Interntionl Journl of Environmentl nd Erth Science 1: 0 Wind-Induced Phenomenon in Cloed Wter Are with Floting-Leved Plnt Akinori Ozki Abtrct In thi tudy, in order to clrify wind-induced phenomen, epecilly verticl mixing of denity trtifiction in cloed wter re with floting-leved plnt, we conducted hydrulic experiment on wind flow chrcteritic, wind wve chrcteritic, entrinment phenomen nd turbulent tructure by uing wind tunnel tet tnk nd imulted floting-leved plnt. From the experimentl reult of wind flow nd wind wve chrcteritic, we quntified the impct of the occupncy rte of the plnt on their reitnce chrcteritic. From the experimentl reult of entrinment phenomen, we defined the prmeter tht could explin the mgnitude of mixing between the denity trtifiction, nd quntified the impct of the occupncy rte on verticl mixing between trtifiction. From the experimentl reult of the turbulent tructure of the upper lyer, we clrified the difference in mll-cle turbulence component t ech occupncy rte nd quntified the impct of the occupncy rte on the turbulence chrcteritic. For ummry of thi tudy, we theoreticlly quntified wind-induced entrinment phenomen in cloed wter re with luxurint growth of floting-leved plnt. The reult indicted tht the impct of luxurint growth of floting-leved plnt in cloed wter body could be een in the difference in mll-cle fluid chrcteritic, nd thee chrcteritic could be expreed uing the mll-cle turbulent component. Keyword Denity Strtifiction, Floting-leved Plnt, Wind-induced Entrinment Phenomenon, Turbulent Structure I. INTRODCTION N cloed wter re with little inflow nd outflow, the Ifluid re trtified ccording to difference in their verticl denitie. The denity trtifiction form due to difference in temperture, turbidity nd lt level. The behvior of the wter environmentl ubtnce re impcted by turbulent flow cued by wind-induced flow, which i mechnicl diturbnce, nd convective flow, which i therml diturbnce. When wind ct on the wter urfce of uch cloed wter re with denity trtifiction, the urfce lyer become turbulent due to the wind ction, giving rie to n entrinment phenomenon t the denity interfce. Thi phenomenon, which reult from mixing between the upper nd lower wter lyer, ffect the wter qulity in the cloed wter re. If there i little turbulence in uch cloed wter re, little mixing occur, nd the wter qulity become wore. In previou tudy of wind-induced entrinment phenomenon, Akinori Ozki i with the Fculty of Agriculture, Kyuhu niverity 81-8581 JAPAN (correponding uthor to provide phone: +81-9-64-7159; fx: +81-9-64-7159; e-mil: -ozki@gr.kyuhu-u.c.jp). Mori et l. [1] reported tht the entrinment phenomenon w governed by the turbulent energy, which ccelerted the entrinment, nd the tbility of trtifiction, which inhibited the entrinment. The ccelertion of the entrinment could be expreed in n entrinment coefficient, nd the inhibition of entrinment could be expreed in the Richrdon number ( detiled explntion of thee term i given lter). The mixing cpbility between trtifiction could be quntified uing the reltion between the entrinment coefficient nd the Richrdon number. In ddition, Wu, J. [] nd Kit et l. [3] clrified the reltion between wind-induced potentil energy t the wter urfce which i cued by the wind current nd the Richrdon number, nd they explined tht the entrinment velocity t the boundry of denity w governed by the turbulent tructure ner the boundry of denity, which cn be ttributed to the urfce turbulence cued by wind ction. Therefore, from the point of view of fluid dynmic, the wind ction i to be conidered one of the importnt fctor governing the wter qulity in cloed wter re. When we conider the wind-induced phenomen in cloed wter re uch mll irrigtion pond nd creek, it i importnt to conider the impct of floting bodie on fluid movement. Becue the fetch i hort in cloed wter re compred with lke or dm, floting bodie my ignificntly decree the re tht cn be cted upon by wind. In prticulr, floting-leved plnt, which hve recently begun to be ued for wter qulity purifiction, my lo ffect the wind-induced phenomen in cloed wter re. To elucidte the mechnim of the entrinment phenomenon, it i importnt to clrify the reltion between the occupncy rte of the floting-leved plnt nd wind-induced phenomen in cloed wter re. In thi tudy, in order to clrify the impct of the occupncy rte of floting-leved plnt on wind-induced phenomen in cloed wter re, we firt conducted n experiment on wind flow on the wter urfce, wind wve, entrinment phenomenon nd turbulent tructure by uing wind tunnel tet tnk. Bed on the experimentl reult, we quntittively expreed the impct of the occupncy rte of floting-leved plnt on the fluid chrcteritic tht dominte entrinment phenomenon in cloed wter body. II. EXPERIMENTAL METHOD A. Tet Tnk nd Setting Condition of Plnt The tet tnk w mde of crylic plte (length 6 meter width 0.3 meter depth meter). The wind tunnel 67
