ADCP MEASUREMENTS OF VERTICAL FLOW STRUCTURE AND COEFFICIENTS OF FLOAT IN FLOOD FLOWS

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1 ADCP MEASUREMENTS OF VERTICAL FLOW STRUCTURE AND COEFFICIENTS OF FLOAT IN FLOOD FLOWS Yasuo NIHEI (1) and Takeiro SAKAI (2) (1) Department of Civil Engineering, Tokyo University of Science, 2641 Yamazaki, Noda-si, Ciba, , Japan, pone: ; fax: ; (2) CTI Engineering Co. Ltd., Honcou, Aoba-ku, Sendai-si, Miyagi, 98-14, Japan ABSTRACT To ceck te accuracy of coefficients of float, wic are widely used in discarge measurements wit float and image processing, we examine te coefficients of float by conducting ADCP measurements for flood flows in te Edo River and te Ara River in Japan. We compare te observed results for vertical flow structure wit classical wellknown velocity distributions, suc as te logaritmic profile and Aki s teory. Te latter teory is used to evaluate general coefficients of float. Te observed velocity distributions are in better agreement wit te logaritmic profile tan Aki s teory. Note tat te observed coefficients of float sow a decreasing trend as te water dept increases and te average coefficients of float are less tan te general values. Tese results for te coefficients of float are also in good agreement wit tose evaluated wit te logaritmic profile Keywords: Coefficient of float; Discarge measurement; ADCP; Float; Logaritmic profile; Vertical flow structure 1 INTRODUCTION River discarge is important for river planning and management. Monitoring of river discarge as been conducted using various sensors and tecniques, suc as te Price current meter, te electromagnetic current meter, te rod-float, te acoustic Doppler current profiler (ADCP), te radio current meter, and te image processing tecnique (e.g., Muller, 22). Among tese sensors and tecniques, te rod-float, te radio current meter, and te image processing tecnique can measure surface velocity. To evaluate te dept-averaged velocity and te discarge from te surface velocity, it is necessary to adopt a coefficient of float, wic is a ratio of a dept-averaged velocity to a surface velocity (Rantz, 1982). Table 1 indicates general coefficients of float, wic ave been set up in line wit Aki s teory for vertical velocity distribution (Aki, 1932). Altoug te coefficients of :

2 Table 1 Coefficients of float generally used in Japan. Water dept Draft of float Standard values ~.7 m water surface m.5 m m 1. m m 2. m m 4. m.96 float ave been confirmed troug various laboratory experiments, few field data ave been reported for te coefficients of float because no appropriate tecnique for measuring te vertical velocity profile in rivers as been developed. On te oter and, acoustic Doppler instruments like ADCP tat are generally used in flow monitoring in oceans can measure vertical velocity profile and water dept simultaneously (e.g., Pettigrew et al. 1986). Terefore, te ADCP is appropriate to obtain field data for te coefficients of float. In order to ceck te accuracy of coefficients of float troug field measurements, in te present study, we attempt to examine te coefficients of float by conducting ADCP measurements for flood flows in large rivers. We compare te observed results for vertical flow structure wit classical well-known velocity distributions, suc as te logaritmic profile and Aki s teory, wic is used in te evaluation of te general coefficients of float. Furtermore te measured coefficients of float are also compared wit te teoretical values. 2 METHODS OF FIELD MEASUREMENTS AND DATA ANALYSIS 2.1 FIELD OBSERVATIONS Te river-flow measurements wit te ADCPs were performed in te Edo River and te Ara River, wic flow into Tokyo Bay in Japan. As sown in Fig. 1, a total of six measurement stations (Stns. E1, E2, and E3 on te Edo River and Stns. A1, A2, and A3 on te Ara River) were cosen. Te average widts of compound cross sections in bot rivers are 4-7 m. A 1,2 khz ADCP (Teledyne RDI) was used for river-flow monitoring in te present field measurement. Te ADCP can measure te vertical distribution of te treedimensional velocity wit fine vertical resolution in wic te minimum cell size is 1 cm. On te Edo River, a down-looking ADCP was set up near te water surface wile a ;

