- Email: [email protected]
Secondary currents: Measurement and analysis
Atmósfera 29(1), 23-34 (2016) doi: 10.20937/ATM.2016.29.01.03
Secondary currents: Measurement and analysis GASTÓN A. PRIEGO-HERNÁNDEZ División Académica de Ciencias Básicas, Universidad Juárez Autónoma de Tabasco, carretera Cunduacán-Jalpa de Méndez, km 1, Col. La Esmeralda, 86690 Cunduacán, Tabasco, México FABIÁN RIVERA-TREJO División Académica de Ingeniería y Arquitectura, Universidad Juárez Autónoma de Tabasco, carretera Cunduacán-Jalpa de Méndez, km 1, Col. La Esmeralda, 86690 Cunduacán, Tabasco, México Corresponding author; email: [email protected] Received: May 8, 2015; accepted: October 28, 2015 RESUMEN que describen la distribución de velocidades. Algunos fenómenos naturales que presentan estas funciones son los huracanes, los cuales son generados por las diferencias de presión; los ciclones, cuya fuente primaria de energía es el gradiente horizontal de temperatura, y los remolinos, que están ligados al gradiente de presión hidrostático. En el caso particular de los remolinos, éstos generan velocidades secundarias, las cuales son fenómeno también se observa en tornados, donde la fuerza centrífuga es mayor en la parte superior y luego va disminuyendo hacia el fondo, mientras que en los ríos se detecta particularmente en curvas y uniones terización es fundamental. El objetivo de este estudio fue estimar las velocidades secundarias en la unión de dos ríos, a partir de mediciones de campo realizadas con medidores acústicos Doppler. Un segundo objetivo lo que su entendimiento ayudará a pronosticar cambios morfológicos en los ríos. ABSTRACT Fluid dynamics has the purpose of understanding the movement of liquids and gases by functions that describe the distribution of velocities. Some natural phenomena that present these functions are hurricanes, generated by pressure differences; cyclones, developed by the horizontal temperature gradient; and eddies, associated with a hydrostatic pressure gradient. In the particular case of eddies, they generate addition, this phenomenon is observed in tornados, where the centrifugal force is greater in the upper layer and decreases towards the bottom, whereas the pressure gradient moves from a high to a low pressure; while in rivers it is detected particularly in bends or joins. Understanding the development of secondary hence their characterization is fundamental. The objective of this study was to obtain the secondary velocities developed as an effect of the union of two water currents, based on data acquired from Doppler
© 2016 Universidad Nacional Autónoma de México, Centro de Ciencias de la Atmósfera. This is an open access article under the CC BY-NC-ND License (http://creativecommons.org/licenses/by-nc-nd/4.0/).
G. A. Priego-Hernández and F. Rivera-Trejo
24
HIIHFWDNLQGRIUHVXOWVWKDWDUHGLI¿FXOWWRREWDLQLQDQ\RWKHUZD\7KHÀRZPHFKDQLVPVDUHUHODWHGZLWK erosion and sedimentation processes; therefore, understanding them might help to evaluate and predict morphological changes in rivers. Keywords: )ORZVWUXFWXUH$'&3YHORFLW\¿HOG
1. Introduction 8QHTXDO IRUFHV JHQHUDWH YHORFLW\ FRPSRQHQWV RQ DGLUHFWLRQWUDQVYHUVHWRWKHÀRZZKLFKSURGXFHV DFLUFXODWLRQQDPHGVHFRQGDU\FXUUHQW7KLVÀRZ coupled with the longitudinal movement, causes a KHOLFDOÀRZWKDWIRUPVRUPRGHOVWKHVHFWLRQLQWR WKHFXUYHV 3HUNLQV )XUWKHUPRUHLWLVVWDWHG WKDWLWLVQRWSRVVLEOHWRUHDFKDQDGHTXDWHGHVFULSWLRQ RI WKH ÀRZ LQ FXUYHV RU VKDOORZ ZDWHU IURP one-dimensional models and even from classical two-dimensional models, such as the Saint-Venant HTXDWLRQVGXHWRWKHHVVHQWLDOO\WKUHHGLPHQVLRQDO QDWXUHRIWKHÀRZ :HEHU *LYHQWKHVHIDFWV a better understanding of hydrodynamics presented LQFXUYHVDQGMXQFWLRQVFKDUDFWHUL]HGPDLQO\E\WKH VHFRQGDU\ÀRZLVQHFHVVDU\7KHYHORFLW\RQWKHVH DUHDVLVQRWXQLIRUPO\GLVWULEXWHG 2GJDDUG UDWKHULWLVORJDULWKPLFGXHWRWKHÀRZUHVLVWDQFH produced by the bottom when turning on the same radius. Hydrometric windlasses are used in traditional measurements of currents in channels (Priego et al., KRZHYHUWKHVHDUHRQO\DEOHWRPHDVXUHWKH PDJQLWXGH RI WKH YHORFLW\ YHFWRU LQ WKH PDLQ ÀRZ GLUHFWLRQ,QUHFHQW\HDUVLQRUGHUWRH[SHULPHQWDOO\ FKDUDFWHUL]HWKHYHORFLW\¿HOGDQGÀRZGLVFKDUJHLQ ULYHUHQYLURQPHQWVDFRXVWLF'RSSOHUFXUUHQWSUR¿OHUV $'&3 KDYHEHHQGHYHORSHG+RZHYHULWVXVH LQ 0H[LFR LV VWLOO LQFLSLHQW PDLQO\ GXH WR ODFN RI knowledge about its use and capabilities. In most of WKHGRFXPHQWHGFDVHVLWVXVHLQ0H[LFRLVOLPLWHG IRUÀRZPHDVXUHPHQWSXUSRVHVZKLFKUHVXOWVLQKLJK FRVWVVLQFHWKHVHGHYLFHVDUHH[SHQVLYHDQGUHTXLUH skilled personnel for its operation. These devices base their functioning on sound, in order to measure the particles suspended in water and obtain velocity FRPSRXQGVRIWKHÀRZLQWKUHHGLUHFWLRQV)URPWKLV NLQGRIGDWDDQGDSSO\LQJWKH5R]RYVNLLGHYHORSPHQW LWLVSRVVLEOHWRHVWLPDWHWKHVHFRQGDU\FXUUHQWVWKURXJKWKHIROORZLQJHTXDWLRQ v2 = gS + 1 ∂τr = 0 r ρ ∂z r