Interntionl Journl of Environmentl nd Erth Science 1: 0 conited of piece of block-bord on the tet tnk (length 6 m width 0.3 m depth 0.3 m) (cf. Fig. 1). Inted of uing rel qutic plnt, we ued imulted plnt mde from polytyrene in the form of plte. The plte hd thickne of 3.0 mm. In thi experiment, the occupncy rte percentge of the wterwy length on the wter urfce w chnged from to 1,, nd 3 (cf. Fig. ). We et the imulted plnt t both end of the tet tnk. Thi reon for thi plcement w tht floting-leved plnt re generlly ditributed concentric circle-wie from the circumference towrd the center in cloed wter bodie [4]. Regrding the experimentl tep, we firt exmined the wind flow nd wind wve chrcteritic of the tet tnk uing imulted plnt nd defined the pplicble rnge of wind velocity for thi tudy. In ddition, we clrified the impct of imulted plnt on wind flow nd wve chrcteritic. Secondly, we conducted n experiment regrding the entrinment phenomenon of two-lyered trtified flow nd exmined the vrition of denity trtifiction nd turbulent tructure. Finlly, we theoreticlly quntified the impct of the occupncy rte of the plnt on wind-induced phenomen in cloed wter re bed on the experimentl reult. B. Wind Flow Experiment The tet tnk w filled with freh wter. Wind w generted by n ir blower. The blowing power w turned up grdully t pecified wind velocity. The meurement vlue were the verticl wind velocity ditribution, the ir temperture nd wter urfce velocity. The wind velocity w meured with hot-wire velocimeter, nd the wter nd ir temperture were meured with thermocouple. The wind velocity ditribution, temperture nd wve height were meured t two point, 3.0 meter from windwrd (St. 3.0), 5.0 meter from windwrd (St. 5.0). In ddition, in order to meure the urfce flow velocity ( ), pper with dimeter of 5 mm w floted on the wter urfce, nd the time required for the pper to p through fixed zone w meured t St. 3.0. Dt from over 30 intnce of pge through fixed zone were collected, lthough ce in which the pper rode on the wind or on wve were excluded nd we defined the urfce flow velocity pge ditnce divided by pge time. C. Wind Wve Experiment The tet tnk w the me in the wind flow experiment. The meurement vlue were wve profile. The wve profile were meured with reitnce wire wve guge to which two pltinum wire were trung. The mpling time for the wve profile w econd, nd the mpling frequency w 0 Hz. The wve height w meured t 5 point:.0 meter from windwrd (St. A), 3.0 meter from windwrd (St. B), meter from windwrd (St. C), nd 5.0 meter from windwrd (St. D). D. Entrinment Phenomenon Experiment A two-lyered, trtified denity flow w induced in the tet tnk. The upper lyer contined freh wter, nd the lower lyer contined lt wter. To void impulive brekdown of the denity interfce, the blowing power w turned up grdully to the pecified wind velocity. The meurement prmeter were the wind velocity t 0.15 meter bove the wter urfce, nd the wter temperture nd linity t vriou increment in the verticl direction. The wind velocity w meured with hot-wire velocimeter t.75 meter from the windwrd end of the tnk, the linity w meured with conductnce meter, nd the wter temperture w meured with thermocouple. The profile of linity nd wter temperture were meured t 3.0 meter from the windwrd end nd the intervl between meurement in the verticl direction w 5.0 millimeter. E. Turbulent Structure Experiment The equipment nd method were the me in the entrinment phenomenon experiment. The verticl nd horizontl flow component of velocity were meured t 5.0-millimeter intervl from the denity interfce to the wter urfce with n X-type hot-wire velocimeter. We et up the velocimeter t two point, 3.0 meter from the windwrd end of the tnk (Point A) nd t the edge of the imulted plnt (Point