = zf -,z 1 )- 9-77 ----
~). Yc~~'~"-7:~2 1-~~zJfiLtZ~<~Z~' 3d 1'; =-°) lJ%1,a 1-"f
-• 59"5/f): 1_ L.,Z 0,ere`51 u 53KZk) Lonpet- thajiNS oci61) 11, -• 9"7
file]qi,:i4I11)30/t4114.1:_felATrifirXf111/0/firI,Tc.. t 4,1a. 14(109
rs -1-I C` ct a ,a t_ p u1 Ii. Lot? a- H111hs ~~..47 ~ T- s **CM la 6,i
1=r 1 ~`) ()Ia,Jair I) 7RIi .fi lrt= fk i '( P'Q LT-7-
41-2k 40/tL„, b}ti-;, 6J .Il l ofto-rcl=latL
(17A r.LZ 1'9, L(1)itA L.IS,=407•0)--~}~KColtiA /'tifI#LI-71.1t A7km:)
I) 1:** 'f *q % a -e1=k ,z'i.>1Jo /Iftiti-)4"4 -*& ;(A
Tt f'%rr~ o `~ ~z.4111%101E0,o5,41A%07)%17 Iz-_I,‘1173 k;~.P~
Ittt4L,7k)r. t#
- 4 -
2. Vi L
W l i- -4 )it\)~^.1,zo) .ii-A(t a 1 R-7 =tt,R4I to -176
/7a M2 A 1=*ct;tfi 104;;V'l-b°'7t99 WE o) (L)-
t,t-41111-"g it 4'ao A2'1 t'~75k--,11 ¢o 1a)*()
fit, 4 k^v.) b -os 'h 1= ~ z P O 3h T IR 9P-;-t 54--N tz i 1 °
I - TA- o z„1, tt k/A la 1 1:0 c4% u•/i,
14t Lq,Z1‘9. -Z• M.IoT1Rm84z3_L-1=,Z= ktt7m=i _tP-A,ie..:`ta,
2-1. =ftatt~”11z7~Z
tit-4 ~Ta) 411 lc, en t z NT-0)
attw•vHlu+ilk)U=iVK-- I ,:u~ -r H fi3
a3 - —UH" (IA] at
(2)
Z,. w 11t+CaTT-77-T4 TI-77-A44.-E-11_7t-i-41, ~~Q LA, v- " LI2J
,N% -r.9 t Y151-4(11-r]•,3O?74L, Hil c ,. (= 7:0(16-4s-1) i'if9
/V-5 -g-, 5 C=9a•ocm/S2) 1JPOI], ilk 11 V ch (r1nt1)o$'«N'2^ti, iA1 (=55pos
cm2/s) I-1 i(t 55t93 3%,I.5.'f fht, r 1a T 7 )-tL', Vii (_ aX r 1 a ) la 7k-tiq
7I-~t.• T^°1--q-, OHZ (_ t ay~)1~-77-7°7=2-7 2a.
44* n•'7 1-"i T( I 'fr 0) %+v;r C 1-}ear5, (975) LPU'<. 3-kit
- 5 -
_ = to l (Li (3)
(3)X1=R17 Ifansen(1956)ttr .s.'l=TI7Z2.6X103(s=100y,o)M.14111t X-C51-.710))
= 5tn C(2m/T)(4)
(4) :Iz tI1 4teiti3b gv' 1 T1a. _,zia90Ona-0.012VI rt" iv"7ZPi z
(+), (2) (/) ralr7~~~%14i,r ri5g10 1::11'*i-F : 1-.1LV-07", ~k
tkfkitX R_11 5N11I E[0 a'U'' AA=zvrn tari
t* I , `Co fi"'ffL 1-7 A-DI (Lee.ldertse, 17~) l= ~,Z17T,r ,
2-2..4olif=r'')l/Iz:7()Z
2-1 T''"1; 1i,oT1(1-43-EY7rX) *I'At- o , i-1 $+1Jiz9il~
TIL -(f1.2). -L1g10.51 f1691::
Pow arti Bi 2m/2 a)
~ ~~I~l~~zt^~o
OP! tO () 1^mtT 69 fi"~XnoNlZtl~~aj~o_47) )--ti"'ot
-N I:- LX( -4.2e ( t t (=t, -rot ) (_~• 13
X ti, (X„,t) = ( ho t a%) 7‘0) 0-If•CXC„OXxo.t),t) 1')•Tcn.k l;
z, 114 (Lfl10,e-t-H: l"S ,1969 )
akX)t U ( .),t), t i = UA () ,t) klA 040,-0 ,6%. VH w l.\I`h0, t)/ -C)
- 6 -
Ikm
Fig. 2
%6 km----Y3 km
The
in a
!rc
%3 H
arrangement
grid box.
of labeled particles (40)
xo
U(x0,t0)
U(X,t)
XotLX
Fig 3. The trajectory
particles with
of the
initial
n-th labeled
position Xo
(5) i . 11 - '. t~Z ~ T ; ~; ~ 7 ~~v w (~( t) .o 091t —6' 5-c5 -A 01 L. (.0)4
1`k tk 0) L.rzifu(L'Z 4 )'a • at Ring X (%.,,,t) t) I4 (5) °) 5 y' ~
titwt.-L Okitot t(=tDtbt 3t ^ _ of ,49
Z` i5 t>111 -i7"4 i't-t13 (4-4112 lii7; f ), -~It Z" ~+J7~~a~ 1
01-17 I - LZ Is . 04- 69 I~ ~ . ( ro,t) cl;~
-b`..r, 1k 22)30 ox( 1=` I-51-- 17-n~431Ue„ .1W ,42A r--_,
t1-1 axc(=ftotuA (,Dt)dt) Er-41 L. ,Z (5) ~' 7 ~'7 w~~ ~L
`6179•'-751_44 . .~lto+ist7`oritti 3. Efulta i
s X"l(g..,t)ia *0) -5-V A`.3,
L
Xn (nD,t) =X110 tw (^\ nD,t)+cW( ,o,t)df• ~+ uA (Xno.{) 7 dt (6) to
(6)*' RI' "7'1E1 =*-4.14•17".1 I- L7 ")77'7_%‘,a 1
Zl PI1=&173ofFARO At -1-a. (5 oAq,
'(li( Z't 1-1 . t'9 of a 6141 131' 414 gaTJA 4-C&019 7a 1t. . ib
L 1) ( L) Lo,,ret- ni't . '*Erd.
**JO") 0,1E4,47I= t1 Z. *it)- "1g1l0)1(, i0/3 5-R- . <5^"-zt~~l~ ~^
th 14)4-,1:-.1-1, ~2 0 ~111~•' ~ ~`..~ ] A~ A~~~ t-"~~z., ~ i~ia.
Ts` 1.. 4r-0-'3i- tit LT ,
tUt{*(X•,t),t) = W ( o,-t) t V (%o, 'Oat V, W ()`Co,-t) (v)
az (-)IEIVT - 81..4L t ~~~o '(I is (T) '~ ~, - T1 -3 Y , 7,1
Zti _o) (7)' (6)' t=~,u-c- At crql 1 1:::"-LI_ .,L705,
- 7 -
L`k t0A-- t" V.4 31 ~C. t" 9 19 Fs-0 ), 1= =ii ~ ~~ I = +
T"a7)30 "17.93 L r (1976)IJ, 7n
I. I fiH/1 z“=41-Ai~T~9 II 1= r ,z ti q (=,r- 9 1 o k ,- >>,l-t) =
R LZ 11'a° ~ 1'- G~ - ~~~ d7 t t gilVOMi2LIz i13 7 it rs
1.,.011z1T"-A4k t-pl 1' ,111 l=7T97,
—f(kz^= -4LIPig10—a)4-41=-#00) l t^ifLiP),(r)t N71=
at ~~z 1 RAN bc5 ,Y34-k, 7,1rr<. top(la)1(l«L)
= i 1011, at = L. Yc°»tNIa)' -a b (6)t'1=~,z 9C Jl=dt ~Z -Vo) fP 1 1111)4 FA** L-"' 4z„- *it* , ofd *, t,
*131,-1 9'f4•75--.)79 (at)r_'r < aI vsreff4 (1 v)L`4-t * L i)v7i - t&,f
4f113 fkL_L7.11 tAz!4zn --tr att. L-6,15
h L1 3 ii Et 3"it lf, i I Km LXtift t 11 atm B Si 1=1,7 of L7b ~~~ ~
1) <9 .j° ' , t, ~7 1E. -I1 9'14•7•,97°
~a~i~LXrr Lu0Le 7^=ataifki.""Z_Z44kIS". 17,5--•,7°lI0 s YE nix 3 —
Att i oIc,i aitto9-rxt-- FRI -vT-11,.j.-q r zs'.
4 dt01J*tft-8tZ\I-•?`")~s.g.-v as (5)A:-7, ital. L (5)7-, it
7R-0A-p 51. I11-12—A -6,1 3 t
)(7) kisatiI= '~ *~ tt3 9 I= 03-1-1'7- - (x-)1a, 1 G^ l r-
1-1±cr= a lgo-hph-k-2*0I4#1<TT-47z 'N)1=° r= 4.0o0 1- -3t
(- IL41j"-m1= L-T'). 17,7-P° i_ 9',is = I u-F_~ ~ 1) J
Z--vs (i1 #=1, I Afffe4 x I I= 1; .
- 8 -
3. 31Teg oD
3-1. i1 #r
%/ it,111' 1z lro)t Tt, .. I -z ; r u, Q L t) / A J.t -tf T2 r/
Nlp'?'LLZk1-54)Z„ o,s-')TdLi;T-- ).I24I4.%:,0$.ztU"'Rgi
tit1:119a. 761=43 k I)71- gtiztfil54l7ll-3.1)"'` 1=ct,Z
'c~ 17S'z. ella Lz1i'=~a
tsm r •I - ^^Z, DKT-a () (4) :ILA% ,v Td ificv = 710)-411
U ( ,t) = at on • cos C(2r/T)•t t 9 )J
1Ih (t) ='l'o c6S [D A- "t
(g)
C9)
Z• 1 `d 11ic fii o latoD fiivi ivi, n/S , )110 T IS tiAti IT1 M L.1-31 `4
(I) Uo=1.00(44i/s), (3= 1t/4 Tgott grv'fliTArt7Ltt-)
(IL) Uo=10-4• ('s), (i)=1E/4 oto) x-)
(1) Uo=1,00 Cm/s), ?= 7r4'Io Carla X & )
(W) up. IV-4.14 ('^"/s ), `,)= 74. 10-4 (fitkoi a -v 1 o rt7 tt- )
=it5 4)T-7,0 7,W-i,rgk R,6v'"502WV Pal I- C60kif,
=F1 .4 iz rr3 (.)I( I-&it'~~~a:.
k) s, 'Vknl=Agilt ( . Yrisrgo-44e311"~
cI ,P (I t )F , P1)-o.1wi 1---_•—t, tf1s.<~t4f4,# fa-'c" d)
r R~~ ~~,, z~j ~T nP (l~, iTi -c~''TQoi )1= Ia 1 itIti Ito as 1= 573 I. LtY,
Fi%-)f 4-51Torl,41=1a. au'i[o1'cY') IRm X '269 .. Uo =it72oi
to 'r ill 141 c PEEela rd rElb t^' ‘14 (1i14 * )1 Y's 1= ;,74 mz , Y~
9
(km) 9-
7,
5-
10
5
U.
