Research Topic Updated on Oct. 9, 204
Mixed Cohesive/Non-cohesive Sediments Sedimentation in Estuary: Flocculation Deposition Erosion Transport Consolidation *: It has been recognized that when the fraction of fine-grained sediments is larger than about 0%, a mixture consisting of cohesive and non-cohesive sediments may exhibit cohesive properties. 2
Mixed Cohesive/Non-cohesive Sediments -D fractional sediment transport equation Q Q t U x tk tk Ebk Dbk qtlk tk (k=, 2,, N) Q tk E bk D bk β tk U q tlk total-load transport rate of size class k erosion rate deposition rate correction factor flow velocity side inflow of sediment per unit channel length Deposition Rate: D B C bk k sf, k k B a k w sf,k C k channel width deposition probability or adaptation coef. settling velocity section-averaged sediment concentration 3
Coefficient α k For non-cohesive sediment, k is the adaptation k coefficient, calculated by /6 a a a exp.5 h h h u sf, k * (Armanini and di Silvio, 988) For cohesive sediment, k is the deposition probability coefficient, which is related to the bed shear stress as / 0 b bd,min bd,max bd,min b bd,min bd,min b bd,max b bd,max 4
Settling Velocity w sf,k For cohesive sediment, sf,k is calculated by Wu and Wang s (2004) formula, through which the effect of flocculation is considered K K K K sf d s sa t sf median settling velocity of flocs sd d50 median settling velocity of dispersed particles K d / d K s d Ksa k r.0 50 kc k C 2 n n d r 0 C Cp C C p d 50 medium diameter d r reference diameter, about 0.025 mm n d coefficient, approximated to.8 C concentration, in kg/m 3 C p sediment concentration at the maximum settling n, r, k, k 2 coefficient, ranging from to 2 n r k coefficient, equal to kc p / k2c p K t kt b / p ktb / p n t n t 2 0 p p k t, n t, n t2 p empirical coefficient threshold bed shear stress at maximum K t 5
Erosion Rate E p E * bk bk bk p bk E * bk fraction of the k th size class in the surface layer of bed material potential erosion rate of the k th size class For non-cohesive sediment For cohesive sediment E B Q * k sf, k * bk tk AUtk * b Ebk BM ce n ce critical bed shear stress for surface erosion M erodibility coef., related to bed material properties n coefficient, equal to 2.5 6
Critical Bed Shear Stress The incipient motion of non-cohesive sediment is affected by the cohesion if non-cohesive and cohesive sediments coexist in the bed material. ck, n ce p p / p p ck ck, n ce ck, n c c min c max c min p c cmin cmin c cmax c p p p p p p cmax ck,n critical bed shear stress of the size class in the situation where only non-cohesive sediment exists ce critical bed shear stress for cohesive sediment p c fraction of cohesive sediment p cmin minimum fraction of cohesive sediment, below which the critical bed shear stress for non-cohesive sediment is the same as that when no cohesive sediment exists p cmax maximum fraction of cohesive sediment, above which the critical bed shear stress of non-cohesive sediment is equal to that of cohesive sediment k ce0 d0 d ce ce0 d d 0 k, n (Nicholson and O Connor, 986) initial critical bed shear stress initial critical dry bed density dry bed density empirical coefficients n 7
Bed Deformation The fractional bed mass deformation rate is determined by M t Then the total rate of change in bed mass is bk M t b which can be converted to the change in bed cross-sectional area: Ab Mb p m t p t Bed Material Sorting s D E s bk bk N k M t ( M p ) M M M p t t t t m bk bk * m b bk m bk bed material porosity 8