B). Since the entrinment phenomenon h n effect on the turbulent tructure, we ued mpling time of 30 econd, nd the mpling frequency w 0 Hz. [Experiment for Turbulent Structure] [Experiment for Entrinment Phenomenon] [Experiment for Wind Wve] [Experiment for Wind Flow] imitted plnt 0.3m wind x St.A.0m wve guge Point A Center of tet tnk 3.0m Center of tet tnk 3.0m St.B 3.0m St. 3.0 3.0m hot-wire velocimeter nd thermocouple conductnce meter St.C m Point B Edge of the Plnt St.D 5.0m St. 5.0 5.0m hot-wire velocimeter 0.3m Wind tunnel m Tet tnk m [Internl fluid] -Experiment for Wind Flow nd Wind Wve: Freh wter -Experimentl for Entrinment Phenomenon nd Turbulent Structure: Denity Strtifiction with Freh nd Slt Wter 30cm Fig. 1 Schemtic digrm of the experimentl pprtu Polytyrene Plte 30cm Imitted Floting-leved plnt 5mm (Without Plnt) 1 occupncy 1 plte on ech edge occupncy plte on ech edge 3 occupncy 3 plte on ech edge Fig. Method ued to imulted floting-leved plnt 68
Interntionl Journl of Environmentl nd Erth Science 1: 0 III. EXPERIMENTAL RESLTS A. Reult of Wind Flow Experiment Fig. 3 how the wind-velocity ditribution in the verticl direction meured t ech meurement point for ech occupncy rte of the floting-leved plnt. It h previouly been reported [5] [6] tht the wind ditribution ner the wter urfce complied with logrithmicl low, nd our reult correponded with thi finding. In ddition, the wind velocity increed, the velocity grdient ner the wter urfce becme lrge. Thee reult indicted tht the turbulent boundry lyer of the wind wve t the wter urfce w imilr to the wll boundry lyer. A conequence, we were ble to drw regreion line in thee figure, nd we clculted the ir friction velocity uing the following eqution: ( z) 1 z = ln. (1) * κ z0 where (z) i the wind velocity t height z, * i the ir friction velocity, κ i the Krmn contnt, z i the height from the wter urfce, nd z 0 i the roughne contnt. Fig. 4 how the reltion between the clculted ir friction velocity nd the wind velocity t m bove the wter urfce,, for vriou condition of the imulted plnt. Here, w clculted uing the regreion expreion. A hown in Fig. 4, the occupncy rte of the plnt increed, the ir friction decreed lightly t both meurement point. Thi finding might be explined by the fct tht the chrcteritic of the reitnce encountered by ir differed between the plnt urfce nd the wter urfce. Hence, it w necery to quntittively elucidte the reitnce chrcteritic of the plnt t different occupncy rte. Generlly, the verticl trnporttion of momentum t the wter urfce i equl to the her tre cting on the wter urfce. Thi trnporttion i importnt becue of it reltion to problem uch the development of wind wve nd wind-induced flow. The her tre, which ct on the wter urfce, cn be expreed in reltion to the wind velocity from m bove the wter urfce follow [7]: C * d =. () Thi method i clled the Bulk method. Although the Bulk method i uully ued when determining the wind-induced flow in the ocen, we ued it for clculting the reitnce coefficient in the preent tudy becue thi method mke it ey to derive the formul nd becue there re mny experimentl reult uing thi method. Fig. 5 how the verged reitnce coefficient under vriou condition of the occupncy rte of the plnt. Kru nd Turner [8] hve reported tht when rnged from 3 m/ to 16 m/, the verged reitnce coefficient rn from 1.7 through 1.33. Our reitnce coefficient were lightly greter thn the vlue defined by Kru nd Turner. There were mny reon tht there were individul difference between reercher when clculting the reitnce coefficient uing the logrithmic lw. However, our reult indicted difference in the occupncy rte of the plnt. The reitnce coefficient tended to decree with incree of the occupncy rte of the plnt. Moreover, thi tendency w trong t leewrd. Therefore, we could conclude tht luxurint growth of floting-leved plnt ffect the wind on the wter urfce. In thi tudy, wind flow w mooth on the imulted plnt nd met reitnce on the wter urfce. * (m/).0-3 - -1 0-3 - -1 0.0 Height from wter urfce (m) -3 - -1 0.0 Height from wter urfce (m) -3 - -1 0.0 Height from wter urfce (m) -3 - -1 0 0.5 0.3 0. 0.1 0 Height from wter urfce (m).0 (Without Plnt).0 Height from wter urfce (m) -3 - -1 0 1 occupncy.0 Height from wter urfce (m) -3 - -1 0 occupncy.0 Height from wter urfce (m) -3 - -1 0 Height from wter urfce (m) 3 occupncy Fig. 3 Wind velocity ditribution t ech meurement point for ech occupncy rte 0.0 1 (m/) 1 3 * (m/) 0.5 0.3 0. 0.1 0 0.0 1 (m/) Fig. 4 The reltion between clculted ir friction velocity * nd wind velocity t height of m from wter urfce for ech occupncy rte 1 3 Fig. 6 how the reltionhip between urfce flow velocity nd ir friction velocity * t St. 3 for ech occupncy rte on floting-leved plnt. Regrding the reltion between urfce 69