where v is the velocity, ȡ is the water density, r the curvature radius, Sr the cross slope, IJr the transverse shear force, and g the acceleration of gravity. The ¿UVWWHUPLQ(T LVWKHFHQWULIXJDODFFHOHUDWLRQ the second is related to the slope of water on a transverse surface, and the third is the turbulent shear force. 5R]RYVNLL DQG .LNNDZD et al LQGLFDWHGWKDWWKHPDJQLWXGHRIWKHVHFRQGDU\ÀRZ is directly related to the water depth for the curvaWXUH¶VUDGLXVDQGWKHYHUWLFDOSUR¿OHVRIWUDQVYHUVH YHORFLW\ZKLFKYDU\VLJQL¿FDQWO\ZLWKWKHÀRZUHsistance of the bottom. However, secondary currents LQ WKH FRQÀXHQFHV DUH FKDUDFWHUL]HG E\ FRPSOH[ hydrodynamic conditions and which knowledge is essential for the development of a general theory; KRZHYHU DW SUHVHQW IHZ ¿HOG GDWD DUH DYDLODEOH %HVW %ULGJH :HHUDNRRQet al 6RPH FRQFHSWXDO PRGHOV EDVHG RQ H[SHULPHQWDO work (Lane et al., 1998; Roberts, 2004; Song et al., LQGLFDWHGWKDWWKHK\GURG\QDPLFFKDUDFWHULVWLFVRIWKHFRQÀXHQFHVLQFOXGHDQDUHDRIVWDJQDQW ÀRZ XSVWUHDP ZKLFK JHQHUDWHV D VKHDU OD\HU RU VHFWLRQ DEUXSWFKDQJHRQGLUHFWLRQRIYHORFLWLHV EHWZHHQWKHMXQFWLRQRIWKHWZRÀRZV7KHVXUIDFH of this convergence generates a helical cell on each VLGHRIWKHVKHDUOD\HUDQGÀRZVHSDUDWLRQRFFXUV LPPHGLDWHO\GRZQVWUHDPRIWKHFRQÀXHQFH 0RVOH\ %HVW 5R]RYVNLL DQG %DWKXUVW et al XVHG HOHFWURPDJQHWLF ÀRZ PHWHUV LQ GHWHUPLQLQJ the transverse and longitudinal components of the velocity vector. Other authors such as Rhoads and .HQZRUWK\ SURSRVHG WR LGHQWLI\ VHSDUDWHO\ WKHFRQWULEXWLRQVRIWKHXQHYHQÀRZDQGWKHKHOLFDO PRWLRQIRUWKHYHORFLW\¿HOGRIFURVVFXUUHQWV DVD ¿UVWDSSUR[LPDWLRQSULPDU\DQGVHFRQGDU\YHORFLWLHV were calculated, and the components of the cross currents were determined. Primary (vp DQGVHFRQGDU\ vs YHORFLWLHVGH¿QHG by Bathurst et al ZHUH WKH FRPSRQHQWV RI the resulting velocity (vr DWVRPHGHSWKRQWKHÀRZ FROXPQ )LJ ZKLFKZDVRULHQWHGLQDGLUHFWLRQ
Secondary currents: Measurement and analysis
25
parallel and orthogonal to the average depth of the YHORFLW\YHFWRURQWKHYHUWLFDO )LJ 7KHVHYHORFities were calculated as: vp = vr cos (ij±
vs =vr sin (ij±
, ij tan –1 (v x / v y , and where –1 Ø = tan (Vx / Vy VyZDVWKHDYHUDJHGFURVVÀRZ velocity on the depth, Vx the average velocity in the main direction, vx the velocity measured in the downVWUHDPGLUHFWLRQRIWKHÀRZRQHDFKSRLQWRIWKHZDWHU column, and vy was the transverse velocity measured at each point of the water column. The orientation RI WKH YHORFLW\ YHFWRU¶V DYHUDJH RQ GLIIHUHQW YHUWLFDOVWKURXJKWKHFKDQQHOGH¿QHVWKHDV\PPHWULF ÀRZSDWWHUQRYHUWKHFURVVVHFWLRQFRQVLGHULQJWKDW individual vpYDOXHVIRUHDFKYHUWLFDOGH¿QHDQXQHYHQ ÀRZ LQWHQVLW\ DW SDUWLFXODU ORFDWLRQV RI WKH ZDWHU column. The secondary velocity vsGH¿QHVWKHDYHUage circulation on the normal plane of the velocity vector at each vertical; thus, it indicates the intensity RIWKHKHOLFDOPRYHPHQWZLWKLQWKHDV\PPHWULFÀRZ (Ashmore et al z vp vs
r
Fig. 1. Velocity vector components on a water column DGDSWHGIURP:LQWHUZHUSet al.
Y
vs
X
vp
vs
vp
Fig. 2. Secondary velocity perpendicular to the primary velocity going downstream (adapted from Lane et al
7KHVSHFL¿FREMHFWLYHRIWKLVVWXG\ZDVWRFKDUDFWHUL]HWKHEHKDYLRUDQGPHDVXUHPHQWRIWKHVHFRQGDU\ ÀRZ LQ WZR VLWHV ZKHUH WUDQVYHUVH YHORFLWLHV ZHUH fully developed. The second objective was to repreVHQWWKHVHFRQGDU\FLUFXODWLRQLQULYHUFRQÀXHQFHV EDVHGRQWKHUHVXOWVVKRZHGE\5R]RYVNLL DQG Bathurst et al. 2. Methodology 2.1 Location The selected measurement areas were located in the PXQLFLSDOLW\ RI &HQWUR7DEDVFR 0H[LFR )LJ considering: (a WKHFRQÀXHQFHRIWKH*ULMDOYD&DUUL]DOULYHUV ¶¶¶1 ¶ ¶¶: DQG b D FXUYHGRZQVWUHDPRIWKHFRQÀXHQFH ¶¶¶1 ¶¶¶: 2.2 Measurement techniques The measurements were performed using an ADCP RiverCat from Sontek® PRGHO 0 )LJ PRXQWHG RQ D ERDW )LJ 6HYHQ FURVVVHFWLRQV RQWKHFRQÀXHQFHRIWKHULYHUZHUHVHOHFWHGDVZHOO as eight sections on the curve. These measurements were carried out by traveling from the left to the right EDQNKDYLQJDSSUR[LPDWHO\PRIVSDFHEHWZHHQ each transverse, as shown in Fig. 6a, b, respectively. In each cross-section, three measurements were made and an average discharge was obtained. 2.3 Data processing Data were collected with the RiverSurveyor software 6RQWHN DQG 9LHZ$'3 VRIWZDUH 6RQWHN ZDVXVHGWRREWDLQWKUHHGLPHQVLRQDOYHORFLWLHV
G. A. Priego-Hernández and F. Rivera-Trejo
26
UTM 2150000 2080000 2010000 1940000 1870000
N O
E S
United States of America
360000 420000 450000 540000 600000 660000 720000 780000 UTM
1994000
Gulf of Mexico
UTM
México Pacific Ocean
1988000
Caribbean sea
0 212.5425
850
1,275
km 1,700
504000
510000 UTM
516000
Fig. 3. Location of the study area.