3 E1 N Ara River E2 E3 Tama River A1 A2 A3 Edo River 15 km Tokyo Bay Fig. 1 Map of measurement stations Table 2 Hydrologic events in wic field measurements were conducted. Y. P. (Yedogawa Peil) and A. P. (Arakawa Peil) are te base levels in te Edo River and Ara River, respectively. No. Period Stations H.W.L. 1 Aug. 912, 23 Edo River: Stn.E [Y.P.m] 2 Oct. 68, 24 Edo River: Stns.E1 and E [Y.P.m] 3 Oct. 9~11, 24 Ara River: Stns.A1, A2 and A [A.P.m] 4 Oct. 2123, 24 Edo River: Stns.E1 and E [Y.P.m] Ara River: Stns.A1, A2 and A [A.P.m] 5 July 27~28, 25 Edo River: Stn.E3 8.2 [Y.P.m] 6 June 16~17, 26 Edo River: Stn.E [Y.P.m] 7 July 19~2, 26 Edo River: Stn.E [Y.P.m] bottom-mounted, up-looking ADCP was used for continuous flow measurements in te Ara River. Te cell sizes in te vertical direction are 2 cm and 1 cm in te Edo River and te Ara River, respectively. Table 2 lists seven ydrologic events in wic te field measurements were conducted. 2.2 DATA ANALYSIS To evaluate te coefficient of float, wic is te ratio of te dept-averaged velocity to te surface velocity, we need te vertical velocity profile from te water surface to te riverbed. As sown in Fig. 2, te ADCP may not measure te velocity in te surface and bottom layers due to te measurement performance of te ADCP. Wen

4 z Observed data Extrapolated values ADCP.45 m z d.1d Fig. 2 Extrapolation procedure of velocities in te surface and bottom layers. u te ADCP are set near te water surface as depicted in te figure, te blank lengt, including te draft of te ADCP, is.45 m. Since, in tis case, te acoustic signal transmitted from te sensors is received on te riverbed, tere is a significant measurement error in te bottom layer, wic as a tickness of.1d. It is terefore necessary to extrapolate te velocity in te surface and bottom layers. Ten, te velocity in te surface layer is extrapolated to be te same as tat in te upper layer of te measurement region. On te oter and, te bottom velocity is evaluated wit te approximation of te logaritmic profile. 2.3 THEORY FOR VERTICAL VELOCITY DISTRIBUTION Te vertical distribution of velocity presented by Aki (1932), wic is used to evaluate te general coefficients of float, as mentioned above, is expressed as 2 2 z z u = I C + 2a + 4a 2, (1) 3 were I is te slope of te water elevation, z is te dept from te water surface, C is Cezy s coefficient (= 1 6 n, and n are te water dept and Manning s rougness coefficient, respectively), and a is te relative dept of te peak velocity. Wen evaluating te general coefficients of float, te relative dept of te peak velocity a is given as te function of te water dept : i.e. a =,.1,.2, and.3 for < 1 m, 1 < < 2 m, 2 < < 4 m and 4 m <, respectively. From Eq. 1, te velocity profile

