#fi # 53 1iW m OCEANOLOGIA ET LINMOLOGIA SINICA

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1 ~28~ ~flj 1997 if 12 JI #fi # 53 1iW m OCEANOLOGIA ET LINMOLOGIA SINICA Yol. 28, supplement Dec., 1997 f: ~aa ~jtil *Jj($ (OO; OIitr.F~~-ifjH$liJf~EJT, ~*1Iifr.F~Jt!l,*V[{;$:iJ~.! "~m'l~tlbu[,~~1li~ W$ ). :jjr~ ~T~R~~;iJXl\!.,~,JAw'1lf1 Navier- Stokes 1JWili2t, i$gro ft~ iliat ~/J\Tj:Vit R~~~.Vit~~~h~frW,.1JW*~T~.Vit~~j:Vit~~~R~Vit~Z~ * *0 ~# **~ili T~.Vit;iJtEm1-jg~~* ~flli:it*~~7~;ff;~mjfilj,jarmjg1ilf 1;~.Vit~~fftE~~tEm1-~~~*~~~h~~m~~T~~*~o *miiu (jz.vit~ ix~ Vft: 7#J,JZ.fj\=-iXVft:,~-~RIf/J\T.i: Vft: ~ me7#j, 't1 me7#j1*~ ~ 89ff1 ;fo11: m 1~lf!g!t51~ T A 1il~I~o Prandde(1987)~WWIitit T -~83%BEJllW~ BE$~;tJ.ilZ51 ~ ~»:~ Vit7#J0 Bradshaw( 1987)om ill ff 1 ~ :!5 - ~ jg 3t ~ /PJ m jli!j 8<]7X~ Vit7#J,J! ;Vi; fij:elfi1l\' 8<] ~~~Vft:~,~ff~~~*MJll~~*~J.iIZ,mfiJ:83T.i:~~oo~~~.*J.ilZh~~~. i~~j!fft,'ilhx~vft:7#j8<]f=~ 0 Spezialef 1982)~ om ill ~ «i]pf mei~~ ~ «i]t{jg If ~ itffik, RPiX ~Vit7#Jitffik8<]ft~~#~~«i]~Iff=~J!ff~«i]~*J.iIZ~8<]~*o~~,~*J.iIZ~~~ its<]a.tt~ ~~~ix~me7#j~it8<]it.o*~mn.~*8<]r~,~~m~~vit 7#J8<]ff1 ~Aft~~ili7#J1**~~~m,~miX~mE7#J8<]~wm~8<]M~~~~it iilli 1) 0 1 'X~mtiif.J!.~~m~ffJ~1±l au au au au 1 ap 2 -;- + U -::) + v -::) + w -:;-- fv = - - -:;- + Y r::; u + F, at ox or o z pox (1) ~,y av av au av 1 ap 2 -:;- + U -::) + v -::) + w -:;- + fu = - - -:;- + y r::; v + F; at ox or a z p ox aw aw aw aw 1 a P 2 -+u-+v-+w- =----g+yr::; w at ax ar az p az au dv aw 0 ax + ar + az = ~~T~'/1:*~,A~1'lf%~#iJ#~Jiim1'lf%o (2) (3) (4) * OO*1Iifr.F~W~ ~(1995.0l-1996_12)~I!IJJj)'i 13. 1i~I!Jl,~,':I:. =f 1967 ~ 3 JJ, m±,i!ijlijf. i&fiilib WlI997 ~ 1 JJ 29 B,~~ B WlI997 ~ 4 JJ 5 B.

