Research Topic Updated on Oct. 9, 2014

Transcription

1 Research Topic Updated on Oct. 9, 2014

2 Entrance of Humboldt Bay, CA 2

3 Coastal Morphodynamic Modeling Conceptual models Shoreline evolution models Beach profile evolution models Coastal area or 2DH models Quasi-3D models 3D models Ocean City Inlet 3

4 CMS (Coastal Modeling System) Alex Sanchez 1, Weiming Wu 2, Julie D. Rosati 1, Lihwa Lin 1, Honghai Li 1, Mitch Brown 1, Chris Reed 3, Tanya Beck 1, and Zeki Demirbilek 1 1 Coastal and Hydraulics Laboratory ERDC, US Army Corps of Engineers 2 Clarkson University, NY 3 Reed & Reed Consulting, FL 4

5 Coastal Modeling System (CMS) Integrated system Inline code Parallelization on PC s SMS Interface Verification & Validation reports available: 5

6 Decomposition of Velocity Velocity split Current Wave Turbulent uˆi u i u i u i u i 0 Total flux hv i z b uˆ dz i V U U i i wi H Q w Datum Wave flux Qwi huwi uˆ idz Current velocity t U i u i Bed z b h hu u dz u dz i z i z i b b 6

7 Continuity Momentum Temporal Hydrodynamics h t Advection ( hv ) x Coriolis-Stokes ( hv ) ( hvv i j) i h p ij fchv j gh t x x x j i i V i 1 si bi th Sij Rij huwiu wj mb x j x j x j j j 0 Wave level Gradient a V U U i i wi Contribution Atmospheric Pressure Wind stress Mixing Radiation stress Roller stress Excess Wave momentum Bottom friction 7

8 Turbulent Eddy Viscosity Base or background value Wave-related component Modified Kraus and Larson (1991) Current-related component Subgrid model 2 c cvu* ch ( ch ) S Mixing length model v v v v t 0 c w S 2 2 c u h l S 2 c v * c h 6 v /3 Dbr w cwf uwsh s cbrh 2e ij e ij l h e ij min c h, y 1 2 m Vi xj V x 8 i j

9 Mean Bottom Shear Stress Wave-current bottom friction c U U c u 2 2 b b i w ws cw 0.65 Bottom wave orbital velocity H s uws T sinh( kh) Bottom friction coefficient cb For currents only reduces to gn h 2 1/3 p bc cbuui c b ln( h/ z0) 1 2 9

10 Surface Shear Stress Wind reference frame C WW si a D i W W U E i i W i W 0 for Eulerian reference frame 1 for Lagrangian reference frame Modified Hsu (1988) drag coefficient C D 2 for W lnW 30 m/s 3 10 max( W,1.5) for W 30 m/s 10

11 Boundary Conditions Wall Boundary 2 F 0 c U f wall wall c wall ln( yp / y0) 2 U U ( U n) n Flux Boundary Q h ( U nˆ ) l tot B B B B U B B frampq h r1 h n B ( eˆn ˆ) B lb n B r B B eˆ B Water level Boundary f ( ) (1 f ) B Ramp E C G Ramp 0 11

12 Cross-Shore Boundary Conditions The alongshore (y) component of velocity is calculated by solving the following equation: x V x 0 th sy wy b cw c U V The cross-shore (x) component of velocity is copied from internal node; The alongshore gradient of water level is zero, or the water level is determined by 0 g x sx wx 12

13 CMS-Wave Spectral wave-action balance equation 2 c N cn x y c N cc θ K 2 N g 2 N cc cos θ cos θ ε N S g 2 b x y θ 2σ y y 2 y Characteristic velocities cx cg cosθ U c c sin θ U x y g y N E( f,θ) σ c θ σ h h U x U Uy U x sin θ cosθ cosθ sin θ cosθ sin θ sin θ cosθ sinh 2kh x y x y x y y Dispersion relation Radiation stresses 2 σ gk tanh( kh) σ ω k U 1 Sij Ew( f, ) ngwi wj ij ng df d 2 13

