workshop on tsunami hydrodynamics in a large river...
TRANSCRIPT
NEOWAVENon-hydrostatic Evolution of Ocean WAVE
Yoshiki Yamazaki and Kwok Fai Cheung
Department of Ocean and Resources EngineeringUniversity of Hawaii at Manoa, Honolulu, HI, U.S.A.
August 14 ~ 15, 2011Oregon State University, Corvallis, Oregon
Workshop on Tsunami Hydrodynamics in a Large River
1. NEOWAVE● Theoretical Formulation● Numerical Scheme
2. RESULTS AND DISCUSSIONS● Tide● Wave Dispersion
3. CONCLUSIONS AND FUTURE STUDIES
OUTLINE
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.
NEOWAVE
Governing Equations● Variables Definition for Free Surface Flow
NEOWAVE
: total water depth (flow depth): surface elevation: still water depth: bottom displacement
where
( )η−+ζ= hD
η
Dζh
h
sea bottom
z
x, y
U, V
W
η
ζ ζ
h
NEOWAVE
( )D
VUVfhyD
qyq
yg
yVV
xVU
tV 22
21
21 +
−η+−ζ∂∂
−∂∂
−∂ζ∂
−=∂∂
+∂∂
+∂∂
Continuity equation
z-momentum equation
y-momentum equation
x-momentum equation
( )D
VUUfhxD
qxq
xg
yUV
xUU
tU 22
21
21 +
−η+−ζ∂∂
−∂∂
−∂ζ∂
−=∂∂
+∂∂
+∂∂
Dq
tW
=∂∂
0)()()(=
∂∂
+∂
∂+
∂η−ζ∂
yVD
xUD
t
Governing Equations● Depth-integrated, Non-hydrostatic Equations in Cartesian Grid
NEOWAVE
( )D
VUVfhyD
qyq
yg
yVV
xVU
tV 22
21
21 +
−η+−ζ∂∂
−∂∂
−∂ζ∂
−=∂∂
+∂∂
+∂∂
Continuity equation
z-momentum equation
y-momentum equation
x-momentum equation
( )D
VUUfhxD
qxq
xg
yUV
xUU
tU 22
21
21 +
−η+−ζ∂∂
−∂∂
−∂ζ∂
−=∂∂
+∂∂
+∂∂
Dq
tW
=∂∂
0)()()(=
∂∂
+∂
∂+
∂η−ζ∂
yVD
xUD
t
Governing Equations● Non-linear, Shallow Water Equations
Vertical Datum The original DEM data’s vertical datum is NAVD
(1). At near river mouth, Astoria, Tongue Point, Columbia River, OR
MHHW 3.305mMTL 2.068m MSL 2.054m MLLW 0.681m NAVD 0.615m
MTL NAVD2.068m -0.615m = 1.453m
(2). At Longview, Columbia River, WA
MHHW 2.148MTL 1.429MSL 1.385MLLW 0.752NAVD -0.764
MTL NAVD1.429m – (–0.764m) = 2.193m
In this BM, we use the average value as(1.453m +2.193m)/2 = 1.823m ~1.8 m
MHHW : Mean Higher-High WaterMTL : Mean Tide LevelMSL : Mean Sea LevelMLLW : Mean Lower-Low WaterNAVD : North American Vertical Datum
Longview
Astoria
NOAA NOS/CO-OPS http://tidesandcurrents.noaa.gov/station_retrieve.shtml?type=Datums
Original Bathymetry Data
Modified Bathymetry Data
Bathymetry Data Modification
Computational Domain • Low Tide
Skamokawa
Portland
Intermediateboundary
Bonneville dam
Longview
Rivermouth
80m grid2077 x 1195
• Mean Tide Level
Computational Domain
Skamokawa
Portland
Intermediateboundary
Bonneville dam
Longview
Rivermouth
80m grid2077 x 1195
• High Tide
Computational Domain
Skamokawa
Portland
Intermediateboundary
Bonneville dam
Longview
Rivermouth
80m grid2077 x 1195
• Low Tide
Computational Domain● Grid Resolution near the Boundaries
• Mean Tide Level
Computational Domain● Grid Resolution near the Boundaries
• High Tide
Computational Domain● Grid Resolution near the Boundaries
f = 0.025 f = 0.018
Bottom Friction● Darcy’s Friction Factor
Skamokawa
Portland
Intermediateboundary
Bonneville dam
Longview
Rivermouth
f = 0.0275 f = 0.02
Bottom Friction● Darcy’s Friction Factor
Skamokawa
Portland
Intermediateboundary
Bonneville dam
Longview
Rivermouth
— : computed data — : initial condition
Surface elevation (m) Horizontal velocity, u (m/s) Horizontal velocity, v (m/s)
Initial Condition● River Mouth Boundary Conditions
(1) (2)
(1)
(2)
— : High tide — : MTL —: Low tide
Tide Effects● Hydrostatic Solution
(Non-liner Shallow Water Solution)
Surface elevation (m) Horizontal velocity, u (m/s) Horizontal velocity, v (m/s)
— : High tide — : MTL —: Low tide
Tide Effects● Hydrostatic Solution
(Non-liner Shallow Water Solution)
Surface elevation (m) Horizontal velocity, u (m/s) Horizontal velocity, v (m/s)
— : Hydrostatic solution — : Non-hydrostatic solution
Wave Dispersion Effects● Hydrostatic and Non-hydrostatic Solutions
•Mean Tide Level•No Discharge
Surface elevation (m) Horizontal velocity, u (m/s) Horizontal velocity, v (m/s)
Maximum Amplitude • Low Tide (Bathymetry Data)
Skamokawa
Portland
Intermediateboundary
Bonneville dam
Longview
Rivermouth
• Low Tide
Skamokawa
Portland
Intermediateboundary
Bonneville dam
Longview
Rivermouth
Maximum Amplitude
• Mean Tide Level (Bathymetry Data)
Skamokawa
Portland
Intermediateboundary
Bonneville dam
Longview
Rivermouth
Maximum Amplitude
• Mean Tide Level
Skamokawa
Portland
Intermediateboundary
Bonneville dam
Longview
Rivermouth
Maximum Amplitude
• High Tide (Bathymetry Data)
Skamokawa
Portland
Intermediateboundary
Bonneville dam
Longview
Rivermouth
Maximum Amplitude
• High Tide
Skamokawa
Portland
Intermediateboundary
Bonneville dam
Longview
Rivermouth
Maximum Amplitude
(1). Bottom Friction Tests(2). Grid Refinement Scheme Implementation(3). Natori River for the 2011 Tohoku-oki Tsunami
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.
Conclusions and Future Studies● Conclusions
● Future Studies
● Inundation Modeling of Siletz River
Four Cascadia rupture models based on the 2008 National Seismic Hazard Maps.
APPENDIX 1: River Modeling Example
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), 970-985.
— : LZ model — : MT model — : BT model — : GA model
Subfault and Slip Distribution
Sea Surface Deformation
APPENDIX 1: River Modeling Example
GA model
● Inundation Modeling of Siletz River
APPENDIX 1: River Modeling Example
Time sequence of Surface elevation (GA model)
Surface elevation at Siletz River Bridge
Surface elevation at Millport Slough Bridge
● Inundation Modeling of Siletz River