Fig. 4. RiverSurveyor M481 system.
Fig. 5. ADCP, RiverCat and GPS on the boat.
Secondary currents: Measurement and analysis
a)
27
b)
)LJ0HDVXUHPHQWVHFWLRQV D FRQÀXHQFH E FXUYH.
GDWD7KH VRIWZDUH SHUPLWV H[SRUWLQJ GDWD WKDW DUH DOUHDG\ SURFHVVHG LQ IRXU ¿OHV WKUHH DUH WKH FRPSRQHQWVRIÀRZYHORFLWLHV vx, vy, vz DQGWKHIRXUWK contains the depths (h )URP WKHVH DQG EDVHG RQ (TV DQG VHFRQGDU\DQGSULPDU\UDWHVYHORFLWLHVDWWKHMXQFWLRQDQGWKHFXUYHZHUHLGHQWL¿HGE\ determining the hydrodynamics for each case. 2.4 Bathymetry and cross-section 8VLQJ WKH ¿HOGV WKDW FRUUHVSRQG WR WKH JHRJUDSKLF position and depth of the stations, level curves were graphed using the softwares AutoCAD2007 and 7HFSORW 7HFSORW 2.5 Digital elevation model (DEM) ArcMap 10.1 software and a vector model (triangle LUUHJXODUQHWZRUN7,1 ZHUHDGDSWHGWRLGHQWLI\WKH surface with varying degrees of detail, depending on WKHFRPSOH[LW\RIWKHUHOLHILQRUGHUWRKDYHDFOHDU idea of the river channel’s shape. 3. Results &RQÀXHQFH The secondary velocities of water in one of the EUDQFKHV RI WKH &DUUL]DO 5LYHU FRQIOXHQFH DUH shown in Figure 7a. In Figure 7b it is notorious that secondary velocities are not fully developed on the ULJKWVLGH GLVWDQFH ZKLOHRQWKHOHIWVLGHWKHVH velocities are clearly developed. This effect is due WRWKHK\GUDXOLFSUHVVXUHIRUFHH[HUWHGRQWKHEDQN Finally, the secondary currents circulation (orange DUURZV LVUHYHDOHGLQPRUHGHWDLOLQ)LJXUHFDV well as the undermining of the river as an effect of these velocities.
Regarding the other branch forming the junction, which corresponds to station 7 on the Grijalva River )LJD VHFRQGDU\YHORFLWLHVDUHGLVSOD\HG)LJXUHE shows that secondary velocities on this section are developed in the right side due to the shear layer DEUXSWFKDQJHRQWKHGLUHFWLRQRIYHORFLWLHV EHWZHHQ WKHMXQFWLRQRIWKHWZRÀRZV)LJXUHFVKRZVWKDWD VHFRQGDU\ÀRZZDVRQO\SUHVHQWRQWKHULJKWVLGHRI the section, and there was an over-elevation of water’s surface due to the radial pressure force , known as the FURVVVORSHLQWKHFXUYHSKHQRPHQRQ )DOFyQ Regarding the measurement of the Grijalva-CarUL]DOFRQÀXHQFHDWVWDWLRQ )LJ D WKHFRPSOHWHO\ GHYHORSHGVHFRQGDU\FXUUHQWVDUHH[SRVHGLQ)LJ EF Figure 9b also shows the fully developed secondary velocity throughout the cross-section of the junction; in addition, the cross slope phenomenon can also be observed. Figure 9c shows the secondary circulation caused by the shear layer. An interesting point to HPSKDVL]HLVWKDWWKHHIIHFWSURGXFHGLVWKHUHVXOWRI WKHVHFRQGDU\ÀRZVRIERWKEUDQFKHV 3.2 Curve The secondary velocity for a transverse section in the GRZQVWUHDP FXUYH RI WKH *ULMDOYD&DUUL]DO FRQÀXHQFH )LJD LVVKRZQLQ)LJXUHEF)LJXUHE shows the secondary velocities caused by the centrifugal force due to the channel curvature. The secondary circulation developed on the left side, where the undermining is found, can be observed in Figure 10c. 3.3 Plan view of velocities )LJXUHGHSLFWVWKHYHORFLW\¿HOGLQWKHPDLQÀRZ GLUHFWLRQLQRUGHUWRLGHQWLI\ÀRZSDWWHUQVZLWKWKH
G. A. Priego-Hernández and F. Rivera-Trejo
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a) Carrizal River
1.99104E+06
E8B 1.99096E+06
Flo
UTM
w
Grijalva River
Flow
1.99088E+06
1.9908E+06
511100
511200
511300 UTM
511400
511500
0
b)
Depth (m)
–2
–4
Q = 70.10 m3/s
–6
–0.15 –0.1 –0.05
0
0.05
20
0.1
40
m/s 60 Distance (m)
80
100
c)
Depth (m)
2
4
Secondary velocity Q = 70.10 m3/s 6 55 –0.15 –0.1 –0.05
60 0
0.05
65 0.1
70 Distance (m)
75
80
85
m/s
)LJ D 0HDVXUHPHQWVHFWLRQ OHIWEUDQFK E VHFRQGDU\YHORFLWLHV F FURVVFLUFXODWLRQ VHFRQGDU\FXUUHQWV
Secondary currents: Measurement and analysis
29
a) Carrizal River
UTM
1.99104E+06
Flo
w
1.99096E+06 Grijalva River 1.99088E+06
Flow E7B
1.9908E+06
511100
511200
511300 UTM
511400
511500
0
b)
Depth (m)
1
2
Q = 45.7 m3/s
Secondary velocity
3 -0.35-0.3-0.25-0.2-0.15-0.1-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 m/s
0
20
40
60
80
Distance (m)
c)
Depth (m)
1
2
Secondary velocity 3
-0.25-0.2-0.15-0.1-0.05 0 0.05 0.1 0.15 0.2 0.250.2 m/s
65
70
75 Distance (m)
80
85
)LJ D 0HDVXUHPHQWVHFWLRQ ULJKWEUDQFK E VHFRQGDU\YHORFLW\ F FURVVFLUFXODWLRQ VHFRQGDU\FXUUHQWV
G. A. Priego-Hernández and F. Rivera-Trejo
30
a) Carrizal River
1.99104E+06
Flo
E1
w
UTM
1.99096E+06 Grijalva River
Flow
1.99088E+06
1.9908E+06
511100
511200
511300 UTM
511400
511500
0
b)
Depth (m)
2
4
6 Q = 114.40 m3/s
8
Secondary velocity
50
100 Distance (m)
-0.12 -0.1 -0.08 -0.06 -0.04 -0.02
0
150
0.02 0.04 0.06 0.08
0.1 -0.12 m/s
c)
Depth (m)
2
4
Q = 114.40 m3/s
6
90
100
110
120 Distance (m)
-0.12 -0.1 -0.08 -0.06 -0.04 -0.02
0
130
0.02 0.04 0.06 0.08
140
150
0.1 -0.12 m/s
)LJ D &RQÀXHQFHPHDVXUHPHQWVHFWLRQ E VHFRQGDU\YHORFLW\ F FURVVFLUFXODWLRQ VHFRQGDU\FXUUHQWV
Secondary currents: Measurement and analysis
31
1.99E+06 1.99E+06
UTM
1.99E+06 E3
1.99E+06
Grijalva River
1.99E+06
Flow
1.99E+06 1.99E+06 515000
515200
515400
515600
UTM 0
2
Depth (m)
4
6
8 Q = 109.8 m3/s Secondary velocity