14 Surface Roller As wave transitions from nonbreaking to breaking, part of the energy goes into the aerated region known as surface roller as momentum and later transferred to the flow below Roller energy balance (2 E c ) x sr Assumptions Roller direction in same direction as waves Nonspectral Roller dissipation Roller stress j j D D R sr f D r e br g E c 2 sr D 2E w w ij sr i j E D D f e sr br sr D Rolle energy density Wave breaking dissipation Surface roller dissipation Efficiency factor Roller dissipation coefficient 14

15 Coupling between Flow and Waves Steering process Roller included in wave model Sediment transport and morphology change included in flow model Flow and Wave models may have the same or different grids 15

16 Sediment Transport Model Datum Total load transport equation Bed change equation z t b h zb Bed hu C r C hc t x x x z b k t k D k E k c k a q bk tk j tk sk tk sh tsk Ct* k Ctk tk j j j z z b b 1 pm t sk Ctk Ct* k Dsqbk t k x j x j u U r sk C C C tk k tk C k C C qbk Uh k* tk* 16

17 Total-load Correction Factor tk 1 r (1 r ) U u sk sk sk bk Suspended-load correction factor Assuming logarithmic velocity and exponential concentration profiles sk z a b Uz b uc dz a k c dz k E ( A) E ( ) ln( A / Z)e ln(1/ Z)e k k e ln(1/ Z) 1 1e ka 1 k 1 k sk A (1 A) k h / k sk A a / h Z z / h 1 a E ( x) x e t t dt 17

18 Sediment Transport Formulas Lund-CIRP (Wu and Lin 2011) qbk* 1 crk fbk p1 ks12 ccw, m exp 4.5 ( s 1) gd cw 3 k q h f p c U 1 exp ( s 1) sk* 1 k sk 3 s k 1k s Rk gd k sk Soulsby-van Rijn van Rijn Watanabe 1.5 1/2 e k crk k U U d qbk* fbs p1 k Uh ( s 1) gd h k 2.4 1/2 e k crk k U U d qbk* fbs p1 k Uh s 1) gd h k /2 Ue k U crk dk 0.6 sk* ss 1 k * k ( s 1) gd h k q f p Uh d 2.4 1/2 Ue k U crk dk 0.6 sk* ss 1 k * k s 1) gd h k q f p Uh d Wu and Lin (2014) bmax k crk qtk* fsrsk fb(1 rsk ) s p1 k AWat U g 18

19 Grids Used Regular Cartesian Nonuniform Cartesian Telescoping Cartesian Stretched Telescoping Cartesian Quadrilateral (Un)Structured Triangular Unstructured Hybrid Unstructured 19

20 Galveston Entrance Channel, TX 20

21 Columbia River, USA Hybrid mesh ~16k cells 20 m to 3.5 km resolution 21

22 Laboratory Study of an Idealized Inlet 22

23 Channel Infilling Van Rijn (1986) DHL (1980) Van Rijn and Havinga (1995) 23

24 Depth, m Depth, m Clear Water Jet over a Hard Bottom Initial depth: 0.15 m D50: 0.6 mm Hard bottom: 0.31 m Inflow velocity: 0.6 m/s Time step: 30 sec Simulation duration: 4.25 hrs Manning's coefficient: 0.03 s/m 3 Transport formula: Soulsby-van Rijn Initial Bed Measured, 1 hr Measured, 2 hr Measured, 4 hr Calculated, 1 hr Calculated, 2 hr Calculated, 4 hr Distance, m Initial Bed Measured, 1 hr Measured, 2 hr Measured, 4 hr Calculated, 1 hr Calculated, 2 hr Calculated, 4 hr Distance, m 24

25 Grays Harbor, WA 2001 Field Study 6 Tripods deployed from May 5 to July 2001 Weekly topo and monthly bathy surveys along m spaced transects Grab sediment samples taken at tripod locations 25

26 Model Setup Forcing Tide from Westport Harbor (corrected phase) Winds from NCDC Blended Sea Winds Waves from CDIP buoy (42 m depth) River flows from USGS Hydro and sediment transport 10 min time step Ramp of 5 days Waves 2 hr steering interval 30 day simulation (~10 hrs PC) 26