5 normalized by te dept-averaged velocity u um Te coefficient of float α z 1 = C + C 2 3 u m (= C I ) is given as 2a + 4a z 2 α z is derived from Eqs. 1 and 2 as follows: u = u m mz = C C 2a + 2a z z (2) z 2, (3) Te oter teory of te vertical velocity profile is te logaritmic profile for rougbottom turbulent flow, wic is expressed as u 1 z = ln + Ar, (4) U κ ks were U * is te friction velocity, A r is te constant (= 8.5), z is te eigt from te bottom, and k s is te equivalent rougness eigt. Te normalized velocity profile and te coefficients of float are evaluated from Eq RESULTS AND DISCUSSION 3.1 VERTICAL FLOW STRUCTURE To compare te teoretical and observed results for vertical velocity profiles, Fig. 3 sows te vertical distributions of te normalized velocity u um. As typical examples of te observed data, we coose te vertical velocity distribution at Stn. E2 (Edo River) in Event No.7 and tat at Stn. A3 (Ara River) in Event No.3. In tese cases, te water depts are 6.24 m at Stn. E2 and 9.4 m at Stn. A3. Aki s teory and te logaritmic profile, based on Eqs. 2 and 4, respectively, are also indicated ere. In Aki s teory, Manning s rougness parameter n is given to.325 m -13 s, wile te relative eigt of te peak velocity a is given at.,.1,.2, and.3. In te logaritmic profile, n is set at.15,.25,.35, and.45 m -13 s. Figure 3(a) indicates te fundamental property of Aki s teory, wereby te peak velocity appears on te water surface at a = and te dept of te peak velocity increases wit a. It is also noteworty tat Aki s teory does not satisfy te no-slip condition on te bottom boundary. In oter words, te velocity on te bottom is not zero. Comparison of te observed results and Aki s teory indicates tat te teoretical values at a =. or.1 ave better agreement wit te observed data at Stn. E2. In te case of Stn. A3, close agreement between te observed and teoretical results is not

6 z ' Obs. a=. a=.1 a=.2 a=.3 Edo River z ' Obs. n=.15 n=.25 n=.35 n= z '.5 1. u u m Ara River z ' 1. u u m (a) Aki s teory (n =.325 m -13 s).2 u u m (b) Logaritmic profile u u m 1.5 Fig. 3 Vertical distributions of te normalized velocity at Stn. E2 (Edo River) in Event No.7 and at Stn. A3 (Ara River) in Event No.3. Te solid lines and dots sow te teoretical and observed values, respectively. Te unit of n is described wit SI units. obtained. Since te water depts are larger tan 4 m in tese cases, te general coefficients of float are evaluated wit a =.3. However, te observed results agree better wit te teoretical results at a =. or.1 tan tose at a =.3. On te oter and, te comparison of te observed results and te logaritmic profile reveals tat te observed data agrees better wit te teoretical values wen n =.25 m -13 s at Stn. E2 and n =.35 or.45 m -13 s at Stn. A3. From te above comparison, note tat te observed data generally conforms better to te logaritmic profile tan Aki s teory. To examine te relative dept of te peak velocity a in detail, te contour of te streamwise velocity at Stn. A3 is sown in Fig. 4. In te figure, te result at Event No.3 is cosen. Te velocity in te surface and bottom layers is not depicted because, as mentioned above, te ADCP cannot measure te velocity in te surface and bottom layers. Te solid lines corresponding to te eigts of a =.1 and.3 are also sown ere. Since Stn. A3 is located in a tidal reac, te tide influences te water elevation. As

7 z ' [m].4 Contour interval:.2 ms a a = = a =.1 a = Oct.9 Oct.1 Oct.11 Fig. 4 Contour of te streamwise velocity at Stn.A3 for Event No.3. suc, tere appeared several peaks in water elevation, as sown in Fig. 4. Te streamwise velocity became maximum not at te rising stage, but at te falling stage just after te ig water level. Tis is attributed to te superposition of te ebb-tide current and flood flow. Note tat te relative depts of te peak velocity are located above te upper measurement region, i.e., < a <.1. Terefore, no peak in te velocity appears at a =.3. Tis corresponds to te above discussion for Fig COEFFICIENTS OF FLOAT To compare te observed and teoretical values for te coefficients of float α z, Fig. 5 indicates te correlations between te water dept and te coefficients of float in bot rivers. In line wit Table 1, te coefficients of float of 4 m and 2 m in lengt are evaluated wit > 5.2 m and 2.6 m < < 5.2 m, respectively. In te figure, te movingaveraged values for α z are plotted as points. Furtermore, te general values of α z indicated in Table 1 are sown. In Aki s teory, n is selected at.325 m -13 s in te figure. Te common results for te Edo and Ara Rivers are tat most of te observed coefficients of float are less tan te general values of α z. Te observed values of α z for te draft of 4 m in lengt are for te Edo River and for te Ara River, indicating tat te general value of α z for te draft of 4 m in lengt (=.96) is.4-.1 larger tan te observed data. In bot teories, te coefficients of float α z sow a decreasing trend as water dept increases. Tis trend agrees well wit te moving-averaged values for te observed. In Aki s teory, te teoretical values at a = or.1 are in relatively α z