10
12
0
20
m/s -0.14
40 Distance (m)
-0.12 -0.1 -0.08 -0.06 -0.04 -0.02
0
60
80
0.02 0.04 0.06 0.08
0.1
2
Depth (m)
4
6
8
10
Q = 109.8 m3/s Secondary velocity 15
20
25
30 35 Distance (m)
40
45
50
55
)LJ D 7UDQVYHUVHVHFWLRQRQDFXUYH E VHFRQGDU\YHORFLW\ F FURVVFLUFXODWLRQ VHFRQGDU\FXUUHQWV
G. A. Priego-Hernández and F. Rivera-Trejo
32
Grijalva-Carrizal confluence 1.99105E+06
a)
CAE8B
1.991E+06
CAE1B CAE2B
UTM
1.99095E+06
CAE3B
1.9909E+06
CAE4B
GRE7B
1.99085E+06
1.9908E+06
CA = Carrizal River GR = Grijalva River curve CO = Grijalva-Carrizal confluence Ground velocity 511200
511400 511500 UTM Curves downstream of Grijalva-Carrizal confluence 511300
b) 1.991E+06
GRG = Grijalva River curve Ground velocity
1.991E+06 CRGE4
UTM
1.991E+06 CRGE1
CRGE2 CRGE3
1.991E+06 1.991E+06 1.991E+06
515000
515200
UTM
515400
515600
Fig. 11. Plan view of velocities.
secondary currents in the hydrodynamic operation of WKHFRQÀXHQFH )LJDE +HUH$'&3VFDQJHQHUate these velocity vectors, and by interpolation they allow to generate main current lines, which are linked WRFRPSOH[SURFHVVHV IRUH[DPSOHWKHWUDQVSRUWRI sediment or contaminants. 3.4 Digital elevation model '(0VRIWKH*ULMDOYD&DUUL]DOFRQÀXHQFHDQGDFXUYH downstream, as well as the combination of secondary velocities obtained in different measured transverse sections, are shown in Figure 12a, b. This representation allows carrying out a comprehensive analysis of the hydrodynamic effect of these secondary velocities on the river channel. 4. Conclusions The behavior of secondary currents shows a rotational effect that rarely is measured and drawn. The PHWKRGRORJ\ SURSRVHG E\ 5R]RYVNLL DQG
Bathurst et al. WR HVWLPDWH WKH VHFRQGDU\ currents, works well compared to theoretical predictions. :HGUHZWKHVHFRQGDU\FXUUHQWVDQGWKHLUGHYHOopments over the bed bottom. Although it needs to EHFRQ¿UPHGZHIRXQGWKDWRYHUWKHULJKWVLGHRIWKH FRQÀXHQFHVHFRQGDU\FXUUHQWVDUHWRWDOO\GHYHORSHG while on the left branch they can not be fully developed due the geometry. These kinds of results and procedures are useful for researchers interested in studying secondary currents, and it also provides the basis for making changes and developments in order to improve the knowledge of hydrodynamic processes and their relationship to morphodynamic processes in rivers. Acknowledgments This research was carried out within the project CB-2011-166068 of the CONACyT.
Secondary currents: Measurement and analysis
33
Digital elevations model and secondary velocity Grijalva-Carrizal confluence Elevation (m) CAE8B
GRE7B COE3B
-0.78 - -0.01 -1.46 - -0.78 -1.14 - -1.46 -2.82 - -2.14 -3.5 - -2.82 -4.18 - -3.5 -4.86 - -4.18 -5.54 - -4.86 -6.22 - -5.54 -6.9 - -6.22
COE4B
CA = Carrizal River GR = Grijalva River CO = Confluence
Digital elevations model and secondary velocity Downstream curve Grijalva River CRGE1 CRGE2 CRGE3
CRGE4
GRG = Grijalva River curve Elevation (m) -1.956 - -0.8 -3.111 - -1.956 -4.267 - -3.111 -5.422 - -4.267 -6.578 - -5.422 -7.733 - -6.578 -8.889 - -7.733 -10.044 - -8.889 -11.2 - -10.044
Fig. 12. Secondary velocities on the DEM.
References $VKPRUH 3 ( 5 , )HUJXVRQ . / 3UHVWHJDDUG 3 - $VKZRUWK DQG & 3DROD 6HFRQGDU\ ÀRZ LQ DQDEUDQFKFRQÀXHQFHVRIDEUDLGHGJUDYHOEHGVWUHDP Earth Surf. Proc. Land. 17, 299-311. Bathurst J. C., C. R. Thorne and R. D. Hey, 1977. Direct measurements of secondary currents in river bends. Nature 269, 504-506.
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34
G. A. Priego-Hernández and F. Rivera-Trejo
Bridge J. S., 1993. The interaction between channel geomHWU\ZDWHUÀRZVHGLPHQWWUDQVSRUWDQGGHSRVLWLRQLQ EUDLGHGULYHUV,Q %HVW-/DQG&6%ULVWRZ (GV Braided rivers. Special publication 75. Geological Society of London, pp. 13-71. )DOFyQ0 6HFRQGDU\ÀRZLQFXUYHGRSHQFKDQQHOV Annual Review of Fluid Mechanics. 16, 179-93. .LNNDZD+6,NHGDDQG$.LWDJDZD )ORZDQG bed topography in curved open channels. J. Hydraul. Div. ASCE 102: 1327—42. /DQH6130%LURQ.)%UDGEURRN-%%XWOHU- H. Chandler, M. D. Crowell, S. J. McLelland and A. G. Roy, 1998. Integrated three-dimensional measurement RIULYHUFKDQQHOWRSRJUDSK\DQGÀRZSURFHVVHVXVLQJ acoustic Doppler velocimetry. Earth Surface Processes and Landforms 23, 1247-1267. /DQH61.)%UDGEURRN.65LFKDUGV30%LURQ and A. G. Roy, 2000. Secondary circulation cells in ULYHUFKDQQHOFRQÀXHQFHV PHDVXUHPHQWDUWHIDFWVRU FRKHUHQWÀRZVWUXFWXUHV"+\GURORJLFDO3URFHVVHV14, 2047-2071. 0RVOH\ 0 3 $Q H[SHULPHQWDO VWXG\ RI FKDQQHO FRQÀXHQFHVJournal of Geology 84, 535-562. Odgaard J., 1982. Bed characteristic in alluvial channel bends. Journal of Hydraulic Engineering, 1268-1281. Perkins H. J., 1970. The formation of streamwise vorticity LQWXUEXOHQWÀRZ-)OXLG0HFK44, 721-740. Priego G., A. HernáQGH] 9 *DPERD DQG ) 5LYHUD 'HWHUPLQDFLyQGHOWLHPSRGHPXHVWUHR\SXQtos de aforo en una corriente natural. XXII Congreso Nacional de Hidráulica, Acapulco, Guerrero, noviembre de 2012.