27 Sediment Transport Setup Grain size distributions? Expect coarser on bar and beach face and finer in trough No before and after Spatially constant initial grain size distribution Lund-CIRP transport formula Bed porosity = 0.3 Adaptation coefficient 10 bed layers Initial thickness of second layer and below = 0.5 m Uh / ( L ) t t s L (1 r ) L r L t s b s s L 10m L Uh / ( ) 0.3 b s s s s 27

28 Computational Grid 55k cells 200k cells CMS-Flow grid 28

29 Current Velocities (May 14, 2001) Transition Region 29

30 Results - Bed Change Measured Computed Areas of calculated deposition and erosion are highlighted with black polygons Similar erosional and depositional trends Erosion of outer bar Deposition at inner bar face Erosion of inner trough face Measured bed change shows more variability Periodic features Transition region

31 31 Transects

32 CRESTS3D (Coastal, River, and Estuarine Simulation Tool System) Weiming Wu Clarkson University, NY, USA 32

33 3-D Model CRESTS Coastal, Riverine and Estuarine Simulation Tool System A Phase-Averaged 3-D Shallow Water Flow Model Finite volume method Coupled with CMS-Wave Coded with CMS Flow Model SMS as GUI 33

34 Sketch of Flow and Sediment Transport 34

35 3-D Shallow Water Flow Equations u v w x y z 0, u ( uu) ( vu) ( wu) 1 pa 1 0g g dz t x y z x x z x u u u 1 Sxx 1 Sxy 1 f x x y y z z x y th th tv x c f v v ( uv) ( vv) ( wv) 1 pa 1 0g g dz t x y z y y z y v v v 1 Syx 1 Syy 1 f x x y y z z x y th th tv y c f u 35

36 Boundary Conditions Free surface kinematic condition u v w t x y h h h, Surface shear stress due to wind C WW si a D i where ρ a is air density, C D is the wind drag coefficient, and W is the wind velocity. The drag coefficient is calculated using the formula of Hsu (1988) and modified for high wind speeds based on field data by Powell et al. (2003). Bed shear stress c u u v 0.5 U, c v u v 0.5U bx f b b b wm by f b b b wm where u b and v b are the x- and y-velocities near the bed; c f is the bed friction coefficient; and U wm is the maximum orbital bottom velocity of wave. 36

37 Coupling with CMS-Wave Model Spectral wave-action balance equation (Mase et al. 2005): 2 N ( c ) ( ) xn cn y ( c N) w 2 N 1 2 N CCg cos CCgcos 2 t x y 2 y y 2 y N Q Q b v where N = E(x,y,σ,θ,t)/σ; E is the spectral wave density representing the wave energy per unit water surface area per frequency interval; σ is the wave angular frequency (or intrinsic frequency); θ is the wave angle relative to the positive x-direction; C and C g are wave celerity and group velocity, respectively; c x, c y, and c θ are the characteristic velocities with respect to x, y and θ, respectively; w is an empirical coefficient; ε b is a parameter for wave breaking energy dissipation; Q v represents the wave energy loss due to vegetation resistance; and Q includes source/sink terms of wave energy due to wind forcing, bottom friction loss, nonlinear wave-wave interaction, etc. c C cos U c C sin V x g y g c h h U 2 U 2 V V sin cos cos sin cos sin sin cos sinh 2kh x y x y x y 37

38 Wave Radiation Stress Formula of Mellor (2008) 2 2 ki( f ) k j( f ) cosh k( h z) sinh k( h z) ij 0 2 ij ij D S k( f ) E( f, ) E ( f, ) d df k( f ) sinh kdcosh kd sinh kdcosh kd, where E is the wave energy, k is the wave number, θ is the angle of wave propagation to the onshore direction, f is the wave frequency, h is the still water depth, D is the total water depth, z is the vertical coordinate referred to the still water level, and E D is a modified Dirac delta function which is 0 if z η and has the following quantity: E dz D h E /2 38

39 3-D Mesh System Quadtree rectangular in horizontal, and σ coordinate in vertical Hybrid triangular and quadrilateral grid version in the horizontal is under development) 39