I__J
(P U=Uo.COS(cut-t-p) 2n,
V =0.25.COS(cot)w =/1-
....................
(I)
B
0
10
5
0
10
u
u
(Il)
.3 2 1
A
f--
2 1 B
(DI)
'3 2 1 I.
A
5 i • '3' 2 1 B
(IV)
0
0 1 (m/s)
0 TL/4
0 5 10 1520 20
Fig. 4. The horizontal distributions of the amplitude
and the phase lag of an artificial velocity
field (the left side), and the trajectories
of two marked particles (A and B) during two
tidal cycles (the right side)
o) f.o -,r Li,ftr rIz-T••I - ^= 142%0 9)-K /3it`Ptir-b14-u, t)17 -to 4t'
Ltlo 4 _17, 411,1ttpg' 4I3 = V 9f 1 gl 1‘ 9,
3-2. *Wl-k A 214
3-1'I' ^= 7F~ lT'- 5 ~-1= ~~Z. ~1.. i~ CEO) *C i]")±1r7a mfi` t"27-V, .t. L# l"3 k-44(1-S's
k"miaait 471Clit" kilk4 t_115 t017Teik-.4 &)r 21+7".111\••1= 4
-14 27-4114197; WITE
gN';Tt)1=. o)7T'7 %?.AM) Oki( =ffm-44.7 (1) (2)Z-b' 5 *4 5 t1`Aiir J
(Fl.1)1711- 5ifilt-T uol (-1-uiz .^'~~. F.SA4••61= )-6,zl--9 . }2'97)-0
t/ I=4*7d-b`11)09-Et-3 Mz:4&Aiti) u,v`>'~i~a~#~r"s
L3-'0 ` I : 6g LZ 13=27;z-7,k, ,(-41 1 Am vt \-z l l T 6,) 11'L Is
2,5141/s u"7a-b°•, WAtfi`.77= ' 3X k.V2-7 (4^-I51(fi-,-F_^a6,5m/sig
Z"XT)7o 4i/-413t iz -Wary /V44a) = LI, .o) i>*()) z 6ti No) 4,4t
ko15't79Tee (I426)51=ZB7tH-rt
)k--(k170 **I k4 1It-77 51LT%' t:fc.) ol-Ii/ M Eq.
5 "~` Ta (Y-5 lz ,1, P ,b-' . 101alto % 7a bcZ i • 7)4 Am tz.
`~~ la 01110 07"4)1a-be\ 91-'901I c tIa 010197-Pao zenfag -0)tK
Yai *9 0, 6 4."/S Z"-t 201I". i(l l_ < ~ ~'Z = 1 ~ fxl l= ~i ~7 ~ ~ - -I~ ~ ' 1= o t l l a La)
imp:,:41(4:Tkr '1=JA-fthl , 1I -=ARAiN*11 a)1 7-- i'a.
- 10 -
(A)
Fig. 5. The
(A)
ci,,,.....----:„._-_, ( „______T„\ , ,,,o, cl)
(B)
calculated M
u component
2co-amplitude lines
and (B) v component.
(A)
(cm/s):
0 III ! 71 ft°/ / /11 i_ ,
PHASE LAG
d V-mrtp d M2
(M7)61 \ 7
0
-2
(B)
Fig. 6. The
(A)
calculated M
u component
2co-phase
and (B) v
lines (lunar
component
hours):
•
i‘
. • ,
/1 /1 i I
I-1----- _____--_,,,„ ... • . _ - . . :..,., ----,---„,------.1,...---- ___
,i___,___ z . . ---- ---F‹___-----.,„,,,,.. ______ . . .. :
, .,--------NNN.-- i \-_____ /\/1\)\\.\ \., . . . • ,\ IN\\\\• • t\ -N.,____ , , 0 \ , .. ......
\‘,N__,), II t \ k\ \N_,_____,-/, , i 4 4
\ V4...-____ A/IV \ .. --\ \ . . ............
^ \ .... -
1 ' \ \ .
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
-60 - 30 (CM/S)
15
Fig. 7 The pattern of the tidally-induced Eulerian
residual current
1a -1-1h\aca o I. (11 l*i5'IA 7.9.3 t-71. ulakOp-b- ifiggien1811zWad)
%'h2go UV- E7 (c.tz441, crit I= T. rrl .t1 ' c,:It.lr .
~ ;~. Lzen *ctik 1= t 4t*„ Lza) Mz 4c.17 R =9 F14t,?). y',ottn
F ?,z)1 , ,r ,~^ cal M2 Irrt,F~•rriPc r;". or) H2% IGAU"= -590AILO
fi\ir ) -i'(1), i%9 ri Aye a 31----"X r-- -7(a 4. c*.-4t0 0)~~^~-~3 $ >^
i i~~~ (1\~tl_ ,~^z~~$L~h1a 1 ^~ tz )77; L)) FI0 I i4. " 3IT qr-~•~~
't . L T i 2eA Wig 0.7 % 1<cg: =')ontW 91,: * 0 11.4 (0 p i~ LZ k l 3 . B Alf c ®Ir.
(i) (11) o) Ont2 r1'a ; Ac n O * 1. 5 00(114 1 clip = ~~z L7 a 3. N= a S
_ttrs-7T Ac-r,41-AAcitM' 7400 4.3=.t13. Lit9 filrx< t*L7) I(f t
9911z 4:A AS0fi1 3s4)81 I=•. '). r (x1%47k6991,; n ,a fScl *RA :—,z1130
al I (111)O) , 45 5--€19fcrA 'I11z_x-31 CO Ito 5112k-k# 041" - T 1-7u 3 . 6E/5. cz),9
Iingr_VS-ftio)jl*•. -Lz0C.LZ113,.-or~^1-7-17`3.Zmzrla.
y_. it 7- la 47 tilja it us o- 3 ~114141.7 iJ : .5z Mn<. MI*
4dAtt-t'XI42ktiet-V14 )11At7z\13:ttfr.LZ,13. ?V). NWr-;' r- 3: 11.*4tE
~,Lz#14114-I.2 , )1-'45 itit (trim" LL.--m ITo) t'rkt;•zl\~
(a)a)icc®)1=1a.(1), AcC+t z(13. _)ftla FINAI P(NZ
1=1'3 ~i 3 ,x h"' ~r3s ~575 (a 1- 4."1; 1) I17'' "= 79-" Lza)'Tt~I t-41EIDA LZ
ll~tt`7Z"T;)do off) a)1, o F11.71=0174'li (:%141.17;i 1'I~~•I~~ %~~~c u~j,I~11~~11~Z".'~flC'
7.1a 4-3,"4-L1.LZ71( .iOtia (I)t C1004;411= < kArg1=11,z1),
(I) Cu)o) Aje, 1=7Fzt'1.1z c•=-2r3 '1em tI*c M —^a . ' ,r-
+itOfTIT iT va9 * VI ten I=c1).76o RI. 5-te6I= ~.i.41z1)
a#>1.0 / 12Ai 0.)+NAr .RitII : -Attut i 1= '11z • ft,7
5Ts i<. ~~ 3n"1~1I=-Cira.
1= t>r~r_ o 1 . r S< Lz%I. p7)= t
i ti.M =1.itt MA ' o) ?^")71^L ll` S(I Z _131")bilL *d+ i3'1 .1= Cr 41 Is
- 11 -
(A)
: A B C
1
D E F G f K L M M ~1 N N 0 P Q R S T U V W
TIME=O HR
Fig 8A. The initial state of the inner
waters.
(shading) and outer
(B) Casel
r - I i I 1
..45h
•
6 Pr
(C) Casef---_-
1.5
__-
^^ ^
1
fi0hr
90 hr
Figs. 8B and 8C.
The states of water exchange
at every 1.5 lunar hours in
cases I and II, respecitvely.
(shading denotes the inner
water.)
(D) Case Ill
:.;.: ... • ,z. % ! • .)" .- '
:\i '.\•„. . % ..', ..'.-. • '-.
• • •: . ,. --: • ---.L-,..:..2.:—:--, , "
-. ', .. ; '',,, - -. .•.:.:(c-::
: .—'."::.:-'-..•,.—..----,...._,?-z' :.'N-:,,,.:",•:::1,-..1,... -.."..1-.;:.....," :-::,.. ys.:.:'' ,,::::.•.: .-:-..::,:::;.: .
f' IF`
•
TIME=12
)::,::..
1
OHOUR
„. .::.,....._...:„._....,:::•,,:i.„ .......„.
r_.. .., , ... .... _..i .c.-
.....
UR
•
•
•
Fig . 8D. The state of
water exchange after
a cycle of the M2 tide
in case III.(shading
denotes the inner water. )
,, .t1
/
/
Fig. 9 The trajectories of several representative particles
in the vicinity of the strait over a cycle.
The solid and broken lines show the former and the
latter half of the trajectories, respectively
The squares show the positions of the particles
at 3 lunar hours.
k')714--KIK. k < ; i4 1141; itt..Ti • tr_~C01il= zt 09 iz
Ck1; 1= ~ U r (114 i$ o n: ) 4-* , *M3-0'-% 4'et4iw) 1tl?r-4
L-c Ia (1)0144 r- t1Z tif77. Aii i;I=3321-- w.14'
9'71-l=1,7 114> -cM;1z 94 ft vi f 3 -4 t17 L. j ra:l 1r 1-7ra
tt.)`7^1.
