Tom T.-J. Hsu, Assistant Professor Civil & Coastal Engineering University of Florida High Resolution Numerical Modeling of Cohesive Sediment Transport in Estuary and Continental Shelf Taiwan-U.S. Source-to-Sink Research Workshop – NSYSU, Kaohsiung, Taiwan. Feb 2008.

Wright & Nittrouer [1995], Estuaries. Dadson et al. 2005, JGR-Earth Surf. Fate of Terrestrial Sediment in the Coastal Ocean  Initial Deposition  Resuspension 2. Negatively buoyant plume: Occurrence of hyperpycnal flow in Taiwan’s rivers: 1. Positively buoyant plume: Stable density stratification. Flocculation process.  Estuarine Turbidity Maximum (ETM); frontal trapping.

Motivation Large-scale coastal models, e.g. Delft3D, Mike21, NearCoM, NOPP-CSTM, … and many others, require accurate parameterization on wave boundary layer processes. NOPP-CSTM (Community Sediment Transport Model): ~10m ~20cm Need detailed field measurements and theoretical/numerical modeling on boundary layer flow and sediment transport dynamics near the bed. NOPP-CTSM, figure provided by Dr. John Warner (USGS) NearCoM, figure provided by Dr. Fengyan Shi (U Delaware).

Eel Shelf slope ≈ 1/200 Traykovski et al. [2000], Cont. Shelf Res. Wave-supported gravity-driven mudflows e.g., STRATAFORM at Eel river: Overview: a recent review paper Wright & Friedrichs (2006), Cont. Shelf Res.

Fluid Mud Modeling Develop a 1DV numerical modeling framework for fluid mud transport based on Fast Equilibrium Eulerian Approximation (Ferry & Balachandar 1994) to the Eulerian Two-phase formulation – Mixture ApproachMixture Approach  Existence of fluid mud: Hsu et al. (2007). turbulence-sediment interaction, downslope gravity-driven mudflow. turbulence-sediment interaction  Floc properties and floc dynamics: Winterwerp (1998), Khelifa & Hill (2006) Floc properties and floc dynamics  Erodibility (Type I erosion): critical bottom stress depends on cumulative eroded mass, which is due to consolidation. Erodibility  Rheological stress: e.g., Bingham-plastic. Wave- mud interaction. Rheological stress  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

Model Formulation (Hsu, Traykovski, Kineke 2007, J Geophys. Res.) z x, cross-shelf y, along-shelf α  : fluid density  s : floc density Eulerian Two-phase Formulation for fluid and sedimemt e.g. Hsu et al. Proc. Royal Soc. Lond, SMALL particle response time T p <<1; T p ~D 2  s Fast Equilibrium Eulerian Approach, Ferry & Balachandar Int. J. Multiphase Flow, x, momentum: y, momentum: sediment volume : concentration Mixture approach

Based on two-phase theory that incorporates turbulence damping due to sediment (e.g., Hsu & Liu 2004, J. Geophys. Res.): Stratification due to sediment. Eddy-particle interaction. Carrier fluid turbulence closure: Fine sediments: E s >>E E

Given fixed floc size D and fractal dimension n f : Floc Properties:  : fluid density = 1000 kg/m 3  s : primary particle density = 2650 kg/m 3 D 0 : primary particle diameter = 4 m   a : floc density primary particle floc aggregate Modeled as “fractal structure” n f =2 Manning et al. (2007), Cont. Shelf Res. Typical estuarine mud: n f =2~2.5 (e.g., clay, silt, fine sand, d 0 ~< few m  ) Winterwerp and van Kesteren (2004)

Erodibility: Tidal mud flats at Willapa Bay, Washington, USA In-situ measured erodibility data by Stevens et al. (2007), Cont. Shelf Res.: M (kg/m 2 )  c (Pa) Type I Erosion: (e.g. Sanford and Maa 2001)

→ Bingham Rheology Rheological stress closure: d=22 mµ, s=1.44: c=140 g/l c=100 g/l c=50 g/l

Wave-supported Gravity-driven Mudflows Sherwood et al. [2004] Fluid mud at Po Prodelta EUROSTRATAFORM: Traykovski, Wiberg and Geyer [2007], Cont. Shelf Res. x, cross-shelf y, along-shelf α=0.002 z Case 1: Moderate Concentration Event Erodibility: Type I erosion with Stevens et al. (2007): Floc Properties: D=24 mµ,  a = 1440 kg/m 3,  n f =2.26 Rheology: OFF Floc dynamics: OFF Hydrodynamic Condition: r.m.s. wave velocity=0.52 m/s, weak currents EUROSTRATAFORM data obtained in collaboration with Peter Traykovski.

Case 2: High Concentration Event Erodibility: Type I erosion with Stevens et al. (2007): Floc Properties: D=21 mµ,  a = 1440 kg/m 3,  n f =2.2 Rheology: ON Bingham rheology with Floc dynamics: OFF Hydrodynamic Condition: r.m.s. wave velocity=0.51 m/s, weak currents Large erodibility and rheological stress are required to model the observed wave-supported gravity-driven mudflows

Based on our numerical model study, we find: 1.critical mechanisms controlling wave-supported gravity-driven mud flows are: Total amount of available unconsolidated mud Turbulent-sediment interaction (density stratification) Floc properties (fractal dimension) Rheology 2.detailed intra-wave time-dependent erodibility and floc dynamics are of less importance 3.need concurrent measurements on floc properties and rheology Summary - Wave-supported Gravity-driven Mudflows