2 200 :liiw~{4: u = v = W = 0, z = 0 (5) au av ax = ay = W = 0, z-+-oo, (6) ~Yi: r:j:ljj<.jp;q + Rtr L I, h 5fU L" Ts,-ru-~jg.:ttm:Rtr,j -~1J~~Jftm:Rlt LI' r.: RltT ff-!fm~:i: <P~F%,Fy,F=Z.7'~,#JPI1gJtZ <P = <PI +<p'/, u*jg.:tvierltta<.j*~ Jf:ftg,j -~tt$j:i:,t;i :f-ta (1) P:1~i1J : 1 a PI 2 a " a " a = - p ay + Y II VI - a x < U tv I > I - a y < v tv I > I - a z < w' tv' I > I awl awl awl awl at + UI ax + VI ay + WI a; 1 a PI 2 a r a " a " ( 11 ) = :;- - g + Y II WI - a < U {W I > I - ay < v {W I > I - az < W {W I > I P oz x aui avi awl ax ay az- aui au'l aui au'l aui au'l at at + UI a; + UI a:; + u/ a; + U'I a x aui au'l,aui au'l + VI ~ + VI -,,- + V I -::;- + V'I --::;-- oy oy oy oy aui au'l aui au'l + WI -;- + WI --::;-- + W'I -:;-- + W'I -.,,- - ful - fu'l a z az o z -oz.1. a PI.1. a P'I 2 2, =,,-.., + Y II UI + Y II U I + Fx: P ox P ox (2), (3)P:~1bl, jgl)1fi'~'h:;~-ft, (4) P:~ :.1jZ-:ftg (*~) PI I:)1~i1J : a~ a~ a~ a~ -;- + UI -::;- + VI -::;- + WI -..,- - fu, o t ox oy o z aul avi awl) (au'l av'l aw'i) ( =0 ax ay az ax ay az 1 a PI 2 Fa" a " a = - p a x + Y V UI + x - a x < U IU I > 1 - a y < V IU I > 1 - a z < ui' IU' I > I avi avi avi avl at + UI ax + VI ay + WI a; +fii, P:(9-12)q:r, < >1*ffi1±LI,TI, RltT*~Jf#Jo ~ (1 )-( 4)P: a<.jnbfp: (7), (8)~ P:T~-ftJf#JjJW (9)-( 12)P:, 1~~UtJt$J:i: U '), v'j, W '» p') jjw: a u' I (J u' I a UI a u' I i3u' I,a UI,i3 u' I ----at + UI ax + U'I a; + U'I ax + VI ay + V I ay + V I a y (7) (8) (9) ( 10) ( 12) au'l,aui,au'1 + WI a-; + W Ia; + W Ia-; - fu,.1. a P' I + Y sr 2 U' + (~< r, a " a " ) p ax Y I ax U {W I > I + ay < U tv 1 > I + a z < U {WI > I ( 13)

3 201 av'] av'],av],av'] at + ll] Tx + II } ax + II } ax av'},av},av'} + V1 ay + v } ay + v 1 ay av'1,av1,av'1, + w} -;;; + W 1 az + W 1 az + fu 1 1 ap'1 2, (a " a = - p ay + -y V v 1+ ax < v III I> I + ay " a,,) < V IV } > I + az < v 1w 1 >} (14) aw'l aw'l,awl,aw'} at + ll] ax + II I ax + U I ax aw'} awl aw'l + v} a y + V'I ay + V'I ay aw'1,aw1,aw'1 + wi Tz + W I Jz + W } Tz (15) _ l.. ap'1 ~ 2, ( ~ " ~ - - p a z ~ y V v I + ax < W }ll I> I + ay " a " ) < W IV I > I + az < W }w1 >} au'l av'1 aw'l =0 ax ay dz (16) 1.2 te L" T, RltT {f- u, h RltT8<Jttt7#J:It CP'1 :ls]pj~jvtcp'. = CP. + CP'., 1W*J;] L" T,, Rltr!P 7X~:FfVft:RJtT8<J~:IS]i!,J *~ttt7#jit,1ta(13)-(16)*3f1~~j: au,,au', au', au, + Usa; + u, --a; + u, --a; + u', a x a Us au' s a UI a Ul + VI ay + VI a y + V, ay + u", a y au,,au', au', au, + v, ay + v, ay + v, ay + v', ay au, au', aui aui + WI a-; + WI a; + w, a-; + w', a-; au,,?u', au',,au, + w, a; + w s a-; + w, a-; + ui, (J z (17) 1 a P, 1 a P' s 2 2 = Y V u + y V u' p ax p ax ' s ( a,, a " a " + (J x < u IU I > I + a y < u LV I > I + a z < U [WI (14), (15)j.\';~{~, J;]1J'iI'~$gj~-*,(16)j.\';~ JVt:

