Workshop on Tsunami Hydrodynamics in a Large River NEOWAVE. Non-hydrostatic Evolution of Ocean WAVE

Transcription

1 Workshop on Tsunami Hydrodynamics in a Large River NEOWAVE Non-hydrostatic Evolution of Ocean WAVE Yoshiki Yamazaki and Kwok Fai Cheung Department of Ocean and Resources Engineering University of Hawaii at Manoa, Honolulu, HI, U.S.A. August 14 ~ 15, 2011 Oregon State University, Corvallis, Oregon

2 OUTLINE 1. NEOWAVE Theoretical Formulation Numerical Scheme 2. RESULTS AND DISCUSSIONS Tide Wave Dispersion 3. CONCLUSIONS AND FUTURE STUDIES

3 NEOWAVE Governing Equations Depth-integrated, Non-hydrostatic Equation Consideration of Weakly Wave Dispersion through Non-hydrostatic Pressure. (Stelling and Zijlema, 2003; Yamazaki et al., 2009 & 2011) Numerical Schemes Semi-implicit, Finite Difference (FD) Model Explicit Hydrostatic solution Implicit Non-hydrostatic solution Momentum Conserved Advection (MCA) Scheme Shock Capturing Scheme for FD Models (Stelling and Duinmeijer, 2003; Yamazaki et al., 2009 & 2011) Two-Way, Grid-Nesting Scheme Implementation of the inter-grid boundary condition to describe non-hydrostatic and discontinuous flows.

4 NEOWAVE Governing Equations Variables Definition for Free Surface Flow z x, y ζ ζ W h h U, V η sea bottom D = ζ + h where ( η) D ζ h η : total water depth (flow depth) : surface elevation : still water depth : bottom displacement

5 NEOWAVE ( ) D V U V f h y D q y q y g y V V x V U t V η ζ ζ = + + Continuity equation z-momentum equation y-momentum equation x-momentum equation ( ) D V U U f h x D q x q x g y U V x U U t U η ζ ζ = + + D q t W = 0 ) ( ) ( ) ( = + + ζ η y VD x UD t Governing Equations Depth-integrated, Non-hydrostatic Equations in Cartesian Grid

6 NEOWAVE ( ) D V U V f h y D q y q y g y V V x V U t V η ζ ζ = + + Continuity equation z-momentum equation y-momentum equation x-momentum equation ( ) D V U U f h x D q x q x g y U V x U U t U η ζ ζ = + + D q t W = 0 ) ( ) ( ) ( = + + ζ η y VD x UD t Governing Equations Non-linear, Shallow Water Equations

7 Vertical Datum The original DEM data s vertical datum is NAVD (1). At near river mouth, Astoria, Tongue Point, Columbia River, OR MHHW 3.305m MTL 2.068m MSL 2.054m MLLW 0.681m NAVD 0.615m MTL NAVD 2.068m m = 1.453m (2). At Longview, Columbia River, WA Astoria Longview MHHW MTL MSL MLLW NAVD MTL NAVD 1.429m ( 0.764m) = 2.193m In this BM, we use the average value as (1.453m m)/2 = 1.823m ~1.8 m NOAA NOS/CO-OPS MHHW : Mean Higher-High Water MTL : Mean Tide Level MSL : Mean Sea Level MLLW : Mean Lower-Low Water NAVD : North American Vertical Datum

8 Original Bathymetry Data

9 Modified Bathymetry Data

10 Bathymetry Data Modification

11 Computational Domain Low Tide River mouth Intermediate boundary 80m grid 2077 x 1195 Skamokawa Longview Portland Bonneville dam

12 Computational Domain Mean Tide Level River mouth Intermediate boundary 80m grid 2077 x 1195 Skamokawa Longview Portland Bonneville dam

13 Computational Domain High Tide River mouth Intermediate boundary 80m grid 2077 x 1195 Skamokawa Longview Portland Bonneville dam

14 Computational Domain Grid Resolution near the Boundaries Low Tide

15 Computational Domain Grid Resolution near the Boundaries Mean Tide Level

16 Computational Domain Grid Resolution near the Boundaries High Tide

17 Bottom Friction Darcy s Friction Factor River mouth Intermediate boundary Skamokawa Longview f = f = Portland Bonneville dam

18 Bottom Friction Darcy s Friction Factor River mouth Intermediate boundary Skamokawa Longview f = f = 0.02 Portland Bonneville dam

19 Initial Condition River Mouth Boundary Conditions (1) (2) (1) : computed data : initial condition Surface elevation (m) Horizontal velocity, u (m/s) Horizontal velocity, v (m/s) (2)

20 Tide Effects Hydrostatic Solution (Non-liner Shallow Water Solution) : High tide : MTL : Low tide Surface elevation (m) Horizontal velocity, u (m/s) Horizontal velocity, v (m/s)

21 Tide Effects Hydrostatic Solution (Non-liner Shallow Water Solution) : High tide : MTL : Low tide Surface elevation (m) Horizontal velocity, u (m/s) Horizontal velocity, v (m/s)

22 Wave Dispersion Effects Hydrostatic and Non-hydrostatic Solutions Mean Tide Level No Discharge : Hydrostatic solution : Non-hydrostatic solution Surface elevation (m) Horizontal velocity, u (m/s) Horizontal velocity, v (m/s)

23 Maximum Amplitude Low Tide (Bathymetry Data) River mouth Intermediate boundary Skamokawa Longview Portland Bonneville dam

24 Maximum Amplitude Low Tide River mouth Intermediate boundary Skamokawa Longview Portland Bonneville dam

25 Maximum Amplitude Mean Tide Level (Bathymetry Data) River mouth Intermediate boundary Skamokawa Longview Portland Bonneville dam

26 Maximum Amplitude Mean Tide Level River mouth Intermediate boundary Skamokawa Longview Portland Bonneville dam

27 Maximum Amplitude High Tide (Bathymetry Data) River mouth Intermediate boundary Skamokawa Longview Portland Bonneville dam

28 Maximum Amplitude High Tide River mouth Intermediate boundary Skamokawa Longview Portland Bonneville dam

29 Conclusions and Future Studies Conclusions In this numerical experiment of modeling Columbia River, the effects of wave dispersion, wave breaking, and tide are very minor. The comparison of computed results with difference solutions indicate the non-linear shallow water model is sufficient to model tsunami inundation. Future Studies (1). Bottom Friction Tests (2). Grid Refinement Scheme Implementation (3). Natori River for the 2011 Tohoku-oki Tsunami

30 APPENDIX 1: River Modeling Example Inundation Modeling of Siletz River Cheung, K.F., Wei, Y., Yamazaki, Y., and Yim, C.S. (2011). Modeling of 500-year tsunamis for probabilistic design of coastal infrastructure in the Pacific Northwest. Coastal Engineering, 58(10), Four Cascadia rupture models based on the 2008 National Seismic Hazard Maps. : LZ model : MT model : BT model : GA model

31 APPENDIX 1: River Modeling Example Inundation Modeling of Siletz River GA model Subfault and Slip Distribution Sea Surface Deformation

32 APPENDIX 1: River Modeling Example Inundation Modeling of Siletz River Time sequence of Surface elevation (GA model) Surface elevation at Siletz River Bridge Surface elevation at Millport Slough Bridge