5KRDGV%/DQG67.HQZRUWK\ )ORZVWUXFWXUH DWDQDV\PPHWULFDOVWUHDPFRQÀXHQFHGeomorphology 11, 273-293. Roberts M. V. T., 2004. Flow dynamics at open channel FRQÀXHQWPHDQGHUEHQGV3K'7KHVLV8QLYHUVLW\RI /HHGV/HHGV8QLWHG.LQJGRP 5R]RYVNLL,/ Dvizhenie Vody na Povorote Otkrytogo Rusla.LHY8665SS7UDQVO Flow of water in bends of open channels. Jerusalem Israel 3URJUDPIRU6FLHQWL¿F7UDQVODWLRQV,VUDHOSS 6RQJ&*,:6HRDQG<'.LP$QDO\VLVRIVHFRQGDU\FXUUHQWHIIHFWLQWKHPRGHOLQJRIVKDOORZÀRZ in open channels. Adv. Water Resour., doi:10.1016/j. advwatres.2012.02.003. Sontek, 2007. RiverSurveyor System Manual Software 9HUVLRQ6RQ7HN<6,,QF6DQ'LHJR&$SS Tecplot, 2013. Tecplot 360 User’s Manual Release 1. 7HF3ORW,QF%HOOHYXH:$ SS :HEHU-)(YROXFLyQORQJLWXGLQDOGHODLQWHQVLGDG de las corrientes secundarias en canales con curvas. Mecánica Computacional XXVI, 2230-2249. :LQWHUZHUS - & = % :DQJ 7 .DDLM . 9HUHOVW$ %LMOVPD < 0HHUVVFKDXW DQG 0 6DV )ORZ YHORFLW\SUR¿OHVLQWKH/RZHU6FKHOGWHVWXDU\Ocean Dynam. 56, 284-294. :HHUDNRRQ 6 % < .DZDKDUD DQG 1 7DPDL 7KUHHGLPHQVLRQDOÀRZVWUXFWXUHLQFKDQQHOFRQÀXences of rectangular section. Proceedings of the XXIV Congress, International Association for Hydraulic Research, Madrid, Spain, pp. A373-A380.
Secondary currents: Measurement and analysis GASTÓN A. PRIEGO-HERNÁNDEZ División Académica de Ciencias Básicas, Universidad Juárez Autónoma de Tabasco, carretera Cunduacán-Jalpa de Méndez, km 1, Col. La Esmeralda, 86690 Cunduacán, Tabasco, México FABIÁN RIVERA-TREJO División Académica de Ingeniería y Arquitectura, Universidad Juárez Autónoma de Tabasco, carretera Cunduacán-Jalpa de Méndez, km 1, Col. La Esmeralda, 86690 Cunduacán, Tabasco, México Corresponding author; email: [email protected] Received: May 8, 2015; accepted: October 28, 2015 RESUMEN que describen la distribución de velocidades. Algunos fenómenos naturales que presentan estas funciones son los huracanes, los cuales son generados por las diferencias de presión; los ciclones, cuya fuente primaria de energía es el gradiente horizontal de temperatura, y los remolinos, que están ligados al gradiente de presión hidrostático. En el caso particular de los remolinos, éstos generan velocidades secundarias, las cuales son fenómeno también se observa en tornados, donde la fuerza centrífuga es mayor en la parte superior y luego va disminuyendo hacia el fondo, mientras que en los ríos se detecta particularmente en curvas y uniones terización es fundamental. El objetivo de este estudio fue estimar las velocidades secundarias en la unión de dos ríos, a partir de mediciones de campo realizadas con medidores acústicos Doppler. Un segundo objetivo lo que su entendimiento ayudará a pronosticar cambios morfológicos en los ríos. ABSTRACT Fluid dynamics has the purpose of understanding the movement of liquids and gases by functions that describe the distribution of velocities. Some natural phenomena that present these functions are hurricanes, generated by pressure differences; cyclones, developed by the horizontal temperature gradient; and eddies, associated with a hydrostatic pressure gradient. In the particular case of eddies, they generate addition, this phenomenon is observed in tornados, where the centrifugal force is greater in the upper layer and decreases towards the bottom, whereas the pressure gradient moves from a high to a low pressure; while in rivers it is detected particularly in bends or joins. Understanding the development of secondary hence their characterization is fundamental. The objective of this study was to obtain the secondary velocities developed as an effect of the union of two water currents, based on data acquired from Doppler
© 2016 Universidad Nacional Autónoma de México, Centro de Ciencias de la Atmósfera. This is an open access article under the CC BY-NC-ND License (http://creativecommons.org/licenses/by-nc-nd/4.0/).
