Coastal Engineering 2006, ASCE MODELING TSUNAMI AND RESONANCE RESPONSE OF ALBERNI INLET, BRITISH COLUMBIA

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1 Coastal Engineering 006, ASCE MODELING TSNAMI AND RESONANCE RESPONSE OF ALBERNI INLET, BRITISH COLMBIA Dilip K. Barua, Norman F. Allyn and Michael C. Quick A computational model is developed using MIKE-FM to simulate tsunami and resonance response of Alberni Inlet in British Columbia. Inducing a -times amplification of the incident wave, the 964 Alaska tsunami caused huge damages to Port Alberni and the City of Alberni located at the head of the 65 km long inlet. Simulation of the 964 tsunami shows that the -times amplification has occurred at a sub-resonant period. A search for amplification factors indicates that the maimum amplification at the head of the inlet occurs at an ecitation period of about 40 minutes. The incident wave amplifies by about 5-times at this resonant period of fundamental mode of oscillation. Model simulation indicates that tsunami induced depth-averaged current could reach as high as.5 m/s in an otherwise calm harbor current environment. INTRODCTION Moored vessels in harbor installations are vulnerable to damages caused by long-period oscillation, in particular, when the harbor resonates or nearresonates to the ecitation period. In addition to flooding and inundation, resonant amplification of the incident wave causes high mooring loads on vessels and berthing facilities. Tsunami is a very important mechanism for ecitation of large harbors. The 964 Alaska tsunami triggered by a 9. magnitude earthquake, and its effects on port installations 65 km inside of a long inlet, is a fine eample of resonant behavior of a large water body. Figure presents a schematic of seismic disturbance on a water body and resulting oscillation. Triggered either by plate rupture or slope failures, tsunami is generated as a series of waves propagating directionally away from its source. It is a long wave phenomenon with periods ranging from several minutes to several hours (see for eample, CERC, 984). Tsunami period at a location depends on the distance and travel time of the wave (Stoneley, 96). Therefore, a distant tsunami has a longer period than a local tsunami. But tsunami height measured at a coastal location is a function of long-wave transformation processes (see for eample, Perroud, 959; Ippen and Harlemann, 966) and resonance response and amplification. A justifiable treatment of the problem can best be done with the help of numerical modeling, which could take account of most of the processes Associate and Westmar Consultants Inc., East 45 th Avenue, Vancouver, BC Canada, V5R E6, dkbarua@shaw.ca. Westmar Consultants Inc., W st Street, North Vancouver, BC, Canada, V7M B. Department of Civil Engineering, niversity of British Columbia, BC Canada. 590 Proceedings 0th International Conference on Coastal Engineering, September - 8, 006, San Diego, California.

2 Coastal Engineering 006, ASCE 59 and factors, albeit at the cost of numerical schematization. This paper presents numerical modeling of tsunami-scale waves and resonant behavior of Alberni Inlet in British Columbia. Seismic Disturbance on a Water Body and Effects Shaking Causes Seismic Seiches Local Low Period - Order of Minutes Low Amplitudes - Order of Centimeters Triggers Failures of Land Boundaries Vertical Rupture of Overstressed Tectonic Plates Submarine and Sub-aerial Slope Failures Tsunami Local: Low Period - Order of Minutes Distant: High Period - Order of Minutes to Hours Tsunami Height at a Location - a Function of: Transformation Processes (Shoaling, Funneling, Frictional Damping, etc.) Resonance Response and Amplification Figure. A schematic of seismic disturbance on a water body and effects. Alberni Inlet is a 65 km long narrow fjord located in Vancouver Island on the British Columbia pacific coast (Figure ). The seaward end of the inlet is also known as Trevor Channel. City of Alberni and Port Alberni are located at the head of the inlet. With the depths varying from 0 to 50 m, Alberni inlet is narrow compared to its length, with widths varying from 600 m to km. Somass River, located at the head of the inlet delivers an annual average freshwater discharge of 0 m /s (Tully, 949) into the inlet. Alberni Inlet is an interesting tidal system. Figure shows an eample of tide along the channel, for stations at Bamfield and Port Alberni (see Figure for locations). As in other channels in the region, tide is mied semi-diurnal (Thomson, 98). Bamfield and Port Alberni have nearly the same tidal phase, and there is neither amplification nor rise in mean water level from Bamfield to Port Alberni. This is counter-intuitive, because tide at the head of an inlet usually has a phase lag, and is amplified in relation to the tide at the mouth of the inlet.