Interntionl Journl of Environmentl nd Erth Science 1: 0 Averged reitnce coefficient C d (m/) 00 015 0 005 000 St.3 3.0 St.5 5.0 Fig. 5 Averged reitnce coefficient for ech occupncy rte 0.30 0.5 0.15 0. 5 0 St. 3.0 0 0.1 0. 0.3 0.5 * (m/) Fig. 6 The reltionhip between * nd t St. 3.0 for ech occupncy rte TABLE 1 EXPRESSION FORMLA OF THE RELATION BETWEEN Condition Reltion between nd 1 3 Wu(1975) = 1 * = 0.38 * = 0.31 * = 0.8 * = 0.55 * 1 3 1 3 Wu AND * * flow velocity nd ir friction velocity *, Wu [] h reported tht both reltion could be expreed = 0.55. Nkym nd Nezu [9] reported tht when the * wind velocity w reltively gret nd the wind wve w well developed, both reltion pproximted the expreion formul given by Wu. When compred to the reult obtined by Wu, our reult with no plnt occupncy () were lightly mller. Therefore, it w conidered tht in thi tudy the wve did not develop compred with the experimentl reult of Wu. A comprion of the regreion expreion clculted by the let-qure method of both reltion i hown in Tble 1. From thee reult, under the condition of ir friction velocity below 0.3 m/, both reltion were uneven, nd thee tendencie becme tronger the occupncy rte of the plnt increed. nder the condition of ir friction velocity greter thn 0.3 m/, both reltion were hown liner. When the ir friction velocity w more thn 0.3 m/, the urfce flow velocity increed lightly the plnt occupncy rte increed. Thi occurred becue, when the imulted plnt were preent on the windwrd ide, the urfce occupied by plnt w conidered to be mooth region nd the wter urfce w conidered to be rough region. A reult, it w conidered tht t n ir friction velocity below 0.3 m/, the wind velocity w not ufficient for wind wve to develop on the wter urfce, nd the floting pper w wept by wind. Moreover, it w found tht n ir friction velocity of 0.3 m/ or more w required to cue wind wve to develop. B. Reult of Wind Wve Experiment Generlly, the chrcteritic of the power pectrum ditribution re well known to expre the ttiticl chrcteritic of wve. In thi tudy, we ued the power pectrum obtined in the experiment for verifiction of the wind wve. We divided ll of the obtined dt, i.e. the dt clculted uing FFT, into 048 dt block, nd performed the pectrum clcultion by obtining n enemble verge of the reult of FFT. Regrding the form of the power pectrum, it i well known tht the reult of pectrum nlyi of well-developed wve comply with the following eqution on the high frequency ide: 5 φ ( f ) = βg f. (3) where φ ( f ) i the power pectrum, g i the ccelertion of grvity, f i the frequency nd β i the contnt ( = 9.51 ). Fig. 7 how the clculted reult of the power pectrum for the occupncy rte of nd. Our clculted reult did not comply with thi eqution on the high frequency ide t St. A. Thi lck of complince could be explined by the fct tht the wve w in it erly tge of development nd w too mll to meure with our wve guge. The me reon for the lck of complince with thi eqution could be given for the experimentl ce in which the repreenttive wind velocity w below m/. Therefore from the reult of the nlyi of the power pectrum of the wind wve ugget tht the wveform dt obtined in thee experiment were conitent with the preence of wve except the dt meured t St. A nd the experimentl ce with repreenttive wind velocity below m/. On the other hnd, t St. B, St. C, nd St. D nd in the experimentl ce with repreenttive wind velocity over m/, the clculted reult complied with thi eqution. In the experimentl ce with repreenttive wind velocity of 4.7 m/, β howed the bet greement with the eqution, nd when the vlue of the repreenttive wind velocity increed to more thn 4.7 m/, β tended to become lrge. In ddition, the repreenttive wind velocity becme higher nd the fetch becme longer, the pek of the power pectrum moved to the low frequency ide t ech occupncy rte. Moreover, the occupncy rte of the plnt increed, the power pectrum vlue decreed. Thee reult ment tht incree of wind velocity nd of the length of the fetch hd the me effect on the development of the pectrum, nd the pek of the power pectrum moved to the low frequency ide with the development of the pectrum. A 70