G. A. Priego-Hernández and F. Rivera-Trejo
24
HIIHFWDNLQGRIUHVXOWVWKDWDUHGLI¿FXOWWRREWDLQLQDQ\RWKHUZD\7KHÀRZPHFKDQLVPVDUHUHODWHGZLWK erosion and sedimentation processes; therefore, understanding them might help to evaluate and predict morphological changes in rivers. Keywords: )ORZVWUXFWXUH$'&3YHORFLW\¿HOG
1. Introduction 8QHTXDO IRUFHV JHQHUDWH YHORFLW\ FRPSRQHQWV RQ DGLUHFWLRQWUDQVYHUVHWRWKHÀRZZKLFKSURGXFHV DFLUFXODWLRQQDPHGVHFRQGDU\FXUUHQW7KLVÀRZ coupled with the longitudinal movement, causes a KHOLFDOÀRZWKDWIRUPVRUPRGHOVWKHVHFWLRQLQWR WKHFXUYHV 3HUNLQV )XUWKHUPRUHLWLVVWDWHG WKDWLWLVQRWSRVVLEOHWRUHDFKDQDGHTXDWHGHVFULSWLRQ RI WKH ÀRZ LQ FXUYHV RU VKDOORZ ZDWHU IURP one-dimensional models and even from classical two-dimensional models, such as the Saint-Venant HTXDWLRQVGXHWRWKHHVVHQWLDOO\WKUHHGLPHQVLRQDO QDWXUHRIWKHÀRZ :HEHU *LYHQWKHVHIDFWV a better understanding of hydrodynamics presented LQFXUYHVDQGMXQFWLRQVFKDUDFWHUL]HGPDLQO\E\WKH VHFRQGDU\ÀRZLVQHFHVVDU\7KHYHORFLW\RQWKHVH DUHDVLVQRWXQLIRUPO\GLVWULEXWHG 2GJDDUG UDWKHULWLVORJDULWKPLFGXHWRWKHÀRZUHVLVWDQFH produced by the bottom when turning on the same radius. Hydrometric windlasses are used in traditional measurements of currents in channels (Priego et al., KRZHYHUWKHVHDUHRQO\DEOHWRPHDVXUHWKH PDJQLWXGH RI WKH YHORFLW\ YHFWRU LQ WKH PDLQ ÀRZ GLUHFWLRQ,QUHFHQW\HDUVLQRUGHUWRH[SHULPHQWDOO\ FKDUDFWHUL]HWKHYHORFLW\¿HOGDQGÀRZGLVFKDUJHLQ ULYHUHQYLURQPHQWVDFRXVWLF'RSSOHUFXUUHQWSUR¿OHUV $'&3 KDYHEHHQGHYHORSHG+RZHYHULWVXVH LQ 0H[LFR LV VWLOO LQFLSLHQW PDLQO\ GXH WR ODFN RI knowledge about its use and capabilities. In most of WKHGRFXPHQWHGFDVHVLWVXVHLQ0H[LFRLVOLPLWHG IRUÀRZPHDVXUHPHQWSXUSRVHVZKLFKUHVXOWVLQKLJK FRVWVVLQFHWKHVHGHYLFHVDUHH[SHQVLYHDQGUHTXLUH skilled personnel for its operation. These devices base their functioning on sound, in order to measure the particles suspended in water and obtain velocity FRPSRXQGVRIWKHÀRZLQWKUHHGLUHFWLRQV)URPWKLV NLQGRIGDWDDQGDSSO\LQJWKH5R]RYVNLLGHYHORSPHQW LWLVSRVVLEOHWRHVWLPDWHWKHVHFRQGDU\FXUUHQWVWKURXJKWKHIROORZLQJHTXDWLRQ v2 = gS + 1 ∂τr = 0 r ρ ∂z r
where v is the velocity, ȡ is the water density, r the curvature radius, Sr the cross slope, IJr the transverse shear force, and g the acceleration of gravity. The ¿UVWWHUPLQ(T LVWKHFHQWULIXJDODFFHOHUDWLRQ the second is related to the slope of water on a transverse surface, and the third is the turbulent shear force. 5R]RYVNLL DQG .LNNDZD et al LQGLFDWHGWKDWWKHPDJQLWXGHRIWKHVHFRQGDU\ÀRZ is directly related to the water depth for the curvaWXUH¶VUDGLXVDQGWKHYHUWLFDOSUR¿OHVRIWUDQVYHUVH YHORFLW\ZKLFKYDU\VLJQL¿FDQWO\ZLWKWKHÀRZUHsistance of the bottom. However, secondary currents LQ WKH FRQÀXHQFHV DUH FKDUDFWHUL]HG E\ FRPSOH[ hydrodynamic conditions and which knowledge is essential for the development of a general theory; KRZHYHU DW SUHVHQW IHZ ¿HOG GDWD DUH DYDLODEOH %HVW %ULGJH :HHUDNRRQet al 6RPH FRQFHSWXDO PRGHOV EDVHG RQ H[SHULPHQWDO work (Lane et al., 1998; Roberts, 2004; Song et al., LQGLFDWHGWKDWWKHK\GURG\QDPLFFKDUDFWHULVWLFVRIWKHFRQÀXHQFHVLQFOXGHDQDUHDRIVWDJQDQW ÀRZ XSVWUHDP ZKLFK JHQHUDWHV D VKHDU OD\HU RU VHFWLRQ DEUXSWFKDQJHRQGLUHFWLRQRIYHORFLWLHV EHWZHHQWKHMXQFWLRQRIWKHWZRÀRZV7KHVXUIDFH of this convergence generates a helical cell on each VLGHRIWKHVKHDUOD\HUDQGÀRZVHSDUDWLRQRFFXUV LPPHGLDWHO\GRZQVWUHDPRIWKHFRQÀXHQFH 0RVOH\ %HVW 5R]RYVNLL DQG %DWKXUVW et al XVHG HOHFWURPDJQHWLF ÀRZ PHWHUV LQ GHWHUPLQLQJ the transverse and longitudinal components of the velocity vector. Other authors such as Rhoads and .HQZRUWK\ SURSRVHG WR LGHQWLI\ VHSDUDWHO\ WKHFRQWULEXWLRQVRIWKHXQHYHQÀRZDQGWKHKHOLFDO PRWLRQIRUWKHYHORFLW\¿HOGRIFURVVFXUUHQWV DVD ¿UVWDSSUR[LPDWLRQSULPDU\DQGVHFRQGDU\YHORFLWLHV were calculated, and the components of the cross currents were determined. Primary (vp DQGVHFRQGDU\ vs YHORFLWLHVGH¿QHG by Bathurst et al ZHUH WKH FRPSRQHQWV RI the resulting velocity (vr DWVRPHGHSWKRQWKHÀRZ FROXPQ )LJ ZKLFKZDVRULHQWHGLQDGLUHFWLRQ
Secondary currents: Measurement and analysis
25
parallel and orthogonal to the average depth of the YHORFLW\YHFWRURQWKHYHUWLFDO )LJ 7KHVHYHORFities were calculated as: vp = vr cos (ij±
vs =vr sin (ij±
, ij tan –1 (v x / v y , and where –1 Ø = tan (Vx / Vy VyZDVWKHDYHUDJHGFURVVÀRZ velocity on the depth, Vx the average velocity in the main direction, vx the velocity measured in the downVWUHDPGLUHFWLRQRIWKHÀRZRQHDFKSRLQWRIWKHZDWHU column, and vy was the transverse velocity measured at each point of the water column. The orientation RI WKH YHORFLW\ YHFWRU¶V DYHUDJH RQ GLIIHUHQW YHUWLFDOVWKURXJKWKHFKDQQHOGH¿QHVWKHDV\PPHWULF ÀRZSDWWHUQRYHUWKHFURVVVHFWLRQFRQVLGHULQJWKDW individual vpYDOXHVIRUHDFKYHUWLFDOGH¿QHDQXQHYHQ ÀRZ LQWHQVLW\ DW SDUWLFXODU ORFDWLRQV RI WKH ZDWHU column. The secondary velocity vsGH¿QHVWKHDYHUage circulation on the normal plane of the velocity vector at each vertical; thus, it indicates the intensity RIWKHKHOLFDOPRYHPHQWZLWKLQWKHDV\PPHWULFÀRZ (Ashmore et al z vp vs
r
Fig. 1. Velocity vector components on a water column DGDSWHGIURP:LQWHUZHUSet al.