®0' = I:. 4f1 A, t_Dift q fk ;, ~ g tr. 3. ca) o i rk
mcr 134,7, 1, t. I talii fk6A-14.1 IS Ca)O^=Ia (r)0 IAA tig 9.1t c 7-Lt) CT461e1
(DI)oi 1=I z_o ts tla ;viz Itt(
tiL-CR.I-_-.*t4E-UUzr P12%0;0 Aft h-oPti .o) ti. Ai, op1 m
Y_e) tfA *, 71) S r_ -0ME X £ I =i 1r.. 4"=Ve -11"3
t.,47#34 t. -44aglaa)519-icid*Ii 41,1:0111mIz'rr34114cAlg-ti/Itf-11114-4111131--
Mitt jz Td 7 -92• (4,1 REp;4 ,$ )-g14-i. boIc 1 I
I=~G1=l hai La=L' IZ 4I-4±,a) fq^'*ti ¢1`4*a) c -n"' " 43.
-n°, g1 L---co)
- 12 -
4 Ot
_.. () '1a MA 4 %k1,x L- t 1` 4:t>1c0- K' na (1A..200)7 . `C*r.
rt-Ii" 1 fifltff it I= t 04 or e ( C61)0 E VREs 3) tt 1) it
R V s/va.x LID)
CIO) ~1 4'I~'a VRES Ia, ;43la4tiffn L- I)1MiRSi1-pli34>Ko),140 it- (-1 tlaoz• 3) .gir.l,Zl)a7'1V"S<, Fig.to ,r2R1MIA* 1= '(17V41*PfM#1-3¢~ >Ico~ z,~z11~
t/wax UR60 Fi-Z11= ~~llZla~tj ~' Fu A7~`7..-
T7~^I_ t''711^^z*61rjr_ % *Alik"4:$1(0)'lJ -12`5.VJ*1="i'It r1'1`,Ica)4111..
1= t,Zfr1 b t.2o • Irs.>h-5 . F . 813Ait 8c A -Lir 5 34010)61-W5 U>~ax fi": —t To) I) s V.
`m =, r_ LT'iin,i-n ''~2 i *c6'1`'fd5rs. -1}t1.7.'0 ,14t ydoz',*s 4
7=2“)77 -1715 TiI, t * bn-Of• I z 1T >ItZr 1kq, %Fcg 't`.Y -t 17 -17) 111 1 •T“kft 'CI h SC
~~rd 11-F20-7'7Z(. _3k$Z"(/) 77,19Z=A 7' I t=TaTPZ' ii),T*d-Iitt 5rs-5 :4i(o)k
— 1) 77y77'%„1z cps-Walt CCiatt4*(--s' , r-`'ri jiz tuz ,
Cl ='~~Z' Y 11 'I t-7Z117a•
tZ. Uo)4',17"; r r2itr We 1A- 3 (T)4U' arm ij o) v. VREs 745R04
Tabte 1(=440 0)0) M(=-711Z 8917` I= b'3 E 1-'an-to-1rC2)L -U''(II)041,0 1= < ''`Z .r),L04 i-47`(7491.4-1. Tc,le 11= CI)9
one kfit * rj 4-407'4) 9. (IMAAIS t43 8-7(y7'-P1d. 13-Ac-44-0)11-ti •ra„uJ
M~: ~1=•~r)Z"~ +,1rf 9 *-trO -424. t11:2, >tz I ~~ T-
z 11~.1=, :AA T- 0)kirRZ Ia/ft'ta T>cPk ` 'fk.is 10^-3a /, ti7)rz1. •kh'E'•41
- 13 -
71
:I
.1
ORESkw
VMAX
EXCHANGE RATIO
R = VRES/VMAX
OUTERBASIN
INNER BAS:N
Fig. 10 Schematic view of VMAX and V RES•
WATER VOLUME
V (3 HR.) V (12 HR.)
EXCHANGE
RATIO
TIDAL CURRENT
TIDAL CURRENT +
INDUCED RESIDUAL
TIDALLY
CURRENT
213 x 107
214 x 107
(M3)
(M3)
84,1 x 107
186 x 107
(M3)
(M3)
39.5 (a)
86.9 (7)
Table 1. The calculated values of the exchange ratio
g ftIlt*d)-11-r'-v9,4izkl-f' Lk' PAOew,7a61z d 11t ra••7a.,7 -iton.
t*gi~*Zlr_l'krr- 179 <o) * 0a) 7.1T-7,1-o' i-Akia.
m ='4 4• *it; , zitk1 ?J zk0).401 i_ r„.91 P-2 “iZs t-S43 •;
~ y ti,.. ,t r - Lt . ') , p
e7M8ti tt,l,Z•^7aL&z.~O.
- 14 -
5. ^ 17k. 91-5t ;Et
Z*t Z• .tr 1.LtV/*14c,-) •t,-) Ilw ® 1 4t',-tita 7-l'^(Utztl7l i~ilt In~r
Z" , .r T-213'l:Lfitt,, ) 1=< lT3 11%Sw&LAt~~~„zlasj ~Z
: t 1)`~ rt o o :517-7"1J( . a tm 51-1=.4R:4 1 grPir l !;ft4 )1'9 1 ~~: 1c ra~
Iz-7ZSlt: RV •4rZ'Tth 4.tlz c, =11],?4*‘(._:PcP('er, 19`[31
' E,Z , ;t,k `c.41-: *11 3 t-Tz: Ta— *, RE *41.t411. 1:71.10 L. n
17-X7701Afg'l Ic1)RJ4AK1a i-~cPaj~~Yrrd~o ~ 1~,
~~~•~7-"= fi A4-03- 4 3z-rx1 lct *Ic '-
-c-b' , r k*17-- A-r'r-') =4At :1B WI 49 -A^.el;~ ~il, -*tic 'oa-.5rTigtl" -1L,7 3enif u,T .1_-711z kttt . : )3 J 44a)~,,t
5-1. -.11,71AIVA, o dt1,e -ty.
5A*-110 1: p 4,0;79" 7%,"s A , (s) )054 5 .51)-,71-
Z 2,'13o /, t1'tt®o t ' 7-1%I ,„''Lri C=t.-1-6t) 5,97°Iz t711--111I
114n at.) G 3 d L t^wtl r.3' rtXit /1 F :17.4`17' eo
ri (tw+ti) = Xn Ltm) -t 1Un (tw)•at
-f- (-t- 1bGett.),t}at'•vH(ILAtxtittd dt11 (11)
(11) 1-1,11i UA {) N I.IM ,tj a, 4Ri7 i k-1 4- „'- L..trt D I--g• IT7a th,p) ,w- /~N (±-W )
z'a (Atilt m9I(7X'15-'14.Z ') 9-2'0)t o1qt)-rM ti 4-I:::.t,z �n5)k3 (Air, dk
- 15 -
chE142A'12ePiL4: - I=IS. ;_31A57i11,I1:1= t^t
`algt -7",vt'"kU(7i4'l.z^ 17a (S.111 , MI I ; Hall, nr15.40o Off-1=i` tr ij
1111 ii4=l69-trZ•2-#Ztikf t917- & A^=Alt 7•I7-iT1177'F_X 4-"t)3 Pa34)
c lja I YE)/'tL`). I 1g1P Z" ' S7rci-;? 0.14t-LZ694#0 4111 ( 1'N.^ Et1E U)
k q". -7 *11.3-41z ,f4 51-4-'I, fiti 469-11 t a1* Ti
f.tl& 7-5,7a 1Z•I3. zlL77.-fvf .2_11)**I-.-. t
u .fi`.i 4 1_4kz 07a C14aIt) tgR5)0 -m-T`RAZ_ 4t —fa) ( ~ Jr)$ ~
ILa7 V .-€))$1,=il' b' z IL37 (17fl4JZ 4A-7117 i- II
I z 9 1= FIC ±4,t r d)74,19. 4.69 L I , C 1926) ,a)5-1'101.0.10%01=44% a)3" I Li7"'0.,' 0 :I;.1:, 1l
C= 1=i ii1- F.< , o...7a it Eiiirrr. 3o YC-7• ~'i`Z~ ~a _m ZlL J
-:/•~T"ItiIz ,z*4-e) rtt'ao Ita)14- 1rk t, t s0)44:1!
/ LZ - c z•' ' is 7` t rat ) L~ *3alr". , _ z•` Ir. a,': 41-4t L :420) lck,
4 E13 iL A4 IS It vi — -F-:r tAfti tbi'ke) 1= -71174 , w0414
wej "r" (16195) t" Alt '+11-P113 t!) fa Tit 5. 3k%^ z +f 35 44ep n.7-14
4t:Ai-A0ft 4sE 1= LZ tos, - It* A-4 ' r t.,1= vL*tfi : etk 411:4 -b" 1 U i sq
Ia Io4..,to cw+224 i4-kLAffcfftT1=L4 41,0h-tl'" ='cI zol l=
k 17 a 1t /t4 't" t z. Ip9 c`^/s 'U'' tos ('^'/4 fi^ ' t3I' 1-I
:714yltel) l^ bis q= issC
t914 $Lktfi`.. 21<-0=Al-f,1bt3' t=4.1$'914TfiFltli'lls.#ei z•• '?-t•sm3=2t~,,--77N'5a
4L- a)ftttVs143 1 , 7 74 iTt 61) t-4-). Pal -cll. ft
*aPETt 0976)a);fi11' "O t--1 1 Bill'3). tit=t>;7"t)('fink) 41.7aik,-ho
*I.% (IL17--fvf -ts°)L') I- j Lz^a At rid,x1LI= b ' L7~o
$ kt g 3-2* Z"XY1=(t-51=U4-la$ ^I-~ Lz~~~~~olz••, r>;j
*Icti41•,',k))s) f )1=9fif1=V5^IZ , =A*01044t J) czat
- 16 -
Izg.m :.v_t"7"1 a)l(,.'u*ka)A,~1=la tuh 03/00 -5-7-9.4 st';
raAtir L"7a 91-047K Fq. 8 ontAa^S5r--$a tgltlz
~ c 117 3:11 t I o -4A17-1;C, 4I4t't or , 3 Avg 17-IS-I t1 1= rrh 111i~ 14 *'11 --41)et
k -E*an 1=^a133)-ril1_VI-TA& -b1.9-ihla--1‘41-1&%1(3)7--11 fi`..,
ti it L7, ==Z13 3-2' a)V)2011=-15t 2a16,436ntt4-t*J1I1-v1 1-tOl 4~
CF1c .~1 )a gnift iot I.71.s. 413e t; (1`I26) Rlz.) at 34.`,LI)91= e*cl~..
Itl "Z -1*Zll40)7". 2_-21* almit 1 IRAP4
At 34 i=i .*: 3-2/00 'tL &a 71.,7 1=~~ 1~ 3 ~t ~~ L
411.t. r.ily R a^-14o)AFlo 'El.Z P.')t-§0)3In* rz)h
• l_ ~Z 40)Lipts-Pete: ` (,+R ,roko " == 7-4 7..z "2T -L44 7 l47 4,Z
t,-tirra g--kr) 691`an 01,0^ t=&)
s44,44,$L1Mo) 69fEf ten Crttt. t,'v1= 31E& Iz.