Interntionl Journl of Environmentl nd Erth Science 1: 0 compred with the reult of the experimentl ce with nd 0 % occupncy rte, the power pectrum t n occupncy rte of w low vlue, nd the development rte of the wind wve w low. Therefore, it w conidered tht the exitence of the plnt reduced the wind energy nd inhibited the development of the wind wve. Power Spectrum (cm ) Power Spectrum (cm ) -1 - -3-4 -5-4 -5 β = =3.8 9.51-6 St..0-7 St. 3.0 St. St. 5.0-8 0 1 Power Spectrum (cm ) -1 - -3-4 -5 =5.0 Power Spectrum (cm ) Power Spectrum (cm ) -1 - -3-4 -5 =8.6-6 -6-6 St..0 St..0-7 St. 3.0-7 St. 3.0 St. St. -8 St. 5.0 St. 5.0-8 0 1 0 1-1 -1-1 - = - =4.8 - β = 9.51 β = 9.51 β = 9.51-3 -3-3 Power Spectrum (cm ) -4-5 β = 9.51-6 St..0-7 St. 3.0 St. -8 St. 5.0 0 1 St..0-7 St. 3.0 St. -8 St. 5.0 0 1-4 -5 β = 9.51 =8.3-6 St..0-7 St. 3.0 St. -8 St. 5.0 0 1 Fig. 7 Power pectrum ditribution for experimentl ce nd occupncy rte C. Reult of the Entrinment Phenomenon Experiment Entrinment velocity i generlly given by the coefficient of entrinment E nd the over-ll Richrdon number R i, which re defined e E =. (4) V R i =. (5) ρv where e i the entrinment velocity, V i the reference velocity of flow, h i the wter depth of the upper lyer, ρ i the reference denity, Δ ρ i the denity difference between the upper nd lower lyer, nd g i the grvittionl ccelertion. When the wter flow i two-dimenionl nd the ection of flowing wter under conidertion i rectngulr, the continuity eqution of the flow rte nd the denity conervtion lw for the upper lyer re repectively given h1 ( u1h ) + 1 = e. (6) t x ( ρ1h1 ) ( ρ1u1 h1 ) + = ρ e. (7) t x where u 1 i the cro-verge velocity of the upper lyer, h 1 i the upper wter depth, ρ 1 i the denity of the upper lyer, ρ i the denity of the lower lyer, x i the mintrem direction, nd t i time. In wind-induced flow, the econd term on the left-hnd ide of Eq. (6) i mll. Hence the entrinment velocity i ble to repreent the rte of vrition of the upper wter depth with time, i.e., the decending velocity of the denity interfce, hown below: dh 1 = e. (8) dt Eq. (7) nd Δ ρ = ρ ρ1 yield ρ1 ρ1 Δρ + u1 = e. (9) t x h1 If the lower wter entrined to the upper lyer i rpidly nd uniformly mixed nd diffued in the verticl nd horizontl direction, the econd term on the left-hnd ide of Eq. (9) cn be omitted. dρ1 Δρ = e. () dt h1 By performing integrtion under the condition tht ρ i contnt, we obtin the following from Eq. (8) nd Eq. () h1 Δρ = hi Δρi = cont. (11) where h i i the initil upper wter depth nd Δ ρi i the initil difference in denity between the upper nd lower lyer. Hence we cn ubtitute follow: h h i, Δ ρ Δρ0, ρ ρ, V *. where Δ ρ0 i the initil denity difference of the lyer, * i the ir hre velocity nd ρ i the ir denity. Thu Eq. (4) nd Eq. (5) cn be decribed below time-invrint eqution Δρ0ghi Ri =, (1) ρ* nd, by Eq. (8), the coefficient of entrinment E cn be decribed dhi / dt e E = =. (13) * * In thi tudy, we conidered the reult of the entrinment phenomenon experiment by uing R i nd E, which were obtined by Eq. (1) nd Eq. (13), repectively. Fig. 8 how the vrition rte of the upper wter lyer with time; the depth repreent the height of the denity interfce. Shortly fter the wind blowing the rte w vrible becue the formtion of circultion flow nd the development of internl wve did not occur; however, the rte w linerly proportionl to time. Since previou experiment without plnt [1] hd hown the me tendency, we could conclude tht the lowering of the velocity of the denity interfce w contnt except hortly fter the wind blowing. Hence the entrinment velocity e in the preent experiment could lo be decribed e dh / dt = cont. Fig. 9 how the reltionhip between the entrinment coefficient E nd the over-ll Richrdon number R i in the preent experiment. The entrinment coefficient E cn expre the mgnitude of the entrinment phenomenon, nd the over-ll Richrdon number R i cn expre the intenity of denity trtifiction. From Fig. 9 the entrinment coefficient E in the 71
