HYDRAULIC STUDY on TSUNAMI Phenomenon Must Be
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Coastal Engineeringin Japan, Vol. 6,1963 HYDRAULIC STUDY ON TSUNAMI Yoshiro Fukui* Makoto Nakamura** Hidehiko Shiraishi** Yasuo Sasaki** I.INTRODUCTION Up to present, the visitation of tsunami has inflicted great damageupon our àountry repeatedly.Especially, the fact that the Pacific Ocean coast suffered from the serious disaster due to the Chilean Earthquake tsunami. is fresh inour memory. Tsunami is generated in the open sea as the long wave with very small steepness and draws toward the shoreline.The coast where the great energy of tsunami is transported without reduction has, generally speaking, fairly deep water depth from offshore to the vicinity of the shore line.The Sanriku Coast, north- eastern coast of Japan, that has been frequently attacked by tsunami has a typi- cal feature as mentioned above.Namely, the submarine ditch with 5,000-8,000 metres of water depth lies along the shore line and prevents the decrement of the energy of tsunami. As far as the two-dimensional deformation of tsunami is concerned, the seiche phenomenon must be considered first.In the case of a tsunami the period of which is nearly equal to the specific period of the bay, the energy of tsunami is conserved in the form of seiche motion.Therefore it is accumulated in making the tsunami height inside the bay larger and larger.Secondly, the reflection and contraction of thunami must be taken into consideration.Owing to these pheno- mena mentioned above, the tsunami concentrates its energy in the most interior part of the bay. And the above phenomena become more conspicuous with the increase of the reflection of tsunami from the bay cliff. On the other hand, inside the bay where the near shore water depth is shal- low, the tsunami is breaking and the reflected and concentrated energy is dis- sipated there.Accordingly the tsunami induces a great force of destruction in this zone. Differing from the gravity wave, the breaker of tsunami is more akin to bore because ofts very long wave length and large scale.Moreover, in the case that the water depth becomes shallow abruptly, the above tendency is accelerated. On the other hand, the tsunami that approaches to the entrance of bay in the shape of non-breaker transports its energy to the inside of the bay in the shape of flow.In this paper, the tsunami is classified into two types;i.e.the one is the "progressive breaker type" and the other is the "seiche type." There are many difficulties in .establishing the planning of counter-tsunami measures; that is, how to estimate 1) the tsunami run-up height on shore-land and on dike, 2) the quantity of overflow discharge across a dike crown and 3) the tsu- *Japan Engineering Consultants Co., Ltd. **Agricultural Engineering Research Station, Ministry of Agriculture and Forestry. 68 nami pressure actingon a dike. As to the progressive breaker type oftsunami that is consideredto have the strongest destructivepower against shore land, the authors have analysed itsin. fluence upon dikesexperimentally and theoretically. conventional formulas nd the The authors obtainedthe necessary data to design dikesagainst tsunami. 11. LABORATORY APPARATUS AND TESTPROCEDURE Most of the actual dikesagainst tsunami is zone at very shallow constructed on shore or in inshore water depth.Accordingly, the tsunami those dikes isone of the progressive breaker which strikes against type and may be treatedas a typical bore.The tsunami of thistype has great destructive, tioned.The authors power as Previously men- conducted the experimentalstudy on the tsunami behavior in the shape of bccre.in this experiment size and the other two different water tanks,one is large small, were used inorder to test the scale effect. 1. Laboratory, Apparatusfor Small Scale Tests Thewater tank as shownin Fig. 1 and Photo. 1 one sidewas glassed. was made of steel and its The movable single slopewas set as a dike model and three pressure Plane view gauges were attach. ed on the slope.The bore genera tor of flap gate typewas installed D.M.EtCtnC oscillograph at the other end of thewater tank. / In order to obtain Strain meter many kinds of the length and shapeof bore, the 21.Qm quantity of water stored insi1ethe (c) Sido view (b)Bore generator (a)' flap gate was variedby selecting five positions of theflap gate. The Wave essrire gauges flap gate was fixedvertically by a ,wire rope stretched 'Fig. 1 obliquely to Experimental apparatusfor a small ,ward the storage tank, scale test. and also connectedto two Counterweights through two wires the opposite side ofwater tank in order stretched toward after it is operied. to keep the gate horizontallyin the air V After the waterwas C 1, the flap gate' stored as shown in theside-view of Fig. was opened in a mo- p ment by thecounterweights as soon as the wire fixing thegate was taken off. 2.LaboratoryApparatsgfor Large Scale Tests The water tankshown in ,Fig. 2 and Photos. 