Vka)Z 144.11J l _ 1614 A 0t4 j '(; 311tHaltMiC ,1y 2-210
Pia.121-(I)tuko )144 (A)# r (' CI:LZ II240'1s 1.---41144 L*'-1 3 let , av(1)4
WW1= LZIosc-2/s (z- 44i-tbh1?t 3i 37-71=J`Il-77 *21(~~~%
o) n hm 0.130/344*trg -. 1-r CMS a 3 8 M41/-t-z- , 21011144.-V 3 l ta A,I'c ."
4411 0) 3$ R --2•17 7T- ?. F;a.121= ()Z 14%-' z`•91-
0-4 II zt Co) z"ciFztAi7a. i-rA% 134> -Ifs t 7 At 04 A ' -w)- A01-v
-14m>41t1Z614 "+�,h /2 , -v,"3 tslat4 )z Ia lukd)
00 OD et A 1= ra 4141ten (T) Orr 2 t< • L * 7-7',) K1l 1~
- 17 -
1
Fig, 11 The initial arrangement of labeled particles
(16 particles) in a grid box, The particle
denoted by a black circle is selected as the
the specified particle (described in the section
5-4)
CAA I
-!!-,v;i -1
11d53„tir ttit-+M'
t:1\1101) , 0 \ .' .1.1.,
l 1 k e
3 HRS
•
4 A~
~_ u
rt ) '^ M'~'~a rf - lVt'r
4
t :t ! 4 L r
udnun un+•n''w,,~ a r.4.11',0.
6HRStf ssSy!~j ` F,, t llJrt~~~'w~.,r t°
``''-- + !r;t<'f~=
3' +-,1%-4,-.:-
..,1%.,1%.(31(rco...isaf7~f..x4 ` ., .1'.:,t ,.jl.•s xc~rti
11? ~'N` `rt
•,q'4k~
' '"Vri? )'4' i': ;Pi „I'l '•::: 't)
tt',ttttti,kt,tcl,.tr } , t,_ 'a , •;. B
HRS
~.~ , , .
•&1J3 . y
"~ ).~%-.` ~$' a/}' /~ ~~ J • `.r
® z •
4."(
•
&f '4" ' f
12HRS
} t
J ,~//• v,~
~• G•A; * _ 44
\ s ``~/~ `
(A)
.l&'/ .|2~.a%. ..l~ :,
,t""-• .rk~ ,#!,
f24® ~l~'`~ ~xrw,~4,1
\\r/}} ~44 \~/,#:Q ~~~' ,~
•4
\jft VPo- ,~~
r!r~
~i ••••~i s ;" ••• . r • s7` "'NW,
r a taY i • i`P 1,
.1, 53aC+1I^''
4r r.,?;*- aa'~ ,Ftws'1.r^r
Jai; ttA 41,
24HRS
.- \rt • "\ t o / ".4,A—. °.faFhr4.t....
M•~`r;4 sV.:{aF~•• J..k .,,(.;,
a r.I.
27HRS
~t1,~r1. tv},~ t •s-S 36HRS
0,/". L 444" ~• `
•
r rY'~ •7;'" ,
%is;hj1W..crr:_• sa°1=.If-"^.
„iyPe(iIII at.h .•1r 'ss i i\.
ir
.
.~ •~, AJ 4
it x.*>;!'
"
t ~~
4
. ;' • .
5 '. R -..
Fig. 12A.
of the
of
The time-change
calculated
labeled
The black
the inner
and the
distributions
particles
squares
water
open
the outer
Dot-dashed
initial
in case I.
represent
particles,
circles
water
lines
boundary
and outer waters
represent
particles.
show
of
the
the inner
W U) Q U
I
[
.
•
• ,..
: 1
k
171
*:%- .~-
e,
•
•
•
+.
I
f
r%{«! .~^"42
}
z\-;-t— ~~.!f-,,,I.. %
%kl-r .~C~,3 ^
,A.:4:,,...... .!
i./}a. `` ,A Sy ;.. ~1,N,~.,
'S~\ 2~lk.&-_.
.__J_`
CC _
~~:7:#R Z~f,e
'—-¥L' ! 5~~,(«a- .-v-• .a««-.
' .~-©V-` r4 ~~ :...p.,.......;~ -2/ n%f/k#."-
./..rt--Pus'».".,%).•>- "1"=7:vi' %'1•k2Pi•'- A/z
%~~A'
w 0
_
f @ Q
/ j
0
/ a w
« w
44
m
0 w
\ / 0 0
e
\ u \
u e
f
CU
%
u w
m
\ j
_ P.
0 CU
w
/ CC/ w
0
e _
$-1 e
2
( a -c
a
e
m e
e
P.
e
OP:it
TAr '~¥
»~/~ 33,4?, "I
J' ,\/;4— 4ry ,u1 .16' .. . ~~~~ ' ' 2. •~;qf~
' ~~,&~_
1.:\;(1-f',. .&~|,{ $-( `'
x }
its •
rr
U)
co
4"2;17. a
•••• 'y t o`f\.
H a) m
u
V d - • , t - ~` S
\ 4 aN
•Y•
V }
i a r el •1
tt •
_ -
r-N
.;
a. fS s-4. a
rcr..*~to"~'*ra .1". :I t1r
SC.~y r,.+-
,.a
f4. .,.•
3 j~ ƒ~
&w 4
\
f
ita \¥ `7ia,V.te \: •,.j,
•~~ ' .Qy. /; fa.Ci•-‘ s
4'/ 4/~ • •
}9~.~~~ Z.
t,14 ~2®
ro
ea t
f 4
L.
Sy
{•
.~7
• •R '• ~~ f •_,..74'•
.7 4i' r1. ".1.j yr
C 1 Oi4 o•
er. ys1
rf •r;s1'.05-.'u
.9a4'
•
N4' 4s; 47 71
U,
CD
*vv. z-4--+ Y. 4?Ii .l1• 3.sr
x(a;. it,•.,••~~•::. '.t f ~ ~ r1L
•a •i_.t
~~q'a' .~y4) 1 LF '"" .an, .S'"riff`e
tr
.]Lx•.—
y•
tat.4 •
•
• ••^•~ ••, •
e
e N s cr
t
, .
Y~ ~fy~_ f
n
t 1`
m
CASE
°1,Zly~•~~4x j +s• .t
i tr.;st :~7~r.~3 HRS
i^( 4, cr "•
i..) t t Air 14"t"
5.t /yr,tY wY-rYii4 tl-+xde -d
~ t /~{ t isI
5 + r5•tS~r5 ittt•ti,/r,'`r~w+ ~,'~-=1.At iSpf.) .I ~t~t ~.y*fYhV R;-0...• e YS5 •
rd '~ "5.3
+1. p J
T a
.
.5 •c ~v
aPar
i
•,
..
6 HRS
Yy J., .a ~i J {
i•~y'~.1'~t • ° a
•
7 r. 6- 1ryt
~~lss.Aat • +
•
t
• •
r t <• '
T ~ w
e i
o-------------------
4
• (TM ° a
‘1' " ! P
•
.' •v • • a.9
•
^>~ -' r1 ^of ,i
.1 `<' .~~.1„~4
^•
• 1 4 J . q. » y ti• +.
a `~ ,
fa.~r ati 1+'rC 4N .4 71.1
3 r•
P."4..+ fr' -
^ `rj
'3°1%4: 9 HRS
' Y%
Irti r
.
, ••
.5%......`'},•• t.'4`'•°'
sto-:r isXtr~,'''':
0
~,~°•t t 4.-r%.-3r~°ir T~.t
15HRS
-
a
r
'21 11 5 \ 1 :I !Le t•R4%'
^; \ s/
•A i+
'r• 4%41'= ry ) a, J
.•,, " .
24HRS
L, •\ • 4,
'7,a
s c
.1
y Y''
ti_ x
f~
27HR
'fr itA .1.r, 4';y~
~~l /1 tip z.A1,x~~ ;
' J
7 b
ib
ue•
- ;r z -°3 1P-r
4e..' S q' ^,,. ;‘,1' 4^' • ~ 'ry.~t 1V ~ ^~'e ~lj w1i
•*yr.Ls~~• ,..~ •.bf e
e ? ~
~t J •2.1 _
12HRS
•0
— a `11 L,ti A
a r fr e
Y
f
,„
•c
36H ± it 4
•" •
y ` ' ..4 .
Fig
the
of
12C. The
calculated
labeled
expressed
as case I.
time-change of
distributions
particles
in the same
in case
manner
III,
(C)
5-2. "Z 7ka)I4:.~~
Pia. 120)31ltit1=ai rpa W: ik 91,;t7ko ft LZ s; *Oa (Inr(7100 1,4169c~~v
P i . 77a ct %tii3- t91-%'t-i0-11• o) ; ,LLEr_ (2)a)$blko)Ta ()AMiL<YT
11:4*I= a Td 9. fR% iK~4~; i(tir<Icls)91i-,Z)?a(P)iz 22).
T~$ I;~~zfRI %* (91-3)1=1P')Ct*tr 9((() a) 4E0 ( %'k) Li)i&l%')
9Z—, tz_pf 41- 0=1-A2KtSrUtoy41,4,-v13,QjIlitti',
tal U ° : 7K t boj 1t`fT 69.1p /J ' ii)4 iC 1 - -' () Zgr. ifik0 l PfriA -4$ -7
T. J 17)0n~~z4(t a••l;13rR). o 1& .1k
("Z•rs*t-4tr'(?-c4n•)' z. 04k TJkWnr-o fT>9TS O `MR .(127 'z~~~.
Mg (t) = NICt)/NA (t) (12)
(12)1-7 Z, NI (t) la n (t=o) I,I1- $l fAL*(41-1=-bia b" 'I t(=i•~)TrdWgItii1'T-
1W) IX 0-At I t t=40 t101 1=f;--f 7a 4 E k i It4
L1 7a. ^$TIT t o (t=o)I=fi' LIZ 1I .IIi- 7-9))'• •99A(vbl
ox (7) "I'I I= (KR) -ES v.., L49 C? 1#Iz.**10)TA a q6„
2KimI= L ai& (12) (4 •Cx•lntYw)..o)-LCZ••ViTfja)I=1 9 T j (Tmzrd"0,4a)r
Fil.131,(I),(r)hi'Co)6,-)tUi=$‘11"7a1b*MR~3
tIl o) it ln4-i[NR-7°p k) (T)001P)=1~ %~~~ 1=~
~ Z Twizgtukt t)•" iv-T ur3-)) a LZ k)7- > 0monil 11, d)
0)-1+tl C — t)'-AT:4 (50)401erfevc1, 1e(62) To 7z) , Z O tll ` t..401 *'l I~•' i 1 ~11
(9yer, 19rp)° T-_A/43-r- Mt -tv" 1ffTt1 4)11 1EL< ~h
- 18 -
L
^
'/
/
O.