3 59 Coastal Engineering 006, ASCE Figure. Alberni Inlet in British Columbia. Figure. An eample of tide in Alberni Inlet. Earthquake and tsunami episodes are rather a phenomenon of significant importance along the pacific coast. The 964 Alaska tsunami caused an estimated $0 million damage to the City of Alberni and Port Alberni. Resonance is attributed as the principal cause for amplification and the damaging effects of the 964 Alaska tsunami. Little is known about the real characteristics of the tsunami - gathered information indicated that that the tsunami reached the mouth of Alberni Inlet in about 4 hours after its generation, the estimated periods were between 9 and 96 min, tsunami height at the inlet mouth was about. m, the maimum height at Port Alberni was about.6 m, and that the maimum height occurred at the nd peak. Some earlier works

4 Coastal Engineering 006, ASCE 59 (Murty and Boilard, 970; Dunbar et al, 989; Henry and Murty, 995) indicated that during the 964 Alaska tsunami, the resonance phenomenon caused three-fold amplification of the incident tsunami at the head the inlet. This modeling work shows that the natural period of Alberni Inlet in its fundamental mode is more than what has been reported earlier, and that the 964 Alaska tsunami amplification has occurred on a sub-resonant period. This leads to the fact that amplifications higher than the 964 Alaska tsunami would occur for tsunamis with periods, equal to and closer to the resonant period. By simulating the 964 tsunami, this work searches for resonance period of the inlet and presents simulation for the resonant period. MIKE FLEXIBLE MESH MODEL The governing equations for most two-dimensional shallow water models are nearly the same - the equations implemented in the Mike Fleible Mesh (FM) are described below. The mass and momentum conservation equations (Danish Hydraulic Institute, 004a, 004b) in Cartesian and y horizontal coordinates are: h h hv = hs, t y h h hv = t y η gh ρ τ s τ b ht fvh gh ρ ρ ρ hv hv hv t y o = o o ht y η gh ρ τ sy τ by hty ht fh gh y ρo y ρo ρo y where S = point source discharge = Q/, Q = discharge, = volume of the element, h = total water depth = d η, d = still water depth below datum, η = surface elevation above datum,, y = Cartesian coordinates, t = time, = depth-averaged current in the -direction, V = depth-averaged current in the y-direction, f = Ω sin φ = Coriolis parameter, Ω = angular rate of earth s rotation, y hu S, yy s hv S, s () () ()

5 Coastal Engineering 006, ASCE 594 Φ = latitude of the location, ρ = density of water, a function of temperature and salinity defined by NESCO (98), ρ o = reference density, u s, v s = velocities of point source discharge, τ s,,y = surface shear stress, a function of wind forcing, τ b,,y = bottom shear stress, specified as Manning s or Chezy s number, = V y he y he ρ τ E is eddy viscosity coefficient formulated using Smagorinsky concept as, = y V V y s C E s Tij = lateral stresses representing viscous and turbulent momentum transfer and differential advection A T = = V y A T y y V A T yy = A = eddy viscosity coefficient, specified either as a constant or as Smagorinsky (96) factor. The sub-grid scale eddy viscosity coefficient is given in Smagorinsky formulation as: ij ij s S S l C A = C s = Smagorinsky factor, varies between 0.5 to.0 l = characteristic length S ij = mean velocity gradient or deformation rate, [i, j =, ] = i j j i ij S Mike-FM uses an unstructured fleible mesh to solve the governing hydrodynamic equations. The solution scheme rigorously employs mass and momentum flu conservations on each cell-centered element by finite volume method, and time-marching simulations are achieved eplicitly. The unstructured fleible mesh system is very suitable for spatial discretization of comple geometries and long narrow channels such as Alberni Inlet.