2, 3and 4 was used for large scaletests.The system of bore generator,was almost thesame as that for smallscale tests and six pressure gaugeswere attached at intervals of twenty Photo. 1Experimental water tank fora centimeters along small scale test. 69 )lar.eai Oikm made) H _en-mailflg omellOgeap Etectnc oscdtognma' Stesin mate, Stran male,- Sde nev (a). Bose genta1o. )b) ( I. 3Q.er- 1Wave p,enswe gangeS I 30.5.' 25.5.- 75.5', FIg. 2 Experimental apparatus for a large Photo. 2Experimental water tank for a scale test. large scale test. Photo. 3Bore generator for a large scale Photo. 4 Large scale model of dike. test. the slope of dike model. 3.Measuring Apparatus The water stage gauges were arranged as shownin Figs. 1 and 2.' The water stage .gauges installed in frontof the flap gate and the slope recordthe change of bore shape and the velocity ofbore travelling through these measuring points, and that installed inside the flap gaterecords the decrease of water depth in - r :: attached on Photo. 5 Recorder of wave gauges (large - Photo. 6 Pressure gauges scale test). the slope (large scale model). 70 the storage tank. The lengthof bore was determined from its twosuc- ceeding troughs.The principle of the water stage gauges isas follows; the change of water levelwas replac- ed with that of electric resistanceof two parallel wires, and thissystem was included in a bridge circuit. A portion of recording system is shown in Photo. 5..Strain gauges wereus- ed as pressure gauges, and Photo.6 shows the reverse side of theslope attatched with pressuregauges. The Photo.7Part of pressure gauges ona recordingsystemof the pressure large scale. gauges for large scale tests is shown inPhoto.7. 4.Experimental Results A sample record of theelectric oscillnr is shown in Fig. 3. aph in the case of small scaletests The curves of (a), (b) and(c) were recorded by thewater stage gauges.The curve (a) of the water ® I2O(g/cm) stage gauge installed inside the flap -1 ,.ReIle, bore 9I(g/crs) gauge gate shows that the water depth t Bore presowe SCa1>*. began to decrease just after &02( the gate r a essu gaug opened and kept low waterlevel sI Pressure gauge until the arrival of the reflexbore. ( Pressure gauge The curve'(b) of thewater stage Cl gauge installed in front of the gate p shows the shape of the initialbore. f Ware gauge The curve (c) of the 'j15 water stage gauge installed, in front of the. slope shows first the shape of theincident Fig. 3 Sample recordsby electricoscillo- graph (small scale test). bore and next theduplication of the incident and reflexbore with an ts bo in fir in Photo. SIncident cr breaking borein a Photo. 9 small scale tank. Reflection of bore afterrun- w ning up the slope ina small ar sccale test tank. m 71 Photo. 10Reflex bore. Photo. 11Run-up on the slope in a large scale test tank. the lapse of time.Photographies 8, 9 and 10 show the situation mentioned above. Figure 4 is a sample record of water stage gauges by a pen-writing oscillograph in the caseoflarge scale tests and has the same charac- C Sec - I Sec - teristics as in the case of small scale tests.Photographies 11 shows the Fig. 4 Sample records of wave gauges by run-up phenomena of bore on the pen-writing oscillograph(large slope in a large tank.The curves of scale test). (d), (e) and (f) in Fig. 3 and the six - a curves in Fig. 5 were recorded by pressure gauges.Itisconsidered a from these data that bore pressure a operated impulsively on the slope at the moment when the bore struck ,1 the slope, and kept almost constant value continuously.The height of bore run-up was measured with the 0 1 2 3 4 5 naked eye. Fig. 5Sample records of wave pressure byelectricoscillograph(large scale test). III. VELOCITY OF THE BORE TYPE TSUNAMI In order to explain the hydraulic and dynamic characteristics of the tsunami which Is classifiedas the.. bore type, the velocity of bore and induced flow must binvestigated first of all.The symbols as shown. in Fig. 6 are adopted and the two cross-sections, II and between which the head of bore is included, are determined. The following for- mulas are introduced from the continuity condition of flow. UHüh=CC cUHüh in which C and U are shown in thefollowing formulas. C=Hh (2) H Uand ü in. the above formulas present therespective mean values of U and u. Euler's law of iiiomentum is adoptedin regard to the portion of fluidbetween the two cross-section, I-I and 11-11.The following formula taking inthe direction of flow is led.