/
1/ /•
• ti
7}
f. .
^ 0'
ti
A
•
•
{
•
>rc•
.44`..M.:.,!<•.‘").IL'
1 1
\ 1
<.Pi:C
r t' 1. t
I
r
L
i
i
, n1
ar PC'/
~~~
Fig.
`
L
^
13.
.--
L ,
),. 4\0. iii), 1 . ‘‘. \*' ‘,./1 ' 1i
I, f
71ink.1:/./,1;.
.IAt1
,.....:,.
d , 1
..../
. Y.-.: 0-^^•••
Ns, •. . .e..e- .
...../.'''•
A'•I / I • .„. ' . ' 1-....,-.... 1,• ....,
. 1 •-:. ' . , . , ...... _....• '''''. -''''",:.• . .,. . . C,.."'
N. ..„.:,....... ,. „
' A •. • . , 4 ..• , :7-
-. _ ...s....
U
, .fI ./1
.. ,^^ ,
/ -• "t
, '''........• /
L
14
0.5J F
st
\• u
•
- r J
N,7 ,~f w .7
•
~ 1+
! Y
I
9
1j::zl , ,,,__
~y `1`1
7
C
The distributions
tide: (A) case I,
MR are plotted at
Shading parts show
of the calculated MR after a
(B) case II and (C) case III
the initial positions of the
the areas where the values
cycle of the M2
. The values of
specified particles.
of MR are over 0.7
41:13.4*I i."61^) iLk-h•..rs,7,h.,a.. MR .T-r..;l- l.tr i);,0r I(°7 t•° 169 s:ZMF5ILI
a r r 5r- 0 .0)tp^Ir_1), ^z;4ti -.4.79t.-4-571(4 VAipf. l~1oz••K3<t-rr~? 3 ,r; La))<fii
t14*1'4A Ci1=,'^~3/t419 q (z)#rt.43IA'~^),~Ca~'~°J*-t~~~Z(1k1T,-zbitJEI;_
pa)T ?"n"“s ii t3° 'x7Z. (I)0t 0Ha #.t,1l, t-b° ,,VU1-',4* 0190 l- ,zno -1/
Or$Id) "&51.12-13‘" it 014-7a t.Noii"_ktipt n0 .-t"r)i" 4,ft, RHi,r~gR
10X-4-1.(7) T.T. ") IT- 17,3a 1= Fq. 1413.$I.ikt694v cv
o iAil zi— t c * 4 -1740b G-71' 7 i-%-j 7;:OtiJ"Gg 0 ~~~ , -54,7'U•.ii)*(00,
I '~1=1~ lT~tl~z '~ t))° 7.~'~dlt1-3'11a(1)mt01-1kaeriBik1S
z.‘ cr) iirti`'1r5 `q•• t&ir-A off4 4141 tptwfl.a(Odtl1-1 C0atl)1_ ,z art. -3x,11.4-1.--(
t^7 Y t 117a°
13 t'5 *LOP t^7 No 04 I( , rc=Z•11o.91_ LI "I~t' 5iK-
. *kWfaljni75% f -0I=-D` LZt;ifij11;L:F '3 at-7 Z",
~ 3r ,p I=~, IC IT - ir3 h{RO^l, z1-S-0.7y,(t-Mfi -)30' tL4&e)1t^ fi 1=)b
1=,7: ]Lit ttt71113.I WZ11 .-t)-4-)t)'3, :41_5 t'`7.,07
-11"T ‘I . . *WSItir -nrtra7 t#;(Z11. 1,1tbm;.I~
(AT- L [ Jtl'it^° or Lair .*4-04/1/4:- t>zla-1+14) o9^4-4>-o ,,ln'Peitttlz
( -v< -n'g-1 *pv41_ . t.z11 ;AA<P'° t1I,I 43(~1c777 (1J&
&o)lel.)L1&IS" 1a' ~~ m~ ~,' <z ~ I= ,ZT~~ t = c' la o-k
rd 1=4,7t1Nfi4*, -Ki'dgi1 ff All i'"/4t;'Z•)7-2')o
Fl.I5 F11.161; L=A- z$ Bg 1-T, t.z,t~a° t FT.15-a. CI)mI, HR (foot en
MRY,k9 1z1179n'", 7°U71.-t,l4T-r 45°0*-A
~Zt^73-h''7. t LAkl= t.,zki-f,,,,-K I <t tkt-W7a=t-1J'"*7fi'.° -r_ Fl. 16 i . L4o -t, cTld)
- 19 -
-1.0
-0 .8
-0 .6 `ou-
20 -`o-
-0 .2o'
-u'
-n^
-'^ -' 12
HOUR
100-
r _
100-
20- 10-
2 - - 2 -
-10- - 20 •
-100-
MR OF CASE III
1.0 -
0.9 -
0.8- O
0.7°
0.6-
0.5-
04-
0.3-
0.2-
0.1-
00
MR -1.0
-0.8
-0 .6
-Q4 100
20 10 --
12-23•6 HOURS~~
-100
ja•dt it8.dt
:I =lra•dtl+Ip•dtI D lanown
MR
iC
-1.o I -0
.8 -
--------0 .6 1oo- -0 .4 2
0 - -0 .7 lo-
2
12-2 - 3 -6 HOURS
:8 -100
p a00.O° 00~• ,.°°pp°ot O°
8V°0 G O4OAO° 0 ° o08 O°00°o 2,06. 0B° o
000g0~~°o 0o
8 0 0°c co, o 09 0 0 po0 0
O O O ° O°O
°O
O o 0 0 O O
O/
O O / O
MR -1 .0
^08
-0 .6
_-0.4
-0 .2
12 HOURS
0.5 0.6 0.7 0.6 0.9 1 0 MR of CASE I
MR 1.0
-0 .8
-0 .6
-0 .4
-0 .2
HOURS
Fig. 14 The time-changes
of a(stretch), S(shear),I
and MR in case I during
one tidal cycle.
-y(divergence) is neglected
because it is much smaller
than a and S.
Fig. 15. The comparison
in case III with that
after a cycle of the M
The dc-dashed line is
degrees.
of MR
in case I
2tide.
at 45
0.1 0.2 0.3 0.4
U
Trr T } TZ
i T it'
XTi'X X X,T
YX XX YXX
uklw w w W
CASE I
A
44n 14 44u
u
1
u
u u u
u
~U
Fig.
u
16.
x
T T n T
zz u Z XT z Z
z1Iz TT
trn T T x x x)4(----- x
xxx..
4
CASE III
T
Nu I 1INN
Z
14 N
N
n
B
The positions (small letters) of several water
initially in grid boxes (corresponding capital
in cases I and III after one tidal cycle. The
the initial shapes of water columns containing
the small letters represent deformation of the
or the scattering of water particles included
squares (case III)
v
;~4 Iv
particles released
letters in sqaures)
squares represent
16 particles, and
water columns (case I)
initially in the
(AM) ,L M.(1n)at,IR (3N)1,. `71911 : 1E*a 1611149t -rt(1)1)I
t„045 r-Aro,-h'kir t,TU^7ao 44-1J' 2i' tT *i t t?;4
tY1-rr4'7^^,'L ' ,, %1-srfr Ua44^) _~-1j".4t)'7 -t. 4,V001L
a a) &-t)," 0)14,,g 1tcgicktz s t,4t---Eayfi .irrpAit itf P(rl= -0,i LZ^^~vt1':
-- Z3 (1:)671 1-i IltLktJ)ra-L)LI)a) l_txi"RttiZ %^f tilli=fhT, 17:11Zti.
FV.h c7-art:7Ta 4-#69 1_,1.,'otr 21-1-74 z~^7-aot1tialg091I it;g~a
F,1. I21, I=i' <-7-`orkft&W7rx 4-0)1 MO ag).o;r.4. La)/vail)041, 69-:
1:10-0* d,c S> T *;.'>^o)#gi-iefi[-Mo' q,ir" *WI A ,
1= 1=*t#4-69*t 0TS I-4-ko)1l L-f, T.A7?( ttfamftat.Eqf t.-F:"0"4-A0~Z~^~a)o
, s % 't,tr)} 1 'ib s ^a 1te.17'..A 7t Lk i av f I z # r 'l #4' °> fih . iUk0) /10
I~ ~- b ~I~~~Cr T= y ~ F r 1)'TJ.'MT-8 i r tt 1,<&3 t,'01I
~^a o,®o^f1;; Co- -L o)ra_t 11/ I-1r1 1l1'tttig*1=A
S?a off )o^tp,, f,1a91-A401 CZ LLZb'). t.A.t.-nft0-14 1IFIC fiz 1-r.•.ZK L,~t
A t KT Ali* L7'11. $LkenT.41 -T-tk = ItF^h1= )-L 1 )/Iif c9)
431,1f-13”(I11)a ID 504,5 =,ti1t43.1=R -0,il.,k(7)?/. k st ~~'L,Y 111 3/1k"t
(APPerd:xUrnA-6 h"410T'a57?v`h. .1,it Ara a) f11
I-a'. us~r l~ rX~I~,- % - ~l~VS:?etttgo(u-k4s6,Wt, V=o)1=~lu
Z_0)L- ~5 -vt^ )Kr t7 3ti 1:7)4 m11ZTy7°fi (t="''°t) hlif„~4/r ~]ra%0_(koat~1 o1s((wgat)tKt)PatJ((ELL,1)'rst=a atz ~~t C
.-4-) UV). ;7- -i0Kt4HV zfif .^=t7e4ttti fOt.:_.1.1<4.30 't-rz, 19.1.10
mfi giulAi'ginitI tLxho)1 ()I~laForifJl----Kt<1#1-,)'I)7t7_:IZ
20 -
~a•
a
•
•
($.t.
ci"N‘
•
d•
.;/
R 1 \.)•
.