Consolidation Dry bed density in the first year (Hayter, 983): d d ae pt Dry bed density after year (Lane and Koelzer,953): d d log t d d a,p t Bed Change due to Consolidation: t 0 j dj j dj J J n n n n dj zb, c j j j n j j dj t dry bed density at one-year consolidation time empirical coefficients consolidation time, in hour empirical coefficient consolidation time, in year thickness of the j th layer of bed material dry bed density of the j th layer of bed material 9
Mainstream: from a dam at De Pere to Green Bay ( km) Tributary: Lower Fox River East River (joins the Fox River approximately 2 km upstream from the river mouth) Size Classes: Fine ~ 0.0036 mm Medium ~ 0.036 mm Coarse ~ 0.447 mm 0
-D Simulation in Lower Fox River Flow Discharge at the Dam Sediment Concentration at the Dam Sediment Concentration at the River Mouth (Lin and Wu, 203)
Gironde Estuary, France 2
Gironde Estuary, France 2-D simulation using FASTER2D (Wu and Wang, 2004) Mesh: 57 69 Δt=30 min Period: May 9-22, 974 3
Tidal Flow in Gironde Estuary, France Flood Tide -.80 -.60 -.40 -.20 -.00-0.80-0.60-0.40-0.20-0.00 0.20 0.40 0.60 ws Ebb Tide 4
Water Elevation (m) Water Elevation (m) Water Elevation (m) Tidal Level in Gironde Estuary 2 Simulated Measured (a). PK82 0 - -2 0 0 20 30 40 50 60 70 80 90 Time (hour) (b). Lamena (c). PK47 2 2 0 0 - - -2 60 70 80 90 Time (hour) -2 60 65 70 75 80 85 90 95 Time (hour) 5
Velocity (m/s) Velocity (m/s) Velocity (m/s) Velocity in Gironde Estuary Measured, m below Surface Measured, m above Bed Simulated (a). PK82 0 - -2 0 0 20 30 40 50 60 70 80 90 Time (hour) (b). Lamena (c). PK47 2 0-0 - -2 60 70 80 90 Time (hour) 60 65 70 75 80 85 90 95 Time (hour) 6
Salinity (kg/m 3 ) Salinity (kg/m 3 ) Salinity (kg/m 3 ) Salinity in Gironde Estuary 30 25 Simulated Measured, m below Surface Measured, m above Bed (a). PK82 20 5 0 0 9 8 7 6 5 4 3 0 0 20 30 40 50 60 70 80 90 (b). Lamena 2 60 70 80 90 Time (hour) Time (hour) 5 4 3 2 (c). PK47 60 65 70 75 80 85 90 95 Time (hour) 7
US (kg/m 2 s) US (kg/m 2 s) US (kg/m 2 s) Sediment Discharge in Gironde (a). PK82 0.5 0-0.5 - -.5 0 25 50 75 Time (hour) 3 (b). PK54 3 2.5 (c). PK47 2 2.5 0.5 0 0-0.5 - - -.5 75 80 85 90 95 Time (hour) 75 80 85 90 95 Time (hour) 8
San Francisco Bay 9
San Francisco Bay Mesh 3-D Simulation using CRESTS3D (Wu and Lin, 20) 20
Flow near Golden Gate Bridge 7000 m/s 47000 m/s 6000 (a) 46000 (b) 5000 Golden Gate Bridge 45000 Golden Gate Bridge 4000 44000 3000 43000 2000 42000 000 4000 26000 28000 30000 32000 (m) 26000 28000 30000 32000 (m) 2
Flow near Port Chicago 6000 5000 4000 76000 m/s 75000 (a) 74000 m/s (b) 3000 73000 2000 72000 000 7000 0000 Port Chicago 70000 Port Chicago 68000 70000 72000 (m) 68000 70000 72000 (m) 22
Water Level 23
Currents 24
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, 9(3), 72 90. W. Wu and Q. Lin (20). An implicit 3-D finite-volume coastal hydrodynamic model. Proc., 7th Int. Symposium on River, Coastal and Estuarine Morphodynamics, September 6-8, Beijing, China. Q. Lin and W. Wu (203). A one-dimensional model of mixed cohesive and non-cohesive sediment transport in open channels. Journal of Hydraulic Research, IAHR, 5(5), 506 57, DOI: 0.080/0022686.203.82046. 25