Y
vs
X
vp
vs
vp
Fig. 2. Secondary velocity perpendicular to the primary velocity going downstream (adapted from Lane et al
7KHVSHFL¿FREMHFWLYHRIWKLVVWXG\ZDVWRFKDUDFWHUL]HWKHEHKDYLRUDQGPHDVXUHPHQWRIWKHVHFRQGDU\ ÀRZ LQ WZR VLWHV ZKHUH WUDQVYHUVH YHORFLWLHV ZHUH fully developed. The second objective was to repreVHQWWKHVHFRQGDU\FLUFXODWLRQLQULYHUFRQÀXHQFHV EDVHGRQWKHUHVXOWVVKRZHGE\5R]RYVNLL DQG Bathurst et al. 2. Methodology 2.1 Location The selected measurement areas were located in the PXQLFLSDOLW\ RI &HQWUR7DEDVFR 0H[LFR )LJ considering: (a WKHFRQÀXHQFHRIWKH*ULMDOYD&DUUL]DOULYHUV ¶¶¶1 ¶ ¶¶: DQG b D FXUYHGRZQVWUHDPRIWKHFRQÀXHQFH ¶¶¶1 ¶¶¶: 2.2 Measurement techniques The measurements were performed using an ADCP RiverCat from Sontek® PRGHO 0 )LJ PRXQWHG RQ D ERDW )LJ 6HYHQ FURVVVHFWLRQV RQWKHFRQÀXHQFHRIWKHULYHUZHUHVHOHFWHGDVZHOO as eight sections on the curve. These measurements were carried out by traveling from the left to the right EDQNKDYLQJDSSUR[LPDWHO\PRIVSDFHEHWZHHQ each transverse, as shown in Fig. 6a, b, respectively. In each cross-section, three measurements were made and an average discharge was obtained. 2.3 Data processing Data were collected with the RiverSurveyor software 6RQWHN DQG 9LHZ$'3 VRIWZDUH 6RQWHN ZDVXVHGWRREWDLQWKUHHGLPHQVLRQDOYHORFLWLHV
G. A. Priego-Hernández and F. Rivera-Trejo
26
UTM 2150000 2080000 2010000 1940000 1870000
N O
E S
United States of America
360000 420000 450000 540000 600000 660000 720000 780000 UTM
1994000
Gulf of Mexico
UTM
México Pacific Ocean
1988000
Caribbean sea
0 212.5425
850
1,275
km 1,700
504000
510000 UTM
516000
Fig. 3. Location of the study area.
Fig. 4. RiverSurveyor M481 system.
Fig. 5. ADCP, RiverCat and GPS on the boat.
Secondary currents: Measurement and analysis
a)
27
b)
)LJ0HDVXUHPHQWVHFWLRQV D FRQÀXHQFH E FXUYH.
GDWD7KH VRIWZDUH SHUPLWV H[SRUWLQJ GDWD WKDW DUH DOUHDG\ SURFHVVHG LQ IRXU ¿OHV WKUHH DUH WKH FRPSRQHQWVRIÀRZYHORFLWLHV vx, vy, vz DQGWKHIRXUWK contains the depths (h )URP WKHVH DQG EDVHG RQ (TV DQG VHFRQGDU\DQGSULPDU\UDWHVYHORFLWLHVDWWKHMXQFWLRQDQGWKHFXUYHZHUHLGHQWL¿HGE\ determining the hydrodynamics for each case. 2.4 Bathymetry and cross-section 8VLQJ WKH ¿HOGV WKDW FRUUHVSRQG WR WKH JHRJUDSKLF position and depth of the stations, level curves were graphed using the softwares AutoCAD2007 and 7HFSORW 7HFSORW 2.5 Digital elevation model (DEM) ArcMap 10.1 software and a vector model (triangle LUUHJXODUQHWZRUN7,1 ZHUHDGDSWHGWRLGHQWLI\WKH surface with varying degrees of detail, depending on WKHFRPSOH[LW\RIWKHUHOLHILQRUGHUWRKDYHDFOHDU idea of the river channel’s shape. 3. Results &RQÀXHQFH The secondary velocities of water in one of the EUDQFKHV RI WKH &DUUL]DO 5LYHU FRQIOXHQFH DUH shown in Figure 7a. In Figure 7b it is notorious that secondary velocities are not fully developed on the ULJKWVLGH GLVWDQFH ZKLOHRQWKHOHIWVLGHWKHVH velocities are clearly developed. This effect is due WRWKHK\GUDXOLFSUHVVXUHIRUFHH[HUWHGRQWKHEDQN Finally, the secondary currents circulation (orange DUURZV LVUHYHDOHGLQPRUHGHWDLOLQ)LJXUHFDV well as the undermining of the river as an effect of these velocities.