8 α 1. z Obs. Raw data Averaged data General values Teory a=. a=.1 a=.2 a=.3 Edo River α 1. z Obs. Raw data Averaged data General values Teory n=.15 n=.25 n=.35 n= [m] [m] α 1. z Ara River α 1. z [m] [m] (a) Aki s teory (n =.325 m -13 s) (b) Logaritmic profile Fig. 5 Correlations of te water dept and te coefficients of float α z. better agreement wit te observed data. On te oter and, in te logaritmic profile, te observed α z as better agreement wit te teoretical values wit n =.35 m -13 s for te Edo River and n =.25 or.35 m -13 s for te Ara River. Te observed coefficients of float are also in better agreement wit tose evaluated wit te logaritmic profile tan wit Aki s teory. Furtermore, appreciable differences appear between te observed and teoretical values for α z wen, in Aki s teory, a is set to.3, wic is adopted in order to evaluate te general coefficients of float. Tis fact demonstrates tat te accuracy of te general coefficients of float is appreciably influenced by te evaluation of te relative eigt of te peak velocity a.

9 4 CONCLUSIONS To ceck te accuracy of coefficients of float, wic are widely used in discarge measurements wit float and image processing, we examine te coefficients of float by conducting ADCP measurements for flood flows in te Edo and Ara Rivers in Japan. We compare te observed results for te vertical flow structure wit classical wellknown velocity distributions, suc as te logaritmic profile and Aki s teory, wic is used in te evaluation of te general coefficients of float. Te observed velocity distributions are in better agreement wit te logaritmic profile tan wit Aki s teory. It is noteworty tat te observed coefficients of float sow a decreasing trend as te water dept increases and te averaged coefficients of float are less tan te general values. Tese results for te coefficients of float are also in good agreement wit tose evaluated wit te logaritmic profile. Te above knowledge is useful for te Edo River and Ara River under te flood flows presented ere. However, tere is no positive proof tat tese results can be applied to oter rivers. Terefore, it is necessary to collect field data for te vertical velocity distribution and te coefficients of float under various flood-flow conditions and for various field sites. ACKNOWLEDGEMENTS Tis study was supported in part by a Grant-in Aid for Young Scientists (A) from te Ministry of Education, Culture, Sports, Science and Tecnology (MEXT) (No ). Te ADCP measurement results for te Ara River were given by te Arakawa-Karyu River Office of te Ministry of Land, Infrastructure and Transport, Japan. Te autors would like to express teir deep gratitude to te students in te ydraulics laboratory of Department of Civil Eng., Tokyo University of Science, for teir elp in conducting te field observations in te present study. REFERENCES Aki, K. (1932) On correction of coefficient of te measured velocity of float, specially of float rod, to te mean velocity of flow in a vertical, Proc. of te JSCE, Vol.18, No.1, pp (in Japanese). Mueller, D. S. (22) Use of acoustic Doppler instruments for measuring discarge in streams wit appreciable sediment transport, Hydraulic Measurements and Experimental Metods (CD-ROM). Pettigrew, N. R., Beardsley, R. C. and Iris, J. D. (1986) Field evaluations of bottom- <

10 mounted acoustic Doppler profiler and conventional current meter moorings, IEEE, pp Rantz, S. E. (1982) Measurement and computation of streamflow: Volume 1. Measurement of stage and discarge, USGS Water Supply Paper 2175, U.S. Government Printing Office, Wasington, D.C., pp :9