Interntionl Journl of Environmentl nd Erth Science 1: 0 TABLE II EXPERIMENTAL CONDITIONS FOR ENTRAINMENT PHENOMENON Run No.Occupncy rte 0.15 (m/) ρ 3 (kg/m 3 ) ρ (kg/m 3 ) h i (m) * (m/) 1 6.1 0 1.169 0.1 34.4 03 1.171 0. 0.353 5.4 3 5.9 05 1.168 0.0 0.31 9.1 4 7.9 045 1.171 0. 0.347 37.1 5 6. 07 1.08 7 59. 6 055 1.168 0.0 0.36 8.1 7 1 7. 07 1.181 0.1 0.305 6.6 8 017 1.168 0.0 0.36 5.8 9 8.3 076 1.173 0.116 3 39.6 7.7 01 1.198 0.158 0.395 17.6 11 8.4 7 1.195 84 01 45.7 1 03 1.176 0.61 41. 13 7.5 080 1.183 0.7 0.37 51.5 14 8.1 048 1.190 0.9 0.360 33. 15 7.7 07 1.194 0.141 0.389 0.7 16 7.8 01 1.19 0.113 01 1.1 17 3 7.5 060 1.194 94 0.38 31.5 18 7.7 054 1.08 0.0 0.395 7.9 19 8.1 037 1.0 0.0 19 17.0 0 7.9 08 1.197 0.0 08 15.3 Decending rte of denity interfce (mm) 3 1 1 Time (min.) Fig. 8 Rte of decent of the denity interfce with time for vriou overll Richrdon number R i 1 1 R i Run Run 4 Run 7 Run 8 Run 14 Run 15 Run 19 Run 0 experiment with imulted plnt w much lower thn in the experiment without plnt. And the lrger the occupncy rte of the plnt becme, the lower the entrinment velocity becme. Regrding the reltionhip between E nd R i, the previou / reult of E R i for n experiment without qutic plnt [1] complied with the whole etting condition of the imulted plnt for the vlue of R i rnging from 0 to 0. In ddition, it w reported in thi previou experiment tht the contnt of proportion, which w obtined from the reltion between E nd R i, could expre mgnitude of verticl mixing between the upper nd lower lyer t the denity interfce. A repreenttive velocity for defining E nd R i, Tkhhi nd Sug [] ued men flow velocity to repreent the min trem direction velocity ner the denity interfce m, Kit et l. [3] ued the bckwrd flow, nd r [11] ued the ri uniformity flow velocity for bckwrd flow, nd nd thee previou reercher ll etimted the mgnitude of verticl mixing by uing the contnt of proportion obtined from the reltion between E nd R i. In the preent tudy, we ued the ir friction velocity the repreenttive flow velocity, nd * we quntittively etimted the mgnitude of verticl mixing for ech occupncy rte of the plnt by uing the following eqution. 001 Entrinment coefficient E -4 0001-5 -6 3 00001 1 0 1 0 Over-ll Richrdon number R i Fig. 9 Entrinment rte E plotted logrithmiclly gint over-ll Richrdon number R i TABLE III EXPRESSION FORMLA OF THE RELATION BETWEEN E AND Condition Reltion between E nd / R i / e * = 0.76 * / * = 0.16 e * / * 8 e = * / * 4 e = * 3 / =.0 e m m 1 / =.0 e ri ri / = 5.0 e r r ( ) 1 ( ) ( ) 3 ( ) Tkhhi et l. ( ) Kit et l. ( ) r ( ) / 1 3 R i e = K. (14) * * Tble 3 how the contnt of proportion K which w obtined by Eq. (14). From Tble 3, the mgnitude of verticl mixing between the upper nd lower lyer w exponentilly decreed the occupncy rte of the plnt increed. D. Reult of Turbulent Structure Experiment Fig. how the profile of the time-verge velocity in the horizontl direction for the vriou vlue of the occupncy rte. In Fig., the horizontl xi repreent the dimenionle time-verge flow rte in the horizontl direction, nd the 7
Interntionl Journl of Environmentl nd Erth Science 1: 0 verticl xi repreent the dimenionle upper lyer wter depth. The wind direction w from the left ide to the right ide in thee figure. The expreion z / h i = 1 repreent the wter urfce nd z / h i = 0 repreent the denity interfce. In thee figure repreent the flow velocity of the wter urfce, z i the meurement height nd h i i the upper lyer wter depth. From Fig., it cn be een tht the occupncy rte of the plnt becme lrge, the horizontl flow velocity t ech meured point tended to decree. At point A, the turning point from the wind-driven current to the return current moved towrd the wter urfce with n incree in the occupncy rte. At point B, the occupncy rte of the plnt becme lrge, nd the wind-driven current becme gentle flow. The return current w uniform except in the experiment without the plnt, becue in tht experiment the horizontl flow velocity w ffected by the wll. Fig. 11 how the profile of the time-verge velocity in the verticl direction V for the vriou vlue of the occupncy rte. In Fig. 11, the horizontl xi repreent the dimenionle time-verge flow rte in the verticl direction, nd the verticl xi repreent the dimenionle upper lyer wter depth. The verticl flow velocity define the upwrd flow tht goe from the denity interfce to the wter urfce poitive. From Fig. 11, ince the vlue in the upper 0-3 of the depth