Understanding Sediment Source To Sink – On Modeling Several Critical Processes in the Nearshore Tian-Jian Hsu (Tom) Assistant Professor Center for Applied Coastal Research Civil and Environmental Engineering University of Delaware 2009 International Sediment Transport and Sedimentation Symposium

Fate of Terrestrial Sediment in Coastal Ocean (Sediment source to sink) - Why is it important?  Coastal Ecosystem 1)Heath of coral reef 2)Contaminant Transport  Carbon Sequestration Yes, sediment transport is related to GLOBAL WARMING! Particulate Organic Carbon and nutrients are carried by river borne sediments.  Seabed Properties  They determine surface wave propagation and acoustic wave transmission.  Waterway Navigation  dredging Adopted from MARGINS Science Plans National Science Foundation. In “Mud, Marine Snow and Coral Reefs” by Eric Wolanski, Robert Richmond, Laurence McCook and Hugh Sweatman, American Scientist, 91 (1), p. 44. A soft mud bed at a tidal flat in Willapa Bay, WA

Where are the big signals? Adopted from MARGINS Science Plans National Science Foundation. Large rivers in passive margin – Amazon, Mississippi Small mountainous river in active margin – e.g., Kaoping (Taiwan), Jhoushui (Taiwan), Waipaoa (New Zealand), Santa Clara and Eel (USA). See Milliman & Syvitski (1992) J. Geology.

Physical Settings of Small Mountainous River Episodic high sediment yield triggered by large rainfall due to typhoon or tropic cyclone (sediment concentration often exceeding several g/l). Highly salt-stratified frontal zone. Energetic wave condition. Left: SAR image of Jhoushui river mouth courtesy of Dr. Chang at Center for Space & Remote Sensing Research, National Central Univ., Taiwan. Right: Figures of Landslides and river flooding after typhoon Mindulle (July 2005) are provided by Dr. S.-J. Kao, Academia Sinica, Taiwan. ROMS model results for highly sal- stratified frontal zone adopted from Hetland & MacDonald (2008) Spreading in the near-field Merrimack River plume, Ocean Modeling, 21,

Motivation Large-scale coastal models, e.g. Delft3D, MIKE21, NOPP-CSTMS (ROMS), ECOMSED (POMS) and many others, require accurate parameterization on small-scale processes. NOPP-CSTMS (Community Sediment Transport Model System): ~10m ~20cm Wave boundary layer process and near-bed sediment transport require grid resolution ~ 1 mm Frontal dynamics requires grid resolution ~ cm CSTMS model results provided by Chris Sherwood (USGS) and Rocky Geyer (WHOI).

Fluid Mud Modeling Develop a numerical modeling framework for fine sediment transport based on Fast Equilibrium Eulerian Approximation (Ferry & Balachandar 2001) to the Eulerian Two-phase formulation – Mixture ApproachMixture Approach  Mass and momentum equations:  Turbulent & viscous stresses; rheological stresses.  Sediment-driven gravity flow.  Turbulence closure: damping of turbulence due to sediment density stratification and viscous drag in turbulent fluctuation.  Rheological stress: e.g., Bingham-plastic. Important to hydrodynamic dissipation.  Floc properties and floc dynamics assuming fractal structure. Winterwerp (1998), Khelifa & Hill (2006), Son & Hsu (2008).  Erodibility (Type I erosion): critical bottom stress depends on cumulative eroded mass.  Future work: Directly resolve bed consolidation and fluidization (e.g., Gibson et al. 1967). Evolution of floc aggregate structure. Winterwerp & van Kesteren (2004) dilute turbulent suspension  <  o mobile fluid mud  o <  <  gel lutocline z ~10g/l~100g/l Consolidating bed  >  gel

x-momentum: z-momentum: Floc vol. conc.: Continuity: Eulerian Two-phase Formulation for fluid and sediment ( Hsu et al. Proc. Royal Soc. Lond, 2004.) SMALL particle response time T p <<1; T p ~D 2  s Fast Equilibrium Eulerian Approach, Ferry & Balachandar Int. J. Multiphase Flow, Governing Equations Salt conc.: with z x

Two-equation k-  closure based on two-phase theory that incorporates turbulence damping due to sediment (e.g., Hsu & Liu 2004, J. Geophys. Res.) and salinity: Stratification due to sediment and salinity. Eddy-particle interaction. Carrier fluid turbulence closure: C 3  =1.0C 3  * =1.0 unstable stratification =0 stable stratification

2DV turbulence-averaged fine sediment modeling framework is solved numerically by revising a 2DV time/depth resolving wave model (COBRAS, Lin and Liu 1998, JFM). A non-hydrostatic 2D RANS solver with complex bathymetry. COBRAS can calculate surface wave propagation using volume of fluid (VOF) scheme and is a powerful tool for nearshore where wave effects are important. When sediment concentration and salinity  0, numerical model reduces to original COBRAS for clear fluid RANS model. Numerical Implementation Model results on surf zone wave provided by Alec Torres-Freyermuth, CACR, U. Delaware.