6 Coastal Engineering 006, ASCE 595 MODEL DOMAIN AND BONDARY CONDITIONS The entire Alberni Inlet with the eceptions of some minor channels and inlets, forms the model domain. Canadian Hydrographic Chart #668 (scale : 40,000) is used to schematize the model bathymetry. Figure 4 shows the computational mesh of the model domain. Figure 4. Model domain and schematized bathymetry of Alberni Inlet. The offshore open boundary is an arc that is set in the continental shelf of 0 to 90 m depth. The model consists of a total of 68 elements with 5 computational nodes. To simulate the 964 Alaska tsunami, the.-m high tsunami of 96-min is superposed on a tide-less mean water level as well as on a.5-m high semi-diurnal tide. Since, tsunami represents a series of waves, a 5- cycle wave is applied, and as will be shown later, not all of these waves have the same amplification factors at the head of the inlet. A sensitivity analysis is eecuted to eamine the effects of bed resistance, eddy viscosity and Somass River discharge on results. A. m high monochromatic wave is imposed at the open ocean boundary for this analysis. For the resonant period search, a -m high monochromatic wave is imposed at the open boundary. This wave is applied on a tide-less mean water level at the open ocean boundary. Since the focus is on resonance search, such an approach

7 596 Coastal Engineering 006, ASCE is common (see for eample, Walters and Goff, 00). Finally, the 40-min simulations are made to show the amplifications at the resonant period. RESLTS AND DISCSSION Simulating The 964 Alaska Tsunami Figure 5 shows simulated water levels at the head of the inlet for a 5-cycle. m high, 96-min incident wave (typical of the 964 Alaska tsunami) on the tide-less inlet at a mean water level of.08 m. As observed during the 964 Alaska tsunami, nd peak shows the highest amplification. The. m high incident wave amplified to a.58 m high wave at the head of the inlet, giving an amplification factor of.98. Figure 5. Simulated water levels at the head of the inlet at tide-less mean water level for 96-min period. Figure 6 shows the incident and amplified water levels for the same tsunami riding on a.5 m high semi-diurnal tide (typical of the mean tidal range). As epected, the magnitude of tsunami run-up depends on the tidal phase. For this case, the maimum water level at the inlet head is 5.57 m above Chart Datum (CD) giving a tsunami height of.96 m, and an amplification factor of.0. Figure 7 shows, for the same simulation as in Figure 6, typical standing wave type phase relationship between the water level and the principal current component at the head of the inlet. The maimum current velocity of about.4

8 Coastal Engineering 006, ASCE 597 m/s is overwhelmingly high in an otherwise calm current environment of the harbor Incident water level at the mouth of the inlet Amplified water level at the head of the inlet :48 06:00 07: 08:4 09:6 0:48 :00 : 4:4 5:6 6:48 8:00 9: Date and time Figure 6. Simulated incident and amplified water levels on a.5 high semi-diurnal tide for 96-min period. Run#45: etraction point TM coordinates 6600 m; m 6 Water level Depth-averaged north-south velocity :48 06:00 07: 08:4 09:6 0:48 :00 : 4:4 5:6 6:48 8:00-9: Date and time Figure 7. Simulated water level and current on a.5 high semi-diurnal tide for 96-min period.