of the wter Point A 1.0 TABLE IV EXPERIMENTAL CONDITIONS FOR TRBLENT STRCTRE Run No. Occupncy rte (m/) ρ 3 (kg/m 3 ) ρ (kg/m 3 ) h i (m) * (m/) * (m/) R i 1 8.5 118 1.37 0.16 45 17 59.3 1 8.3 115 1.37 96 3 15 46.4 3 8.3 6 1.36 0.1 3 15 45.5 4 3 8.5 111 1.37 0.8 45 15 48.1 w ffected by wind, the vlue of the time-verge velocity w high nd pred. The flow direction tht nk from the wter urfce to the denity interfce w high vlue. And the vlue becme lmot 0 uniformly under bout 50 percent of the upper wter depth. In ddition, it w likely tht the velocity in the verticl direction differed becue the repreenttive cle chnged with the wind velocity. The time-verge verticl velocity did not how ytemtic difference under ech occupncy rte of the plnt becue the mpling time of the hot-wire velocimeter w not prticulrly long. No lrge difference were oberved between the meured vlue t ny point. From the bove comprion of the men flow velocity for the horizontl nd verticl direction, it w found tht the impct of the occupncy rte of the plnt on flow velocity w not gret. Thi ment tht the dominnt fctor of the entrinment phenomenon w conidered to be mll-cle phenomenon. In order to clrify the impct of thi mll-cle phenomenon, we exmined the turbulent intenity which w obtined by nlyzing the fluctution of flow velocity. Fig. 1 how the 1.0 Point A z/h i 0.8 0.6 0. 1 3 z/h i 0.8 0.6 0. 1 3 -.0-1.0 1.0.0 3.0-1.0-0.5 0.5 1.0 V 1.0 Point B 1.0 Point B z/h i 0.8 0.6 0. 1 3 z/h i 0.8 0.6 0. 1 3 -.0-1.0 1.0.0 3.0 Fig. Time-verged velocity profile in the horizontl direction -1.0-0.5 0.5 1.0 V Fig. 11 Time-verged velocity profile in the verticl direction 73
Interntionl Journl of Environmentl nd Erth Science 1: 0 reltionhip between the horizontl nd verticl turbulent intenitie verged with the upper wter depth nd the vriou occupncy rte. In thee figure, ~ 1 h1 = dz h ', (15) 1 * 0 ~ 1 h1 V = V dz h '. (16) 1 * 0 where i the turbulent component of the horizontl direction, V i the turbulent component of the verticl direction, nd * repreent the friction velocity t the wter urfce. In Fig. 1, the horizontl nd verticl turbulent intenitie verged with wter depth becme mller the occupncy rte becme lrger. Thee figure correponded with the chnge of K, which w obtined from the experimentl vlue for the entrinment phenomenon. It w concluded tht the verticl mixture cpbility between the verticl lyer declined the wter urfce occupied by the plnt becme lrge. Nmely, the mgnitude of the turbulent intenity becme mll becue the upper turbulent tructure chnged. K =E/Ri -3/ 08 06 04 0 00 1 3 K ~ V ~ 0.5 0.3 0. 0.1 Fig. 1 Turbulent intenity verged with upper wter depth nd contnt of proportion K Turbulent intenity verged with upper wter depth IV. THEORETICAL QANTIFICATION FOR WIND-INDCED ENTRAINMENT PHENOMENON In order to expre the entrinment phenomenon t the denity interfce quntittively, we conidered the contribution of the work done by wind tre to the incree in potentil energy t the denity interfce. Fig. 13 how definition ketch of the chnge in the potentil energy due to the wind-induced flow where the mixing lyer i een to be deepened by dh in period of dt. If we deignte tht, t time t, ρ i the denity of the mixed fluid nd Δ ρ i the denity difference t the denity interfce, the rte of chnge de p dt of the potentil energy per unit urfce re cn be written de p Δ + = 1 dh ρ h g( h + dh) dh. (17) dt dt h Neglecting the higher order term, we obtin ρ dh Δρ h Denity interfce t Denity interfce t t = t t = t + dt Fig. 13 Definition ketch of the chnge in the potentil energy due to the wind-induced flow de p 1 1 = dh. dt dt (18) The rte de k / dt of work done by the wind tre per unit urfce re i generlly expreed [8] de k = τ = ρ *. dt (19) where, τ i the wind tre nd i the urfce flow velocity. By compring the rte of incree of the potentil energy of the mixing lyer due to the rte of work done by the wind tre, we cn determine the frction of the work done by the wind ued for mixing t the denity interfce. From (18) nd (19), we obtin de p 1 dh = dek ρ* dt (0) In thi formul, = Ri, ρ* (1) nd dh 1 dt * = E. () We rewrite Eq. (0) by uing Eq. (1) nd Eq. (), nd we obtin de p 1 * = ERi. dek (3) Mori et l. [1] hve reported tht when R < 0 the reltion between de p de k de de nd R p 1/ i k 1/ i i R cn be drwn. So from thi reltion de p 1 * 1/ = ERi Ri. (4) dek From Eq.(4) / E = α Ri. (5) * 74