4 ..-:::-~-.-- -, 202 ( au, ov, Ow,) (au', ov', OW'') == Ox oy oz Ox oy oz x>t( l3 )-( 16):ct:I JM1f:ct:(17),(18)~:ct:?± L" T,,, ~ RNT f'f *f'ffi-1jz-:tt,1~~uixgg Pf me I J1 ffjij 1J f1e : au, au, OUI ou s au, oui au, at + UI a;; + Us a;; + Us a;; + VI oy + V, oy + Vs oy au, oui au, + WI 3; + w, 3; + ui, 3; - jv s 1 a e, 2 ( CJ " CJ " CJ " == - p a; + Y'V ti, + CJx < U IU I > I + oy < U {V I > I + CJ z < U [WI ( CJ " '0 " CJ " ) - Ox < usu, >'+oy < UsV, >S+07 < U,W,», O~ O~ O~ CJ~ at + UI a;. + U, ox + U, OX OVs OVI CJV s + VI -::;- + u, -::;- + V, -::;- oy =r oy CJv, OVI CJv, + WI a z + to, a z + w, a z +fu; (18) (19) 1 CJP, 2 ( CJ == - - -::;- + Y 'V V, + :;- p ox ox CJ II CJ - ( CJx < V,U, > s + a y < v'[u'[ a I I > I + oy < V (V I a " >, + CJz < V,W, a I, > 1+ oz < V [WI > 1 ) O~ CJ~ CJ~ CJ~ at + U[ a; + U, a; + U, a; (20) CJw, CJWI CJw, + VI -::;- + V, -::;- + V, -::;- 0)' 0)' oy Ow, OWL OW, + W/~ + Ws ~ + W, ~ 1 CJP, ( CJ a CJ ) = - -P - 0)' + Y 'V2 W 'ox+ - < W' [U'I > I + a"y < W' {V' I > I + a"z < w' [W/ > I (21) ( a I I CJ " a I - a x < W,U, >, + CJy < W sv, >, + a z < WsW, > s I ) CJUs CJv, OW, -+-+-=0 Ox oy oz (22)

5 ~f!j 203 :1iW(19)-(22)tiaJ TiXi;ttmti9J 2 tilt :1iW(19)-(22) ili(l9)-(22)~, Us, Vs' to, 8<Jilii9J*JM~o,*tiEili ~ixi;ttmti9j;f 3C8<J!fmJ1g., JJtiaJ :1i1l, Pf~*~~IJ~: ~ *.%A~~E], 1 aps 2 a = - - -a + Y 11 uis + a < P Xi Xj a '>: - a < Xj Uis'U'), > s (23) auis -a = 0 Xi (24) au. au~. (23)j.\';~ 2'r.~:r.YrUjr. ax",ujs a~ lfiu±vn3silt, ±mt~tjj tt ~.& ixi;ttmti9j8<j~tjj'i1:~~ ) J :I'IP.*tiET±mt~iXi;ttmti9JzfB]8<Jif ]i3c*o A;t~J.w a~. < UiL'UjL' >d!u~1e.:tmtlr J lt~,.:tmt:x1ixi;ttmtz9'j 8<Ji'FJfI:r.Yr, ~*tie T ixi;ttmti9jb\±.mt~ ~1~ ~~. 0 a~. ) < Uis'U'js > s *tiet ttixi;ttvftz9'jrit /J\8<J Hti9J~iX~Vfti9JzfB]3C*, ~~~ix~ Hti9J ~~.;ffi~8<jw:ffi~o b\:1iw(23)~ (24) PJ~ lj~l'iliz9'j1** ~ ~~ 8<J~~:!:~jg:En #ilj (~ 1): I ixi;ttvft i9j(s R it )1 ~ Fig. 1 ~1 7X~iiiE;lJfiliI~$~:'@:~ Energy cascade of secondary flows 3 ~~ b\~pf~~.:i'ip.~~ix~mtz9'j1e~l'ilii9j1**~8<ji'fjflo~wn:!:~~#.~:1i~ b\±'mt~ixi;ttmti9j~.~~=~*-~w~8<j~.o

6 --_.... _._._._-.---~ ~ ~ :x: iid: '!:~ Il)j~li~JL 310;::$,1997, ili~-'=i~m,28(itiflj) : Prantdl, L., 1987,V[.j;j>.f.J~.jg{it,f>I.~ili!ifit±(:l~ffi), Bradshaw, P., 1987, Ann. Rev. Fluid Mech., 19: Speziale, e.g., 1982, lral. J. Engeer. Sci.,20: CASCADE THEORETICAL MODEL OF TURBULENCE SECONDARY FLOWS Dong Changming, Yuan Yeli, Zhang Qinghua ( First lnstiuue of Oceanography, SOA, Key Laborasory of Geophysiool Fluid Dynamics and Nwnerical Modelling, SOA, Qingdao 26r0J3) Abstract In this study of multi - scale motions, dynamics equations of secondary flows with motion scale less than that of the main flow were deduced from the primary Navier-Stokes equations. The secondary flows dynamics equations present the cascading relationship between the main flow and the secondary flow, and show the machanism of the energy source and dissipation of secondary flows in the system of motions. The results of the present study constitute theoretical base for research on the existence and function of secondary flows in the system of motions. Key words Secondary flow Cascade

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