ML20235X454

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Rept on Propagation of Tsunami to Shoreline at San Onofre, Ca
ML20235X454
Person / Time
Site: 05000000, San Onofre
Issue date: 06/08/1973
From: Loomis H
COMMERCE, DEPT. OF, NATIONAL OCEANIC & ATMOSPHERIC
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ML20235X376 List: ... further results
References
FOIA-87-462 NUDOCS 8710200006
Download: ML20235X454 (10)
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' p le C T M P ! W h " 0 0 4 $ yl7 $ ~ ; ~ 8 . i f i P 4 i REPORT ON~ THE PROPAGATION OF A TSUNAMI-TO THE SHORELINE AT SAN ONOFRE, CALIFORNIA a by Harold G. Loom!.s r ' l . i National Oceanic and Atmospheric Administration j Joint Tsunami Research Effort , l Honolulu,. Hawaii l ' { June 8, 1973 'l ^ r~ l 8710200006 871014 'j PDR FOIA -yg SCH AR A87 -462 PDR l., .v.r n;y;p- :,, .., y

4 4 1 (1) I. INTRODUCTION 1 This is a preliminar;* report describing the time-stepping of a tsunami into the shoI9 in the vicinity of San Onofre, California. The main purpose if th,is work is to show the variation in amplitudes along the shoreline as affected by' { the off-shore bathymetry and the plan-view geomet:7 'or the 1 region. In the preliminary report we kill outline the pro-l cedures and give the main results. A later report will i describe more detailed water motions. t i This work is primarily an application of a previously prepared computer program described in detail in a previous 1 report ( Loomis, 1972). Two new features have t.en added j to the previour computing package.because they were felt necessary for the problem at hand'. The first feature is a more sophisticated way than that used before of intro-ducing a wave at an angle to the boundaries where the vary-ing wave speeds (because of bathymetry) are taken into account. The second change is the introduction of a buffer zone wh'ich more or less ' absorbs energy incident on it. In the case at hand we let the frictional coefficient increase linearly in the lower 10 rows of the grid. The general set up of the problem is shown in Fig. 1. 4 5 m M i O 9' ,y 43 - =

n-a n, -. 7.. ;7, ,x s.e,. k- ) l k. F (2) i ) l /- 1 ) I [ 2 fol G vie. Pts. f k 4X s hy =.Cw' (sogg D a.w h W t-j e l f e s ~\\ i '? '5%. b o 9+. 1 l 1 Ave

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v .i .I } o o / / / / / / /' / M .< b ; x., / l /J 1% >1 U j 10 wi (32..A b ) J -i l 4 I Section of Ocean off California Coast.. Figure 1. . 1 One i Input wave forms of various types were used.- 2. ' Para-general form reported on here is shown in Fig. meters used were .. l ..ct/ r 1 4 (,.2.,rt /h-) b h Lt') = e. ,q,9 U N E%- a c a 8

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7. l ( 3) f t =-5,10 and 20 minutes and ansies of incidence-f period Also, a number of cases were run usins only. $ = 0, 22$?. the first positive hump of the above wave form. J HYDRODYNAMIC EQUATIONS. 2, shallow-water The equations used are the long-wave, j / equations with a quadratic friction term and a nonlinear advection term. The equations are 4 t " ~8"x ~ I"! " ~ ""2 y (1) u ~ ("# t " ~8"y - #Y IY 7 y v l and the equat, ion of continuity is (2) wt = -{hu)7 - (hv)y ) The symbols are defined by: w = water level measured from undisturbed state u,v = x and y velocities h = h(x,y) = depth of undisturbed water s = gravitational constant 0025) f = non-dimensional frictional constant ( ( )g, () ( )t = partial derivatives with respect' y and t to x The details of the differencing and-the grid assign-ments are given in (Loomis 1972), The conditions for-j ,s 3 ? '._? {' ;}. ory .g-a.,, n -, - u,r._ _, _,:, 9,7e vy;, r, p s' '[_ _~r., _s.,,_

c-(4) I this particular problem are described below. 20 miles by 30 miles A rectangular body of water ( 32.2 km by 48. 3 km), bounded on the east by the coast is divided into a square mesh.5 miles (804.7 m) on a side. Hz(1,j) and Hy(1,j) are The offset bathymetry matrices taken to be a common H(i.j). .The depths for H(1,j) are taken from the chart N.O.S. S'101 on a grid spa'eing of These values we're then 1 mile which was a distance of 5/16". A more de-interpolated to the grid spacing of.5 miler tailed calculation would require a better source of bathy-metry than I have at present. A dimensionless frictional coefficient of f =.002 e 1968) was used throughout the region for all t (see Reid, I h=0,o the cases where the incident angle of the wave was In the other care where or parallel to the left boundary. ) = 22iO was used, the friction in the lower 10 rews of 002 grid points was allowed to increase linearly from No noticeable amount of energy was reflected back to 05 into the region from the lower boundary. At a depth The following problem should be mentioned. of 5 meters, the long wave velocity is 7 meters /sec. Thus a wave with period 5 min would have a wavelength of 2100 805 m, we are only going'to = meters. With AI = 6.y This problem was have 2 or 3 gridpoints per wavelength. For waves with periods of met in two different ways: 1 E r s .t m ~ ur-