Interntionl Journl of Environmentl nd Erth Science 1: 0 where α i contnt of proportion. Tht i, we cn expre K, which repreent the entrinment cle t the denity interfce, the rtio of the flow velocity t the wter urfce nd ir friction velocity. In ddition, r [11] h reported tht the element tht determined K included the turbulent intenity, integrl cle, nd eddy cle, which ct on the denity interfce, nd the wvelength nd wve height of vrition of the denity interfce. r defined thee reltion turbulent coefficient by uing the following eqution: 4 / l T =. (6) M h where i the turbulent intenity, i the men flow M velocity of the upper lyer, l i the integrl cle of the turbulent intenity nd h i the depth of the upper lyer. The integrl cle of the turbulent intenity l w defined uing the following eqution, 1 0 l = R( τ ) dτ. (7) 0 R τ i n utocorreltion function defined in the where ( ) following eqution, R τ = t + τ t. (8) ( ) ( ) ( ) Fig. 14 how the reltionhip between K, which w defined bed on the experimentl reult of the entrinment phenomenon, nd T which w defined by Eq. 6. Thi figure how tht the occupncy rte of the plnt increed, the vlue of K nd T decreed. In n experimentl ce without plnt, r found the reltion between K nd T to be K T = 0.7. Our experimentl reult in the ce without plnt howed the vlue of K T to be quite imilr to thi vlue. A the occupncy rte of the plnt increed, the turbulent coefficient T decreed long with K. Therefore, we could explin the decrement of the entrinment ner the boundry of the denity nd the ttenution of the turbulent component due to the occupncy of the floting-leved plnt by uing the turbulent coefficient T nd K T. The coefficient K nd T 1 09 06 03 00 K/T=0.74 K/T=0.65 K/T=0.53 1 3 K T K/T=7 V. CONCLSION From thi tudy, we could conclude tht luxurint growth of floting-leved plnt in cloed wter body ffected the wind flow chrcteritic nd wind wve chrcteritic by decreing the length of the fetch. Furthermore, the energy level of the diffuing lyer nd the entrinment lyer were ttenuted by the ttenution of the wind-driven current, i.e., the urfce hering lyer, the repone of the floting-leved plnt ffected the wter urfce. Therefore, it cn be concluded tht when floting-leved plnt grow on the wter urfce in cloed wter body, the entrinment velocity decree the occupncy rte incree. It i thought tht the plnt ffect the turbulence induced by wind nd cue the wter qulity to decree. Conequently, when floting-leved plnt re ued purifiction technique to improve wter qulity, we recommend mintining the wter urfce re o tht it cn be cted upon by the wind. REFERENCES [1] Mori, K., Tohr, Y. nd Kto O Experimentl Reerch of Entrinment Rte of Denity Interfce due to Wind Induced Current Trnction of the Jpnee ociety of irrigtion, dringe nd reclmtion engineering. 1989, Vol. 144, pp.85-93 [] Wu, J. Wind-Induced Turbulent Entrinment Acro Stble Denity Interfce, Journl of Fluid Mechnic, 1973, 61, pp. 75-87. [3] Kit,E., Berent,E. nd Vjd,M. Verticl Mixing Induced by Wind nd Rotting Screen in Strtified Fluid in Chnnel, Journl of Hydrulic Reerch. 1980, 18, pp.35-58 [4] Ikuhim, K. Subtnce Production of Plnt Community ner Wter, Kyoritu Publihing, Tokyo, 1974 [5] Shemdin,O.H. Wind-Generted Current nd Phe Speed of Wind Wve. Journl of Phyicl Ocen, 197,, pp.411-419 [6] Wu, J. Wind-Induced Drift Current. Journl of Fluid Mechnic, 1975, 68,pp.49-70 [7] Turuy, H. Experimentl Study of Wind Driven Current in Wind-Wve Tnk -Effect of Return Flow on Wind Driven Current-, Report of the Port nd Hrbor Reerch Intitute, 1983, Vol., No., pp.18-174 [8] Kru, E.B. nd Turner, J.S. A One-Dimenionl Model of the Seonl Thermocline The generl theory nd it conequence, Tellu, 1967, 19, pp. 98-6 [9] Nkym, T. nd Nezu, I. Turbulence Structure of Wind Wter Wve, Journl of Jpn Society of Civil Engineering, 000, No.64,Ⅱ-50, pp. 45-56 [] Tkhhi, A. nd Sug, A. Entrinment Coefficient in the Slt-Wter Freh-Wter Strtifiction, Proceeding of Annul Conference of the Jpn Society of Civil Engineer, 1976, No., pp383-384 [11] r, M. Vrition of Denity Interfce nd Entrinment Velocity Induced by Wind Sher, Proceeding of Cotl Engineering. JSCE. 1983, Vol.30, pp.561-565 Fig. 14 The reltionhip between, K which w defined bed on the experimentl reult of entrinment phenomenon nd turbulent coefficient T 75