Fig 17 The trajectories of some representative particles
during the first tidal cycle: (A) case I, (B) case II
and (C) case III The small black squares represent
the initial positions of the particles
rs 7 o l,fi' L-Ata)Va i yO) , i o}:`') 7). I , L C .vi th` y iZ 4ot5, o7 1 1y
*ma qt/.tty tZ•l5-t^-/K "4mA?,
r_-7 () z t bIl.A'a o '> 7z, = l DK nla 40 r-rst ink 1=7z k9 71.1i --9,7 • 974') )
0--Ti 4.‘4jzt <r~11u-4 tir•RA 16 MitIz `0-3
VI a) -9"41, 1 "&l.t7", 11/01343z,•/.L• ~~,z` ~ t~ ~fi g d-n~~~ Lztt o.r~
1 ~ ^>~ ~Fl~_- z~-77'')7},'GiiL){'l .` ..0)
5—s. *i< q471( K(ra
AT: 91--kefi".0 943--;ecF>,Zt^<At` a51-z-V;C.;
tarb."5 -5 YL. PSI< ~% ~IC~fi%r~o ~a=ttrs 0, ,Ke i:;,ttdfi'"e'/;1 J<
Z1;, fp, 7I< 91-; ' Cr.,-h" v(zl :4,a utdtThtlX" :-,K5A=41,K6 ti7 0 (11 '4k
9p,t7k a)32ea`tt -4i T %gic)# r iP•ttpr1 pilift9% Ata'irit3t ii,t7a-~
-17" f-c- ygdo r %)K~9~; ~1<~m ko)4 t , =*5irfi-307 .i I.," P1 30/11.1z-x>7rzliJtkZ(l30)
Z: ~I~IaS.;;t1ZX7a:i4 ..Ltd)=A( '°:I=x-,74-k.4-z
=z: 1,i . LZd kF e; ,kiri i=frt'j 3R.AE~ lzfi`b` 9For-t ry, >ia%
3o Fi~.lzo~cQll~Tt>ftZ~i~a~~r_. 11a1 IIQmPh')iz tx.9i‘A 4, 0 LZt,3.i Is AWmgLit
mr3t)tA PO_ rd1\9'.14'41' ia IPo1 Fi oz IX IR-#t a:Sklakttl==1.a
L1 ow) Pg ik 9}42ktia>;e.IS at.k =w76, 1" •91.5/A
..,Z, 0 % 71<-9F4gAktiMriftttllS nm-tg i.<hA zgeOz 1.I«7z () ~~~i~
(-7-7R a- rd '77-T'S n • 1 1O t=1m *7 9, }tr-5 2111140)11 b` am: 14o^ /1 Lt fz13 4.1)": t-
9-1, 'aqt ,r-irdfpN.L4''a01-13‘. RI ttt-4 k
- 21 -
1 . 2>a] ®O) 9E=/ /\4940 a fA tt113r0),# 132kA (91-% > '))Z•a,~. Fig. 18 R_, tI6
4 11,2 VIA 0) i0) a L&)I- MA /49V L71)39^-5t* 1 114g (t=o) 43st _4a1,7 )T-)IcA`z°*.
2 flitfi FIG')I-XC'6111z Ro)fe1E 1z x1-34,k ~ ; PO 1=1J1R~i,A~9'a.f .1?-i'S)1
715X-5r_ R1 t k, 1=Iltt ') ". 0 2t1 ido1IVL'd'Ilz4- ^41i)) ^)- Pt13' ;-j,)(7)-55 Rz 7,T
f. 1=2 131z1 4 3-11 • RZ m'bl ap 1-... 7 -4-9I-=10~- t t t1~1„-3W.1 .9 k) 2111 1169 1•*2
')1~1~ txl n c~o Ce ,r,. 0I` z•ii'VT.= ~ l~ (m ~~ lf~ %I Q l_~~z. ; ~~ 1 ~91-
% 13 21T1 O) h'J1=rs.iti =-<41;")d~=5o :-Zha afhtimi-5Arzihrz n- a
1)aitiftta) L (F;5.16)1 Zki Iz jr: 'S. A 4, 15K,A r_ ~~Z ~~r 33 Ft1,t*InL
• i f'. f ~ cc 219 14A9&i-) L‘; 0 T7)0) 7 Ti 77. _)It =4Ak-1r4$ Tht 12a M(12;//
7 tZLH `1-P7` b11)(")Ar.0")a, 7 7,1 730. L'L9.M `1I-456b L1- ^ 7t 1`
a >n1 1-4,E350)z'. 21111J1 o1Th-mr^a 01011a11,A0 Z< L")k). 2 AIM00)14 L'M1 r 114
,7LT‘1391-% -tII t Im) Ic_4 [.-44VIAliti4-)gtIa,t1'/•tLATT,74i7-a. ,m2 ©o7F k
91-47Ic(n b:,f1 `j°17 3<a1 Q1-1,wz t 1 I•'z•17)-1r' 31410g1- 111%i37k 9147k i) rOmil -Jr 2 1
AEI NoX')10Po Lt '7 Z•' *o,;4Q IX
0),7lZLzitt'T t7kti4% 7kl:m4e61#e~Z"E.TL1 h"'FI.19Z•?a. II3gIt q'
)b')1;t- R1= z4a itti4 (AYE)o=-7*57I- to (NO2) 9)&03 tit74.) 4t1 rf3~~; i
4-attiqK(--AwA,)0)/77 -ExLZ11'a. ;rn Cr., 1R I , 5 (I)a)tURolr; iJ% 1=Ia=*N%tlZ
= 2Kc1, ,zti-V; 91-A .k >:'9) At P -17"; (m c>L)atIahifibi1• r-1f :*7*k
a)A,Ra1 V ir. L7 Fq.191- (I)o)I t aOtt' ~L a1~i~
r~>-~~440421,•ols 5 to?,), (5)1P(IM Ct. ct_zai*.t (VAMP
11 *14:0 ^ZL 11=itoftti"'r tilav"Yu1u=LZ QI}r(1t)4)t. 1=11 :4 iz
~~7 1` ~ la 1 ~~~"r~<, Lift (i)0)A/7tz'z. AA'=2).,---))117-0.g---51:-_,A/R01 413Atti1'"(I)01,41= CCI•t1'7:;)
vP2a'0'lj'Z'4(IV0 =*kr? .--1,41:10/I11274 11274%Edck1= 3W kti91-= 2ktd)4fl(:L'
T 011=(h . T 1 r-->r7r-,Z Ail2Ktr F 1,71 t-tJ ?D' ~.
4 r.. )1.K,Lq1`,'47k z•m r,1 F t ; 1- 3 41* tYrin
- 22 -
I.
(A
.11.4f :VAN 1v4
R1
rg 5S°`gg9 m °
(A)
Pg1o42E8°.
aE 0. ask tE, s o° ° B1°a
°R 2
Fig. 18. (A) The final positions
(t=T) of the inner water
particles drawn out to the
outer basin at the end of the
first tidal cycle, and (B) the
initial positions (t=0) of the
outer water particles intruding
into the inner basin at the
end of the first tidal cycle.
L
•
A
,4=
~T o.8
(ty''
L •
•
B
i •
4
CL
)
/1
i
s
H
Fig. 19. The distributions
of the calculated NR after
3 tidal cycles: (A) case I,
(B) case II and (C) case III.
Shading denotes the areas
where the values of NR are
from 0.4 to o.6.
6.-AI( I.I4"01,41Gq
sfp z-Zirifftt,4,Q u Liz tia g_fm rat~~ -)"~~z. =ia Esfi,Lz 7KLi`^
~ $ I:: A.14- l.*tt)Tr-2(17X;.:,o 'c0), Ic• o)Zttr, (1), RE) A-U"(3104 o1=~+•^~~k
tt `l (1o) '1a I i Iti€1I--&^1-~t *ZTi'e)z". 2„h,t''3fflt1113( 14j: 1i ilt
-41) I:1' E;ND3 1=1 . c~o~ ~ V^tX IT m MOO z•'a,fitl Iz rR13 4:+0.1 4 ka---x
VRn Ix m ['IAA#Lztl 9pticoe 4 (,74JY30 27, mg1
tnek-tR mi 'aa(r)o1-61.4h0)l b1i. NA* t
91-A 7k. 6')s ,y-scl z,. 541-)* • rs 1 At3-t7 (1)1+(I)°L
V) $.54t Ia g1 Pfr# = .ig• ti'~ tai P)-6% *2( c la§_a, = F („ (T) t
tiz r~,~~1~'a=~^a~aT7 ~,~o '~= z~ (T)69 -.feh. z T ?, z 37-7 Ki%
VRES a
r,l± a)3e.1r_ 1-'715411E V;..ax, VRs A 4U' row ) L ble 2 is = 0).&17' 77-g -r*'d
?II, 1,1=1S I4 ai c i V 0' VR 17'' 3-r_?* to Lz k <_ ~z~~~eo fi8.121f'S
45: 2fitAl ffm1 C' IX I( dRl=l)T% AlilT-= 4,4(-( t"' 01cr) a L
L-z eft >'.fd-to Iti;2kir «o]] a 1161 1:•4/)l_ 4A 1=T4 I-7n3 r, Fia. I81=-r.I 115
r__a0l_;Ai:3*-z pq; 7l<(VRFS)+b'" '[PA AZ <•an-^31J<, 'i01-1,1f(cA / )
~,., ~z<3 ' t7~~o '1 .77, 2R4fIlE1j=rll*I=4“39)-**kc V,X1IM' Vr.xt (^ d)'URfs
747-C, _4't11 V;,.axP)-tlk10 V^,4,x-h1".- t< >`i13:::) 1t1titi1=kr^'P)i<ak.irc;(~1.<
045i/\;,t), L7t1~= 44307, VititT ZsXri7a.7a; 1 VAti'1 I=(14% I:.fit3". 4 kait
I <-49a -g17i, 4E5 > VRIts z,.2,3,0 J.') .t0) .1 3 ,ffltH fEl l="T lit P446 ' \e. 1= v~, :~,
V, )-4.m.tt•stA04 o L1i'Lil-tj",;'A-Rn a)-tan'SZT?t3W-ltAtfilti1\7Dila,Vsrr—)Ii
57V1`~~"di^q~~rR~~ ~La~'JL T`1~'F~e:~d /Ji'• ~'~/'~•,7~`L` z , ~fl ~t4 74 Itofl),
Tolle `z l- )7a iLIKO 3 ([)1ti I)o) ti i1, *m1 ) (T)4111 o 1z;' I T V^ , qrs v'
- 23 -
CASE I CASE II CASE III
VMAX
1ST TIDAL CYCLE VRES
R
(X 107M3)
(X 107M3)
(70)
214
186
86.9
210
185
88.1
211
180
85.3
VMAX
2ND TIDAL CYCLE VRES
R
(X 107M3)
(X 107M3)
(7)
288
198
68.8
292
200
68.4
295
201
68.1
VMAX
3RD TIDAL CYCLE VRES
R
(X 107m3)
(X 107M3)
(70)
316
235
74.4
328
248
75.6
325
247
76.0
Table 2 The calculated
during 3 tidal
values
cycles.
of VMAX'
VRES and cl R
fi40*R"0T-k r (-zaPat,t.T(m)o) e)3a 'rt ‘1-1)aZ )m.4h1-. o^1dct')L'8t^L7t)3
a)60.VIor)V x. VitZ V'K"i=ia ti4 k 45}h4^,. kiL3-Cr L71)3`4n~o
I=i\ *741.3=6D4 €I*. 1.1>1.1YM t)79A1IZtc-2%•<1,6,) t,7z.1,^k ?o --71JiL-,ho^?ata Iz 1 ~IVf iz
A4 L 1 -%* * 3- t^'" XUh tr" ,1-7-,Al 1:1 ffl gti 1= icA 9)- ;' 'I , Z tl :) 0 `' - j ; L4&
i 1Li-c04;10'I n ~-z~^T %' ~ f~'~~ tr' ,'ar I~ rib% f~'~I-> ')3 ~hz~ ~ ~~•.