zy. m. c- ,.77 ) 1 (5). 5 min, we terminated the ocean with a wall at h = 10 meters depth so that the calculation would tell you what kind of a wave you had in 10 meters of water. For waves of period 20 minutes, we replaced all depths of 4 meters or less with 4 meters. The plan, ~ view geomatry remains the same =but' the l \\ shallowest depths are eliminated. This makes very little difference when you remember that x =.805 m a'd a very i n small part of the region is affected. For 10 minute wave l both of the above artifices were used with similar results l in each case. { q Although the equations used are non-linear, the non-linear' approximately terms are not predominant so that' amplitudes can be/ multi- ] I plied by constants. That is, if a 1 meter tsunami offshore causes a 2h me'ter wave at the shore, then a 2 meter tsunami will cause a 5 meter wave at the shore. Obviously, formation of bores and wave breaking would limit that.

1. CONCLUSIONS.

In all of the. cases that were tried, the result was about the same, namely, the normal amplification of long-waves coming into shallower water obtains. That is. a,- wave -is amplified by about 2h in traveling from deep water .j to shallow water. The variation along the coast was between 1 -l emme

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o _.c 4---.-, (6) l 2.4 and 3.5 with the larger number occurring:at points or i The amplification at Arroyo San Onofre was 2 5 for capes. the cases studied. The actual variation in amplifications { i along the 30 miles of coast is shown in Figs. 3 and 4 q i 9 I l J t r. e t 'C O I t e e 9 + .I i ' l .~ ' l

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s i L 2 ...j s-r e t V a W r. j E 11ax. Amplitude-l Sx v JL t >x I h, 1 k ' I h sy Dana Point v i %y xx k 3 i 1 k i xs F. San Mateo Pt. k i 4 1 t San Onofre 3 e y d i 4 l s, . 4 r y >x 8 4 4 g A F-3 g/ co" t t J Figure 3. Distribution of maximum amplitudes along coast for incident p o. wave at 0,r20' min l!p6fiedTind.89m _ amplitude.. [. 'l e ,'d e c'. y,+ y *=s 8-

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o F.,g,,. s 9 yy o._,, y go. ,,_. ~* \\ 4 6 j ,yy- .r.-- - \\; 4 7 + ' i -t ,s, e_ i :. r

'..,n .17 ~ J - -- ,, s ,, r,.4.... i ,.5 rc4i-:. ~e r i.,p ,3 5 i s. - 1 t-i ' l l (8) 'l l -] l i ' l ,t '1 i 2. J i j s / A v i ( Max.. Amplitude . j x s 4 x it. M at. K h A 4 g .1 ,x n l l e -4 i i Dana Point x x 1 1 l l L x - 1 A> 1x 4x 4 l San Mateo Pt. 4 San Onofre A wx A w K^ nA h .A l w p a s x Buffer Zone s V. s i S s 1. I t h Figure 4. Distribution of maximum amplitudes along coast for incident. wave at 22.50, 20 min. period and.89 amplitude. e + t 'vp- 't'* g. .,%'3-M 4 ',f' -?f,.- '"d* t g,6#g"*' f++* 7 s'^5 'd -M+-~ f p-

n. a s j s i (9) l REFERENCES r l i 1. Reid, R. O. and Bodine, B. R., " Numerical Model for Storm Surges s in Galveston Bay," Journal 6f the Waterway.c and Harbors j j Division, Proc. ASCE, February 1968. I 2. Leendertse, J. J., " Aspects of a Computational Model for Long-Period Water-Wave Propagation," Mem. RM-5294-PR, The Rand Corporation, May 1967. } 3. Sielecki, A., " Studies of the Hydrodynamic Equations of Storm . j Surges," Dept. of Meteorology Report, Hebrew University, i Jerusalem, Israel, 1966., l 4. Street, R. L., Chan, R. K. C., and Fromm, J. E., "Two Methods for the Compt cation of the Motion of Long Water Waves -- A l Review of Applications," Tech. Report 136, Dept. Civil Engineering, Stanford University, August 1970. 5. Loomis, H. G., "A Package Program for Time-Stepping Long Waves into Coastal Regions with Application to Haleiwa Harbor, Oahu," HIG Report 72-21, Hawaii Institute 'of Geophysics, October 1972. j 1 d 4 i k .a a 9 ) i r ~ F J, {

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