Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

Sasaki, Mikio

Tanaka, Hitoshi

Umeda, Makoto

English

Hydraulic Engineering Repository

Conference Paper, Published VersionSasaki, Mikio; Tanaka, Hitoshi; Umeda, MakotoTheory of Salt-Water Movement in Iwaki River MouthZur Verfügung gestellt in Kooperation mit/Provided in Cooperation with:Kuratorium für Forschung im Küsteningenieurwesen (KFKI)Verfügbar unter/Available at: https://hdl.handle.net/20.500.11970/109646Vorgeschlagene Zitierweise/Suggested citation:Sasaki, Mikio; Tanaka, Hitoshi; Umeda, Makoto (2012): Theory of Salt-Water Movement inIwaki River Mouth. In: Hagen, S.; Chopra, M.; Madani, K.; Medeiros, S.; Wang, D. (Hg.):ICHE 2012. Proceedings of the 10th International Conference on Hydroscience &Engineering, November 4-8, 2012, Orlando, USA.Standardnutzungsbedingungen/Terms of Use:Die Dokumente in HENRY stehen unter der Creative Commons Lizenz CC BY 4.0, sofern keine abweichendenNutzungsbedingungen getroffen wurden. Damit ist sowohl die kommerzielle Nutzung als auch das Teilen, dieWeiterbearbeitung und Speicherung erlaubt. Das Verwenden und das Bearbeiten stehen unter der Bedingung derNamensnennung. Im Einzelfall kann eine restriktivere Lizenz gelten; dann gelten abweichend von den obigenNutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Documents in HENRY are made available under the Creative Commons License CC BY 4.0, if no other license isapplicable. Under CC BY 4.0 commercial use and sharing, remixing, transforming, and building upon the materialof the work is permitted. In some cases a different, more restrictive license may apply; if applicable the terms ofthe restrictive license will be binding.The 10th Int.  Conf. on Hydroscience and Engineering (ICHE-2012), Nov. 4 – Nov. 7, Orlando, USA 300      THEORY OF SALT-WATER MOVEMENT IN IWAKI RIVER MOUTH   Mikio Sasaki1, Hitoshi Tanaka2, and Makoto Umeda3   In Iwaki river mouth, Japan, there are jetties on the both shores. The construction of the jetties started in 1926, and finished through 21 years in 1946. After the construction of the jetties, the river mouth of Iwaki River is never blockaded (Sasaki M. and Takeuchi T. (2003)). Salt water enters the mouth of the river for the existence of the breakwater while regularly getting on the flow and the backflow of the seaward. Now, the jetties make the estuary water environment and keep the environment steady in the mouth of Iwaki River. Therefore, it is important to make clear the saltwater movement that is relating on the estuary water environment.  In the present study, the turbulent diffusion equation of three dimensions is taken to show the movement of seawater. After taking some assumptions on the phenomenon, the diffusion field in the present theoretical model is divided into several water layers in a perpendicular direction. Finally, the diffusion equation for salinity in any horizontal water layer during backflow of the seaward is given by a new variableξ .   0)1(2)( 212222 =++−+ξββξβdcduflldcdullkkzkokokkkxkok  (1) Where   okookkokkklllxldtu /// 121 ++= ∫ ββξ  (2)  In equations (1) and (2), c is salinity, x is the distance from the sea to the river, t is time, ol is the typical distance of the diffusion field, u is the velocity, 1β  and 2β  are an arbitrary constants, xkl  is mixing length that relates to diffusion factor, zkf  is a coefficient for the mixture between water layers, and k means the k-th water layer. As well as the backflow, the diffusion equation in any horizontal water layer is also obtained during the seaward flow with a new variable.    0)1(2)( 212222 =−+−+ξββξβdcduflldcdullkkzkokokkkxkok  (3) After taking some assumptions for the velocity u, the solutions that satisfy the boundary conditions are given as follows. During the backflow of the seaward   ( ) 0)}exp(1{ 1113 <+−−−= kkkkkkk uCCCc ξα  (4)                                                  1 Professor, Department of Civil and Architecture, Hachinohe Institute of technology, 88-1 Ohbiraki, Myo, Hachinohe, 031-8501, JAPAN (msasaki@hi-tech.ac.jp) 2 Professor, Department of Civil Engineering, University of Tohoku, 6-6-06 Aoba, Sendai, 980-8579, JAPAN (tanaka@tsunami2.civil.tohoku.ac.jp) 3 Associate Professor, Department of Civil Engineering, University of Tohoku, 6-6-06 Aoba, Sendai, 980-8579, JAPAN (umeda@kasen1.civil.tohoku.ac.jp) The 10th Int.  Conf. on Hydroscience and Engineering (ICHE-2012), Nov. 4 – Nov. 7, Orlando, USA 301  During the flow of the seaward   ( ) 0)}(exp{ 121 >+−−−= kkokkkkpkk uCCCc ξξα  (5)  In equations (4) and (5), kC1  is the minimum value of the salinity and kC3  is the maximum value of the salinity at any point kx , okξ is the value when t=0, k1α  and k2α  are constants, and pkC means the last value during the backflow.  If the flow velocity uk is given, the salinity density will be given only by three coefficients, α１k, α2k and lo1k  The value α１k relates to the mixing between the saltwater and freshwater when the sea water goes up in the estuary and the valueα2k relates the mixing between the saltwater and freshwater when the salt water goes down. The value lo1k is the coefficient that is the relation to the position of the front of the seawater. And the value lo1k is also the coefficient that relates to the arrival time of salt water. Therefore, the value lo1k is small at a point near the mouth of a river. On the other hand, the value lo1k grows at a point far from the mouth of a river. The continuous observation by a self-recording measuring instrument was carried out at 1 meter from the bottom in Station 1 where the water depth is 4 meters near the mouth of River Iwaki for four months from July to October in 2007. The present theory is compared with the field observations, and the comparison between the theory and the field observations shows a good agreement as shown in Figure 1. Figure 1 Salinity calculated by the present theory and comparison between theory and observations of salinity at 1 meter in depth near the sea in the mouth of Iwaki River in July, 2007. The solid line shows the theory and the x-line shows the observations. The observations were made at a point of 1 meter from the bottom where the water depth is about 4 meters.  The theoretical solutions of the differential equations for saltwater movement in the estuary are obtained in the present study. The present theory is compared with field observations carried out in the mouth of River Iwaki. The comparison between the theory and the field observations shows a good agreement. The solutions given by the present study can generate well the movement of seawater going up and down in the mouth of Iwaki River  REFERENCES  Sasaki M. and Takeuchi T. (2003) “ History of River Blockage and Stability Condition in Iwaki River Mouth”, Proc. 15th IAHR Congress, Thessaloniki, GREECE,CD-ROM, A3,24-29. 0102030401 2 3 4 5daySalinit

Theory of Salt-Water Movement in Iwaki River Mouth

http://henry.baw.de/bitstream/20.500.11970/109646/1/142_ICHE_2012.pdf

Theory of Salt-Water Movement in Iwaki River Mouth

Abstract

Similar works

Full text

Available Versions

Hydraulic Engineering Repository