IP-1" IL-4,1_61T7)1-ant 71 ti1);_ rt 3 V . VR~
to) a'
1'I.194.51z 011,4414'0"' ,.rg, ((Z I r~Y {r(rtd(^Y~^~~ ~~~' I b":~1
sJ cfr_ ft -of ----77 j-5. gt.)3 z ,%^Zi71M 1415V1-2c7) 7„
P-t1=111 -0194-^,a4` 14F-1.201 (s)oii M'
()1F (m)0'a1,1n1nTr3 Itlt8(m=1,2,3)*^: IAA (1,3t)IvA)A4104
91-(1),aillifq,g)0)Ti _O)ft I (f't"• t=b, iiffi p) :4 Lt 1I (M~I~t a)~ Ep)
;TA F.,/ .2o .L7. $L4'(r4 Iay'A/ ni3-0,10kti. -46f
Ili tasion0)4ti 1= rg-2^C9ktp')fitifi';z(13 (g1)69 3 aiti 1zjomft
5I±_)-0) r , f'1~$l.4(-9)1=,P341*vi# 1r9ri1.,301ftZ`•Ilgonfi T. tit Q *I *L*to)l14
J -tZt -~1=•'1p1p(1)1-. (r)g) f6) *,F') =-r51= I7'?Z 3 Km# lr;z^^3. ...gLkij••
1=11 L*T,^14i'v1=E-riv- ;WA-ethict== h'.,~r.I .L-ac11 L. i1E ‘itoklikLT :4ic1s ')
Lo- S *r- L4O) lZ3 = 7k€9 1=cV.)z4b'z fv-s<• 5-26
1- L1 g771L'Z(I7ao
41-11'14 mta)1=1a tv ttlZ I 'c ti a o`(~T~ h7"`~, c
tO* °tnR(z 74-72•r 97),tt o-t_ I-x7Z, 1-c
Z itr -5 LTAA ') 'Ifiz c :t tr 1a 47-a_11 < r-*11I
a)4 (4lcAh L. :-7"013t fii(r ,1,q(:'/.Z"I7<=tI_rVao =latfg1arJIZi-2
bhkt.3xi-2 y")7}-- Lky a:G 4-41=jv11~Wsfh t=_-77a-0
Ttl L11^o
- 24
AFTER'
A 1 TIDAL [IDLE
RFTEE TIDRL CYCLES
~_
Zs45
t • . • 1
::-°% -• •••.:
• '7"' s
• ; Ae .°
• .4:f'°° I .0%. •
AD TED 3 TIDAL
,.. 0 4. Aeg ,... v.:U:7 •.A. 1.1( : .. 17:;:k4.411"".--------
4,,..r . su .. • .: .
A, °. le:*i•W .... ^. •••
'4•It.. "Vr4V •Iird,r."..
CYCLES
tesSF::
° 11 k:
. sgt a. O.
• .^4•ce...., 17•
i*.
*IN •ej,
Z ee. •••4 •
I. ,e. •
R51
5km
pi•
lv
•
-A* t:
;IN
•••••
• • " ••^^•••
./;(24
.4 .1 ••••••• Ie • •
•Jsi
.4 • ts.
%
"gr .•*°. • 4g°,4.i..
„sr!' /1••••"• B
ei
118.
c.
OC
ing°
Fig. 20. The initial positions
(t=0, denoted by squares) of
and the final positions (t=n T,
denoted by circles) of the
inner water particles drawn out
to the outer basin after n-tidal
cycles in case I (the left side),
and those of the outer water
particles intruding into the
inner basin after n-tidal cycles
in case I (the right side).
B AFTER 1 TIDRL CYCLE
RETER 2 TIDAI CYCLES
m~m "°
•
°8
g^B°.
RFTER 3 T I DRL
g•+ °•
•~
CYCLES
•
•
.i•
b•
b
: F!
'
Eler-
°
°
e°ABBAA°
A
m° °
-x r,
• .'.
•
CASE
5 km
Oj
•
.,',•;-
. •~}+~ .~:•
III
®A°° 4...8 t;' raA° °
toA°°
® °°B 88° .°°
° m o
Fig. 20B. The initial (t=0)
and the final (t=n T)
positions of the inner water
particles drawn out to the
outer basin after n-tidal
cycles in case III (the left
side), and those of the
outer water particles
intruding into the inner
basin after n-tidal cycles
in case III (the right side).
Tcylor (1953), $0Wde.,(1965), Okubo M&'i) 1= p77 : tS z t = —$PK(f) ,rd. ~t
l-F)z' fi,..PAOl-423, -2g) 4
~Vlil, 1/Tt-S)C . ') 'Ktr' L2"T,K7a •tu7 l-0)Z"X"do "t'zfarx
~~=~T~IaM*T L;L9I-i-1Q1,1<ia~
rtii;14l.z. LmT 1 ti ..tfi`«J'i-v'.. 4iis" E./\734 4iTa:L. YL6i I
Wv1IY..~~C~LT Vi-,(6 1,-5 Z„ , "Z•iX, Scba' aCA(14-z,g)
tz, F4.I7r7T-riva tfi4 Z i11,15- ,(Tr-rstiTA) I' Lzar -9I1_ 1 tkr iztv-hw,
44Y0-tiiaO 4 L 4 ,ka),1,a "-trti Zc -Y z. (I)
d1D/, an7417a -',1:1-g ,futr• <Z#i;14at ;itAz 7k-tl,..i '-0 ,i-~eica)4nfrSce"tu•Z
l)~=~Z'J'+'20 2krrY/1 3W'Z• 12' if via-atty 1i7Ll=a'ry-114 irtg
,?irili o_ r psitTt,6,) fi,.. , Lv5/e' Zu io^z-19?z, ^4,-) 34t 4
z'a);P-4w , =i-lz 0,%stot$Rz'ia74<, t5) 7/-I 3,Atza73o _a)Y'~,
•01=7_ r11. ,146., r 1;t,t< 417 ,rat7t,fi=L7
m 1/4 1,,11 4 V4Z-I •tt ` 1>I'titt3o Yc-Z C=)tC-m),)I FIz"R
u(. n1l41-:_4 v~-q .-a1= t 16Na) j i.LO))1/')o)1nOiSLo4L6'-°Jr61JlC< , (A-6)4
(Arren")b% rAZ'(t `0) KIa ~7Ica,nrff raoK t TG-z t F1.21
I~~T ~z^tr Taio ~nJ' V1I TJ0)-ttlorfIEN,7g'°)-Pa-) .t>I1z )30 (im-mr)
mig„ ,41,13fflikz1,kjax1060,12/ iz_ 43 -7dO f t"44_L.Tr-_ <) z•'1o6c~2/s
I~LZlo5cr+2/~ (III)697I, l,t(1) oC=)mI1=CCA"1017-3a•. 5xios
Cp.Z/SiL 7 /i)a~L'f i_~1IJT.'(k)1E 43o )''17)- ..‘1) OiTail»-t•V.
rr, 1
1
ilr
1 % \t 5 0;1~.
I\
{
1,
L I \ \ ..\,,,,,
\r )
•
1
Tr~
CASE I
; q.
\\%
•
)Y 1r 1
.y1 Y',1
1:~~1 1J \, 1 1
jiJy1 ;, i a
'i
J i
e'' ./_
~~ L
) 5 ro
105<
Fig. 21.
M
xi Q
CASE 111
H
>10
6
5
The distributions of the calculated dispersion coefficients
in cases I and III after one tidal cycle . Shading denotes
the areas where the dispersion coefficients are over 106 cm
Dotted lines represent co-lines of 8 x 106 cm2 s-1 .
2s
-1
LIE fit 69 -b` y, 1-2oi -5-1-43t14taiiiLz fit rity -
t5ghlAtit 74110k1:1344( 9-5t14117P 44 rived)
l'ottfax t. t771 3. -4'3 ='-k-r r1"-041 A< I- 1=4. )1't
~~ ' ~~o 7 -~~•}Z)7k- L> te-tr° 0 A-1170 & t1'3417'
itA al-Op -12, -1,-) VfV/73iTIMEILviz
vIta4) (ELo)rWZ-la 41,11# dl.i.ep) (1)0,6--E112x106c~s 1't12a. tg„'
L41.tr-T t ieV-A 1 14. 2 l- xt4*z 5. 71_n.1=‘9»I-aW1Zri rn al. o Frro9
q- 62 7-, ifjo iLdkb"l,, =1• 1 z 7-7 Fir 71(4, 7'0 A)fr-57 1t la ^ z > p7,:FD-5o
i<- 7F(i9rto)=1g701 om1 n4'1- -IT9 1670'47s titi riAi .'4g .(1)-tF
5KZ‘i i t.T 1='')71-Iz~Mr % ti ti0)14'aEt0-7'z••)77~;3113.