40 Finite volume method; Fully implicit; Non-staggered (collocated) grid; SIMPLEC, with under-relaxation; Rhie and Chow s (1983) momentum interpolation for interface fluxes; Upwind schemes: Hybrid, Exponential, HLPA Solvers: Numerical Solution Methods GMRES Drying and wetting: Freezing dry nodes. 40

41 3-D Sediment Transport Model Suspended Load Transport Bed Load Transport c uj k s, k j3 c k t c k t x j x j c x j q u q bykqbk 1 qbk qb k 0 t x y L bk bk bxk bk (k=1, 2,, N) Bed Change z bk 1 p D E q q 1 L m bk bk bk bk t Bed Material Mixing ( bk) bk * pbk m p t z t t m z t b 41

42 Wu et al. (2000) Bed Load Formula Extended to Coastal Sedimentation by Wu and Lin (2014, Coastal Engineering) 42

43 Near-Bed Suspended-load Concentration Near-bed suspended-load concentration is related to bed-load transport rate: c bk = q bk δu bk Bed-load layer thickness: max 2.0 d,0.5,0.01h 50 r Bed-load velocity: / 1 s u bk b gd k cri, k c bk = δ 0.5 p bk d k τ b τ cri,k

44 z/h z/h Wind-Induced Currents Experiments by Baines and Knapp (1965). Wind channel with a cross-section of m by m and a length of 12.8 m. The channel is discretized with square grid cells of side m. Eighteen layers are used in the depth direction. The relative layer thickness (layer thickness over flow depth) from top to bottom is 0.005, 0.005, 0.01, 0.02, 0.03, 0.04, 0.05, 0.065, 0.085, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.05, 0.03 and The bed friction coefficient c f is Measured Calculated, with classical l m Calculated, with new l m 0.2 Measured Calculated, with classical l m Calculated, with new l m Velocity (m/s) Velocity (m/s) Measured and simulated current velocities induced by wind with a speed of (left) m/s and (right) m/s 44

45 Cross-shore Undertow Current Experiment by Ting and Kirby (1994). H=0.128 m, T=5 sec. The cross-shore grid spacing is 0.5 m, and 16 layers with a uniform spacing are used in the vertical direction. 45

46 46

47 Shinnecock Inlet Case 47

48 y zb x 48

49 y Measured (left) and Calculated (right) Morphology Changes between August 1997 and May 1998 dzb: x 49

50 Summary A 3-D shallow water flow model has been developed for coastal sedimentation. A modified mixing length model is used for turbulence closure. The flow model is coupled with CMS-Wave model. The model equations are solved with a finite-volume method based on quadtree-rectangular mesh in the horizontal and σ coordinate in the vertical. The sediment transport model considers multiple-sized, total-load transport. The model has been tested using lab and field measurements. 50

51 Publications Related W. Wu and S. S.Y. Wang (2004). Depth-averaged 2-D calculation of tidal flow, salinity and cohesive sediment transport in estuaries, Int. J. Sediment Research, 19(3), A. Sanchez, W. Wu, H. Li, M. Brown, C. Reed, J.D. Rosati, and Z. Demirbilek (2014). Coastal Modeling System: mathematical formulations and numerical methods. ERDC/CHL TR-14-2, Coastal and Hydraulics Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS. W. Wu, A. Sanchez, and M. Zhang (2011). An implicit 2-D shallow water flow model on unstructured quadtree rectangular mesh. Journal of Coastal Research, Special Issue, No. 59, pp A. Sanchez (2013). An implicit finite-volume depth-integrated model for coastal hydrodynamics and multiple-sized sediment transport. PhD Dissertation, the University of Mississippi, USA. A. Sanchez and W. Wu (2011). A non-equilibrium sediment transport model for coastal inlets and navigation channels. Journal of Coastal Research, Special Issue, No. 59, pp W. Wu and Q. Lin (2011). An implicit 3-D finite-volume coastal hydrodynamic model. Proc., 7th Int. Symposium on River, Coastal and Estuarine Morphodynamics, September 6-8, Beijing, China. 51