9 598 Coastal Engineering 006, ASCE Maimum amplification factor (-) Sensitivity Analysis In absence of any observed data, it is important to eamine the uncertainty of results by varying empirical coefficients such as Manning's number and eddy viscosity coefficients. Simulations indicate that by decreasing the Manning's number from 0.0 to 0.0, the amplification factor has increased from.94 to.9 showing an increase by %. Similar numerical eperiments with Smagorinsky factor shows that by decreasing the factor from 0.8 to 0., the amplification factor has increased by 0.7%. An increase of the factor from 0.8 to 0.5 has decreased the amplification factor by.7%. In this work a numerical eperiment is also made to see the sensitivity of Somass River discharge on amplification factors. Somass River drains an annual average flow of some 0 m /s of fresh water into the head of Alberni Inlet. This volume is very insignificant compared to the volume of inlet. Simulations indicate that Somass River discharge has increased the amplification factor by only.4%. Based on the above numerical eperiments, it can be concluded that the results of this model should be treated with an uncertainty of ±0%. Resonance and Amplification Factors Several numerical eperiments are carried out in order to search for modes of oscillations and resonance period of the inlet. For these simulations, a 5-cycle -m high monochromatic wave is applied at the open boundary of the tide-less inlet for different ecitation periods varying from 40 to 40 minutes. Manning's number and Smagorinsky factor are kept constant at values of 0.0 and 0.8, respectively. Somass River discharge is ecluded from this analysis. Figure 8 shows the maimum amplification factors at the head of the inlet as a function of different ecitation periods. Two distinct aspects of the results can be noticed, especially the eistence of two separate peaks, and the amplifications both at sub- and super-resonant periods Ecitation Period (min)

10 Coastal Engineering 006, ASCE 599 Figure 8. Amplification factors for different ecitation periods. The first is the resonance period of the inlet in its fundamental mode of oscillation. The resonant period of the inlet lies between 40 and 50 minutes, and for any hydrodynamic disturbance such as a distant tsunami, the amplification factor would be about 5. For such a case, much more damage and inundation can be epected. The second is the change in the mode of oscillation from st to the fundamental mode. In the st mode of oscillation the node is within the inlet, and the first small peak for this mode occurs at a period of 70 minutes. As can be seen in Figure 8, the maimum amplification factor at this mode is about. With increase in the ecitation period, there is a small drop in amplification factor as the mode of oscillation shifts from st to the fundamental, then has started increasing again peaking at about 40 minutes. As can be understood, at this period of oscillation, the node is far beyond into the ocean. This type of resonant behavior has been studied in the past for idealized simple rectangular basins. Theoretical analysis and eperiments by Ippen and Goda (96), Lee (970) and Raichlen and Lee (99) also showed amplification factors peaking to the resonant period with separate peaks for different modes of oscillations. This analysis shows that the 964 Alaska tsunami amplification has occurred on a sub-resonant period of oscillation. Discussion by Sorensen et al (00) shows that amplification to a less etent occurs for different sub- and super-resonant periods close to the natural period of the basin. Frictional damping also lowers the natural period of the basin (Sorensen et al, 00). To show the effects, simulation results are compared with a simplified estimate for an idealized rectangular flat bottom frictionless basin. The wave propagated 69 km length of the channel from the open boundary to the head in about 48 minutes, indicating a wave celerity of 4 m/s. This simplified analysis shows that the natural period of the inlet using Merian formula in its fundamental mode is about 9 min. Simulating the Resonance Oscillation Net step in the simulations is to show the resonance amplification for the natural period of 40 min. Figure 9 shows the incident and amplified water levels. For the. m incident wave on a semi-diurnal tide, the maimum wave height at the head of the inlet is 5.9 m, giving an amplification factor of 4.94 m. Figure 0 shows the water levels and principal current component for the 40-min period. The standing wave-type phase relationship is similar to Figure 7. The current magnitude is only slightly higher than the 96-min tsunami. Similar current magnitude indicates that the rise and fall rates of water levels are probably comparable for both the cases of 96-min and 40-min waves.

11 600 Coastal Engineering 006, ASCE 7 Incident water level at the mouth of the inlet Amplified water level at the head of the inlet :48 06:00 07: 08:4 09:6 0:48 :00 : 4:4 5:6 6:48 8:00 9: Date and time Figure 9. Simulated incident and amplified water levels on a.5 high semi-diurnal tide for 40-min period. Run#46: etraction point TM coordinates 6600 m; m Water level Depth-averaged north-south velocity 0-04:48 06:00 07: 08:4 09:6 0:48 :00 : 4:4 5:6 6:48 8:00 9: Date and time Figure 0. Simulated water level and current on a.5 high semi-diurnal tide for 40- min period.