J~%fi— JZ'd I= 7Z. Trj~d , ..k.r1 ' fi"" `=7. ..a)YJ La' 'LJp,(LLz I(MP.
r_o) „ :'-gr o4f Az-T"^'J" I 4h.33m-b' ?- oilIyFM £, ~it f#rJ
- 26 -
8. ?:)
(7 - • 5)-77. , :; sift-1 L7 . /1+tE3 L LZ m
(i) a- . illza)4t-i(k -I. 43,41:001ja)*%i,o)fk'ht Ufti ® .oA r calt1=c,Z
'fl, )71-fi"VA.L, ()).- ^z )--))'" 1 fgiltif l,TaYftlz 2 ak) J' 7 (^7. 'r --5A1z
r =ea v) 1- 1:1=-t ;VIA< 5F(./i. lcJ-3it-13- `=7-Z"'o)7'I1/.;U.
di) ;zr,,it ,fi'./€0M=3;Vfi"Itorvlaiy4-D7"Z`119. ?Iz,l.9 1z,
IJE 4.`j8'7%7 3o t.(1I11"(oti3o-/a) too
vXl:. 7;t lit Lk *71(.i1" JO) a) F7 L` ~ o '. Y( lZ ~t %{ ~~«1 a 1=~~7 1~'~`aL~t
(Iii)~~^ZI~.; 1 t-o) , rd rg'Ittztl,4h-Y.o)tr T1=1.,z,-5'.i -.z-2 1,.
)7J. ~,n g;rhtt=4,Z. RI1')K kfrYa -K1< 41+1:3. 7_1(1)t3 1_
r_r i fJ/1Wot ^=,Y3 ZI=411141kI=1?z;3zZ7I FZ ~9 ,3(
rdkia1 Iz)ht-,z~<=~F~i~.
*W69 I ,-tld . t,- 4-ig, `/ / 1-J) 7l // I1-V2A-7,7 1697"17),
z -~7 ~' I) 71, yo) tlit t- T ,01 CC t i" 1W)k-t% _
1/:"<.17- P1.. i ,l.z/3)4)kok L-A";69 I;.-2t1z. i2 t L.,69 ra
I: lrz VrEll 'O+N1Ia1,<1z•• =' 4 D0filazi' '*1117 T)1)1_< Agi-cz 7a
- 27
o A 01 7kr I a u ),Z . rxi i, % avkl l_
.i-,-)kolt2-6.tas(1 -ta) z50 1=a.;*rzI o,1tfl(r_ 7zitt7a :A.--10 =3c,
(=VaA%k163.L -1~tf Z"4R) -)T R40zp3A41-V. i A<e* k. * t1CZ ' : LZU<X'Vti'"
~„' tll do R0{% '// ,0 I`~Z4 of d lima) j 77 o 5 to-yTta
ate) lika) L< o-tI31=11 tX -L
gig 4 %1-1=5 VA* tz. a/ t. L<. z"#')'1 7; )1(7;12\5-t, (Q/\h,.-1,7t„Vt,T
. AMEATT . L. Kz.. 3 )0 cm' (.rfi'.,5.- 1,
Z 9. L-- ,..--.71tA ATI ~'i_ E>aA1I'2 ; 2Kotb EtE
tl Lir t.-Ca 3l:t"-,ZIZU2ao teclof,77,0O tl_zo,;zkqz.,
4Ti2 O(7) 'El it;4, &L?6.1=13t.Dy,rXc t.I 'l.-Z11=1r„
tt- -- 1z:**ter1..t -11,4,to ' Jt*lz I~Z T7a ~Z~1T7~' l_T—_ `'
E+fi3R ro J .± IZgAMIEal.o I tk.< Lzt) z1 --L-r -vvitr~i--:,viC'fl
- 28 -
APPendix 1
'a r W t M-,etizk((t,-1)( .22a ..4t)Pa i= X(t-1)1- it
^X 0)-lat-LA 4-vft,ayra "cm ai v tl=-h^iZ'- ±4'LZ1111-1=)-:1 Ui.j, Uk)'i
^1 tRfrifi1-t f1f1 (Tatrgrx1 I-43Pir ') x((t.,)iz 1731 C7-, arikt v;41).
ax ~ ~` 11 c1=t Zif^glaq:13-±R—RilZ t417i1~ V~),Vr,+.j,1/t jr cr"V )ri 1 ~ZTMS4.0a '.( ,), i t
t (04 t.,=t».- tot) o i 4.0) ftlA (t) 'p) vT*~ ~~;g .2zo,fi ,)o
LZ. r=~~OUSt, a!dr (.t ) z2mXf -= U~++.),11~t+,}N, 1A - .~, uit2,}H,Vi~ti ~rl~j+i vi.j1 A(l~„th-r+,3ri
>za 4i. i tI_vr,4tfig1=1 0-PS41070)01oz A:, 5l ,yd-)(r
fq--4A 6tdR')t,'61%tu9 Iligitr (Pfig- RIU. (6) ‘c,atgl6)0 IT, a n.. ~r~1
Kw, 0414a)r' Ati14i LF_TR I. *-tfotpal .0)yEl7e:4.4s-tio .Cti$ 4c rat, pfl,,,atF9
thrmatrimlo litiz .Vo 4L1'). t~r.
VI,J+1I
UI+1,J+1uI+2,J+1 X(tm)
U IVI+1,J+1
Fig. 22. Schematic diagram of the calculation of
the particle motion.
- 29
Arpend x II
-1;17w RI, oz. ~i 3 fi,.. ~ ~ ~l~ u~'Ct1.)=(~.U'~ ti< ~~o u'tiv a,
% a~<lat„, ~,z,; ~~~ u'1=-)(17i4 .
41:-k -tr” IL-)7441EAX,43315 (')t.,r^-trt2)p~o,tv:~ LA/ Lt i-) ii ' -' 54k4
(974),
lath„t1) _ yu'LtM)t(A-1)
z••, y^ tv, 11t,..011*- .0.T 144i 6q~-lot6347i.L-r_tt, z••40,u'tiIi wErj,736.
A.at o Ttiit R Not) IT R614). r"- l'S,m f131 7-'tTL (=c maD,r.. *IA Mh 4t 9 -tA-Kt 'i1 i r-s" (at<cT.). zfi.' LA-F9)
5' exf (Thoth, )(A-2)
t . ro4'lAt 6I (A)''iNC I oi='L^=j9, 1 1 Lf ~~71= z%,,h~.
d- du ^-7;(A-3)
du 13 -td j' e) T, l k i-z„7.vo 't77 * 17-vh-0 (h-1)14) - ^tL , b"
tz* ht..) 1 fifq 061 it 77 vcc —ft $~ C 4 ~z <m~~ )Z' h ; ~ r-
riAL-ca z*17' : ft 20)1:k-b"A z5417‘11 (*01Iz1T•Irg, NW* . gy al i=)"7. Lfi't3:k
,,k-s7-614^4^,,ht „7-11* rti*lki.rr., 3r=20, *via tiovg ^: (fk-L - Lit
Ia ;aP 61=t=,P)Vt±r3)•1.
`L~?2a ~ ( ~I L=,~ t C(` '( ~zLy.~o~~~~=Trcir 7_ 7Z L a7`nq ~'L
4~Eleg1V7-I1/TL-criKITS ffiV (t>>T)^=ai^uza = ~°
Y2 = z 6u cS rz(1,t),1 dt
z6' TL•t(A-4)
- 30 -
(A-4) ct 9, $1.l 1 K (J t1 L) .>X1') •3 I: t49
K=z =‘uTL(A5)
6tek 72a(A-s) T,z:,f~~I 4-iLXL
= 2 KtCA -6)
'1 t C. /n Yim-Kttinbv,+hl4" *1= 4-3 itlit Kg (A-6) '-E7' 5 r ~o
- 31 -
References:
Bowden, K. F. (1965): Horizontal mixing in the sea due to a shearing current.
J. Fluid Mech., 21, 83-95.
Dyer, K. R. (1973): Estuaries: A physical introduction. John Wily & Sons Ltd.,
London, 140pp.
Flather, R. A. and N. S. Heaps (1975): Tidal computations for Morecambe Bay
Geophys. J. Roy Astr Soc., 42, 489-517
VItErffi, ®ligt (19%): .olVA4(frItetlitVYt ltitziK
230#_4-;1>4ic1A;t, 51g— 523.
Hall, C. D. (1975): The simulation of particle motion in the atmosphere by
a numerical random-walk model Quart. J. Roy Met. Soc., 101, 235-244
Hansen, W (1956): Theorie zur Errechnung des Wasserstandes and der Stromungen
in Randmeeren nebst Anwendungen. Tellus, 8, 287-300.
f (19'io) 0?rA 31z1'1-)3a* M k3 .t}i)' oASC. ' I'1 ^=' I'z~,i s'i , 38s-3930
451[41/1, 14 , (1970: mit 4?Ic ba)t!tt-(jr). igf-krnPI
41419-g3, 411-42I.
Imasato, N., T Awaji and H. Kunishi (1980): Tidal exchange through Naruto,
Akashi and Kitan Straits. J. OceanogrSoc Japan, 36, 151-162.
)114410, .4,1 , t'l,1744t, Pill)) «975): ifA214.-0) A3X. "t It'fI~F f/i9
43-58.
Leendertse, J. J. (1971): A water-quality simulation model for well-mixed
estuaries and coastal seas. Rand corporation (Vol 2), 156pp.
Longuet-Higgins, M. S. (1969): On the transport of mass by time-varying ocean
currents. Deep-Sea Res., 1, 431-447
~'~ > . * $ ['1 (19%): :#72kOkr-Ti rt-3 %(ko)A. t#t1:-_-7kiz.
7-14.
32 -
Okubo, A. (1967): The effect of shear in an oscillatory current on horizontal
diffusion from an instantaneous sourse. Int. J Oceanol Limnol , 1,
194-204
Parker, D. S., D. P- Norris and A. W. Nelson (1972): Tidal exhange at Golden
Gate. ASCE J. Sanitary Eng. Div , 98, 305-323.
Sommerferd, A. (1962) :±14,t3-1),iici-P (a ' m 1ag&v). t, +c).3-11.
Stokes, G. G. (1847): On the theory of oscillatory waves. Trans. Cambridge Phil
Soc., 8, 441-455.
Sullivan, P_ J (1971): Longitudinal dispersion within a two-dimensional
turbulent shear flow. J. Fluid Mech., 49, 551-576.
Taylor, G. I (1953): Dispersion of solute matter in solvent flowing slowly
through a tube. Proc. Roy. Soc. Lond., 219 A, 446-468.
Tee, K. T (1976): Tide-induced residual current, a 2-D nonlinear numerical tidal
model. J. Mar Res., 34, 603-628.
4034K(1969): Miff.
Wada, A. and M. Kadoyu (1975): The flow condition and the diffusion characteristics
in the Seto Inland Sea Coastal Eng. Japan, 18, 143-154.
,1-401'I (1976): V2°0 = tx--4
aNzt, 19 I — 196.
- 33 -