App #1: Sediment-laden River Plume & Initial Deposition Negatively Buoyant Plume: (>40g/l)  Hyperpycnal flow (Wright et al. 1988, Nature, vol. 332, p. 629)  Buoyancy reversal (due to rapid sediment deposition, Hurzeler et al. 1996; Hogg et al. 1999) Positively Buoyant Plume (~<40g/l):  Frontal trapping, lift-off, etc (e.g., Armi & Farmer 1986; Geyer & Kineke 1995; Wu et al. 2006; Lee et al. 2009).  Sediment settling (Hill et al. 2000): 1)Primary particle (↓ 0.1 mm/s) 2)Flocculation process (↓ 1 mm/s) 3)Convective sedimentation (↓ 1 cm/s) (e.g., Green 1987; Parson, Bush & Syvitski 2001; McCool & Parson 2004) Wright & Nittrouer [1995], Estuaries.

River discharge, U 0 =20 cm/s, c in =47 g/l, Salinity of seawater 35 ppt, c cric =42 g/l Silt: d=20 µm,  s =2650 kg/m 3, W s =0.36 mm/s Hyperpycnal plume – silt Sed. conc. (g/l) Salinity (ppt)

River discharge, U 0 =20 cm/s, c in =26.5 g/l, Salinity of seawater 35 ppt, c cric =42 g/l Silt: d=20 µm,  s =2650 kg/m 3, W s =0.36 mm/s Hypopycnal plume (convective sed.)– silt, clay (primary particle) Sed. conc. (g/l) Salinity (ppt)

Convective Sedimentation/Instability McCool & Parsons, 2004, Cont. Shelf Res., 24, Parsons, Bush, Syvitski,, 2001, Sedimentology, 48, Earlier studies explain this phenomenon based on double-diffusion analogy for salt-finger: e.g., Green (1987), Sedimentology; Chen, (1997) Deep-Sea Research; Hoyal, Bursik, and Atkinson (1999) Marine Geology. McCool & Parsons (2004) carry out first experiment for convective instability with ambient shear flow. They observe convective instability with sediment concentration as low as 380mg/l. Science Issue #1: Is double-diffusion the only explanation of convective instability? How about gravitational settling itself?

Our numerical model results suggest when inlet height is larger (~meters), strong interfacial mixing (K-H waves, Holmboe waves) can suppress convective instability: 1)It is likely that convective instability can occur in the field but with much larger sediment concentration, i.e., 10~20 g/l.  Important for small mountainous river. 2)This problem is strongly related to plume dynamics (e.g., hydraulic control, Armi and Farmer 1986), and interfacial mixing. 3)What is the effect of surface gravity waves? Sicence Issue #2: Can convective instability occur in the field? Recent field study by Warrick et al. (2008, Cont. Shelf Res.) at Santa Clara River, CA observe rapid sediment settling from bottom tripod, which was indirectly related to convective instability (not direct field evidence).

Resuspension  Currents (tidal-, wind-driven, etc) and waves can suspend high concentration cohesive sediment – Fluid mud  Wave dissipation over mud.  Wave-supported gravity-driven mudflows (e.g., Ogston et al. 2000; Traykovski et al 2000; Wright et al. 2001). Adopted from MARGINS Science Plans National Science Foundation. Traykovski et al. [2000], Cont. Shelf Res.

1DV fluid mud model results of wave supported gravity-driven mudflow at Po prodelta. EUROSTRATAFORM data obtained in collaboration with Peter Traykovski (WHOI). App #2: Detailed modeling of wave-supported gravity-driven mudflow and its parameterization (Hsu et al. 2008, JGR - Ocean, accepted). Wright et al. 2001; Marine Geology - Parameterization for coastal modeling

Stiffness: k b =>Bingham-type k b =>Newtonian-type App #3: Wave-mud Interaction – 2DV Modeling The presence of mud can significantly attenuates wave energy (e.g., Gade 1958; Dalrymple & Liu 1978; Sheremet & Stone 2003) Rheological stress closure:

Wave characteristics: H=0.72 m T=6 s L=28 m Mesh characteristics: Min (  y)=2 mm Min (  x)=2.5 cm Fluid-mud characteristics: D=22  m (floc)  f =1340 Kg/m 3 n f =2.1 W s ~0.1 mm Cnoidal Wave Train Propagating over Muddy Seabed *Numerical modeling of wave-mud interaction is carried out by postdoc Alec Torres-Freyermuth

The wave amplitudes present a monotonic decrease in amplitude at various frequency, suggesting both direct interaction (long wave and mud) and wave-wave interaction cause wave x=185 m Wave Amplitude Dissipation kh=1 Clear fluid Fluid mud Clear fluid with increased K s =400mm Nonlinear wave effects - Ongoing work

Mud-laden Wave Boundary Layer Dynamics Clear fluid Fluid mud (a) (b)

1)Improved modeling on sediment-laden plume dynamics for high sediment yield condition. - Small-scale modeling (2DV~1m X 100m); - Coastal Modeling, e.g., Community Sediment Transport Modeling System (3D ~10m X 5km X 5km) Ongoing and Future Works - related to sediment Disposal off Small Mountainous River Schematic plot of sediment-laden river plume produced in collaboration with Dr. Rocky Geyer, WHOI

2)Effects of waves on plume dynamics and sediment deposition (and vice versa) Model results provided by Drs. Fengyan Shi and Jim Kirby University of Delaware. See b)2DV Buoyant plume simulation with free-surface (use VOF scheme): a)NearCoM Simulation (REF/DIF1+SHORECIRC)