Regarding the other branch forming the junction, which corresponds to station 7 on the Grijalva River )LJD VHFRQGDU\YHORFLWLHVDUHGLVSOD\HG)LJXUHE shows that secondary velocities on this section are developed in the right side due to the shear layer DEUXSWFKDQJHRQWKHGLUHFWLRQRIYHORFLWLHV EHWZHHQ WKHMXQFWLRQRIWKHWZRÀRZV)LJXUHFVKRZVWKDWD VHFRQGDU\ÀRZZDVRQO\SUHVHQWRQWKHULJKWVLGHRI the section, and there was an over-elevation of water’s surface due to the radial pressure force , known as the FURVVVORSHLQWKHFXUYHSKHQRPHQRQ )DOFyQ Regarding the measurement of the Grijalva-CarUL]DOFRQÀXHQFHDWVWDWLRQ )LJ D WKHFRPSOHWHO\ GHYHORSHGVHFRQGDU\FXUUHQWVDUHH[SRVHGLQ)LJ EF Figure 9b also shows the fully developed secondary velocity throughout the cross-section of the junction; in addition, the cross slope phenomenon can also be observed. Figure 9c shows the secondary circulation caused by the shear layer. An interesting point to HPSKDVL]HLVWKDWWKHHIIHFWSURGXFHGLVWKHUHVXOWRI WKHVHFRQGDU\ÀRZVRIERWKEUDQFKHV 3.2 Curve The secondary velocity for a transverse section in the GRZQVWUHDP FXUYH RI WKH *ULMDOYD&DUUL]DO FRQÀXHQFH )LJD LVVKRZQLQ)LJXUHEF)LJXUHE shows the secondary velocities caused by the centrifugal force due to the channel curvature. The secondary circulation developed on the left side, where the undermining is found, can be observed in Figure 10c. 3.3 Plan view of velocities )LJXUHGHSLFWVWKHYHORFLW\¿HOGLQWKHPDLQÀRZ GLUHFWLRQLQRUGHUWRLGHQWLI\ÀRZSDWWHUQVZLWKWKH
G. A. Priego-Hernández and F. Rivera-Trejo
28
a) Carrizal River
1.99104E+06
E8B 1.99096E+06
Flo
UTM
w
Grijalva River
Flow
1.99088E+06
1.9908E+06
511100
511200
511300 UTM
511400
511500
0
b)
Depth (m)
–2
–4
Q = 70.10 m3/s
–6
–0.15 –0.1 –0.05
0
0.05
20
0.1
40
m/s 60 Distance (m)
80
100
c)
Depth (m)
2
4
Secondary velocity Q = 70.10 m3/s 6 55 –0.15 –0.1 –0.05
60 0
0.05
65 0.1
70 Distance (m)
75
80
85
m/s
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Secondary currents: Measurement and analysis
29
a) Carrizal River
UTM
1.99104E+06
Flo
w
1.99096E+06 Grijalva River 1.99088E+06
Flow E7B
1.9908E+06
511100
511200
511300 UTM
511400
511500
0
b)
Depth (m)
1
2
Q = 45.7 m3/s
Secondary velocity
3 -0.35-0.3-0.25-0.2-0.15-0.1-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 m/s
0
20
40
60
80
Distance (m)
c)
Depth (m)
1
2
Secondary velocity 3
-0.25-0.2-0.15-0.1-0.05 0 0.05 0.1 0.15 0.2 0.250.2 m/s
65
70
75 Distance (m)
80
85
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G. A. Priego-Hernández and F. Rivera-Trejo
30
a) Carrizal River
1.99104E+06
Flo
E1
w
UTM
1.99096E+06 Grijalva River
Flow
1.99088E+06
1.9908E+06
511100
511200
511300 UTM
511400
511500
0
b)
Depth (m)
2
4
6 Q = 114.40 m3/s
8
Secondary velocity
50
100 Distance (m)
-0.12 -0.1 -0.08 -0.06 -0.04 -0.02
0
150
0.02 0.04 0.06 0.08
0.1 -0.12 m/s
c)
Depth (m)
2
4
Q = 114.40 m3/s
6
90
100
110
120 Distance (m)
-0.12 -0.1 -0.08 -0.06 -0.04 -0.02
0
130
0.02 0.04 0.06 0.08
140
150
0.1 -0.12 m/s
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Secondary currents: Measurement and analysis
31
1.99E+06 1.99E+06
UTM
1.99E+06 E3
1.99E+06
Grijalva River
1.99E+06
Flow
1.99E+06 1.99E+06 515000
515200
515400
515600
UTM 0
2
Depth (m)
4
6
8 Q = 109.8 m3/s Secondary velocity
10
12
0
20
m/s -0.14
40 Distance (m)
-0.12 -0.1 -0.08 -0.06 -0.04 -0.02
0
60
80
0.02 0.04 0.06 0.08
0.1
2
Depth (m)
4
6
8
10
Q = 109.8 m3/s Secondary velocity 15
20
25
30 35 Distance (m)
40
45
50
55
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G. A. Priego-Hernández and F. Rivera-Trejo
32
Grijalva-Carrizal confluence 1.99105E+06
a)
CAE8B
1.991E+06
CAE1B CAE2B
UTM
1.99095E+06
CAE3B
1.9909E+06
CAE4B
GRE7B
1.99085E+06
1.9908E+06
CA = Carrizal River GR = Grijalva River curve CO = Grijalva-Carrizal confluence Ground velocity 511200
511400 511500 UTM Curves downstream of Grijalva-Carrizal confluence 511300
b) 1.991E+06
GRG = Grijalva River curve Ground velocity
1.991E+06 CRGE4
UTM
1.991E+06 CRGE1
CRGE2 CRGE3
1.991E+06 1.991E+06 1.991E+06
515000
515200
UTM
515400
515600
Fig. 11. Plan view of velocities.
secondary currents in the hydrodynamic operation of WKHFRQÀXHQFH )LJDE +HUH$'&3VFDQJHQHUate these velocity vectors, and by interpolation they allow to generate main current lines, which are linked WRFRPSOH[SURFHVVHV IRUH[DPSOHWKHWUDQVSRUWRI sediment or contaminants. 3.4 Digital elevation model '(0VRIWKH*ULMDOYD&DUUL]DOFRQÀXHQFHDQGDFXUYH downstream, as well as the combination of secondary velocities obtained in different measured transverse sections, are shown in Figure 12a, b. This representation allows carrying out a comprehensive analysis of the hydrodynamic effect of these secondary velocities on the river channel. 4. Conclusions The behavior of secondary currents shows a rotational effect that rarely is measured and drawn. The PHWKRGRORJ\ SURSRVHG E\ 5R]RYVNLL DQG
Bathurst et al. WR HVWLPDWH WKH VHFRQGDU\ currents, works well compared to theoretical predictions. :HGUHZWKHVHFRQGDU\FXUUHQWVDQGWKHLUGHYHOopments over the bed bottom. Although it needs to EHFRQ¿UPHGZHIRXQGWKDWRYHUWKHULJKWVLGHRIWKH FRQÀXHQFHVHFRQGDU\FXUUHQWVDUHWRWDOO\GHYHORSHG while on the left branch they can not be fully developed due the geometry. These kinds of results and procedures are useful for researchers interested in studying secondary currents, and it also provides the basis for making changes and developments in order to improve the knowledge of hydrodynamic processes and their relationship to morphodynamic processes in rivers. Acknowledgments This research was carried out within the project CB-2011-166068 of the CONACyT.
Secondary currents: Measurement and analysis
33
Digital elevations model and secondary velocity Grijalva-Carrizal confluence Elevation (m) CAE8B
GRE7B COE3B
-0.78 - -0.01 -1.46 - -0.78 -1.14 - -1.46 -2.82 - -2.14 -3.5 - -2.82 -4.18 - -3.5 -4.86 - -4.18 -5.54 - -4.86 -6.22 - -5.54 -6.9 - -6.22
COE4B
CA = Carrizal River GR = Grijalva River CO = Confluence
Digital elevations model and secondary velocity Downstream curve Grijalva River CRGE1 CRGE2 CRGE3
CRGE4
GRG = Grijalva River curve Elevation (m) -1.956 - -0.8 -3.111 - -1.956 -4.267 - -3.111 -5.422 - -4.267 -6.578 - -5.422 -7.733 - -6.578 -8.889 - -7.733 -10.044 - -8.889 -11.2 - -10.044
Fig. 12. Secondary velocities on the DEM.
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