12 Coastal Engineering 006, ASCE 60 CONCLSIONS A two-dimensional numerical model is developed using the new generation Mike fleible mesh software to study tsunami and resonance dynamics of Alberni Inlet in British Columbia. The model has simulated the reported -times amplification of the 964 Alaska tsunami, and its occurrence at the second peak. Simulations for amplification factor search indicate that the resonance period of Alberni Inlet in its fundamental mode of oscillation lies between 40 and 50 minutes, and that the 96-min Alaska tsunami amplification has occurred on a sub-resonant period. The wave height at the head of the inlet could amplify by a factor of 5 at the resonant period. The model showed that tsunami induced depth-averaged current could reach as high as.5 m/s in an otherwise calm current environment of the harbor. In addition to tsunami amplitude and related forces, this has great engineering significance as far as design current is concerned. REFERENCES Coastal Engineering Research Center, 984. Shore protection manual (Vol. I). Department of the Army, Waterways Eperiment Station, Corps of Engineers, Vicksburg, Mississippi. Danish Hydraulic Institute, 004a. MIKE Flow Model FM - Hydrodynamic Module Reference Manual. Horsholm, Denmark. Danish Hydraulic Institute 004b. MIKE/ Flow Model FM - Hydrodynamic and Transport Module Scientific Documentation. Horsholm, Denmark. Dunbar, D.S., LeBlond, P.H. and Murty, T.S., 989. Maimum tsunami amplitudes and associated currents on the coast of British Columbia. Science of Tsunami Hazards, 7(), Henry, R.F. and Murty, T.S., 995. Tsunami amplification due to resonance in Alberni Inlet: normal modes. In: Tsuchiya and N. Shuto (eds.), Tsunami: Progress in Prediction, Disaster Prevention and Warning, Kluwer Academic Publishers, the Netherlands, 7-8. Ippen, A.T. and Goda, Y., 96. Wave-Induced Oscillations in Harbors: The Solution of a Rectangular Harbor Connected to the Open Sea. Report No. 59, Hydrodynamics Lab., MIT, Cambridge MA. Ippen, A.T. and Harlemann, D.R.F.,966. Tidal dynamics in estuaries. In: A.T. Ippen (ed.), Estuary and Coastline Hydrodynamics. McGraw-Hill Book Company Inc., New York. Lee, J.J. (969). Wave-Induced Oscillations in Harbors of Arbitrary Shape. Report KH-R-0, W.M. Keck Lab. of Hyd. and Water Res., Calif. Inst. of Tech. Murty, T.S. and Boilard, L., 970. The tsunami of Albeni Inlet Caused by the Alaska Earthquake of March 964. In: W.M. Adams (Ed.), Tsunamis of the Pacific Ocean. East-West Center Press, Honolulu.

13 60 Coastal Engineering 006, ASCE Perroud, P., 959. The propagation of tidal waves into channels of gradually varying cross-section. Technical memorandum No., Beach Erosion Board, Washington, D.C. Raichlen, F. and Lee, J.J., 99. Oscillation of Bays, Harbors and lakes. In: Herbich, J.B. (Ed.), Handbook of Coastal and Ocean Engineering, Vol., Harbors, Navigation Channels, Estuaries and Environmental Effects. Gulf Publishing Company, Houston, pp, 07-. Sorensen, R., Thompson, E.F., Briggs, M., Chasten, M.A. and Lillycrop, L., 00. "Harbor hydrodynamics". In: Coastal Engineering Manual, SACE Smagorinsky, J., 96. General circulation eperiment with the primitive equations. Monthly Weather Review, 9(), Stoneley, R., 96. The propagation of tsunamis. Geophysical Jr. Roy. Atstron. Soc., 8(), Thomson, R.E., 98. Oceanography of the British Columbia Coast. Canadian Special Publication of Fisheries and Aquatic Sciences 56, 9p. Tully, J.P., 949. Oceanography and prediction of pulp mill pollution in Alberni Inlet. Fisheries Research Board of Canada. Bulletin No pages. NESCO, 98. The practical salinity scale 978 and the international equation of state of seawater 980. NESCO Technical Papers in Marine Science, 6. Walters, R.A. and Goff, J., 00. Assessing tsunami hazard along the New Zealand Coast. Science of Tsunami Hazards, (), 7-5.