An introduction to cohesive sediment transport modelling Bas van Maren

Contents (1) Introduction (2) Sand transport and morphology (3) Mud transport and morphology (4) Sediment transport and morphology in Delft3D E = Erosion rate [kg/m^2/s] M = Erosion parameter [kg/m^2/s] Τb = bed shear stress [Pa] Τe = erosion treshold shear stress [Pa] Destabilizers => Arenicola / Lugworm: lives in burrows in the sediment at depths of 20-40cm. It feeds on organic matter in the sediment by drawing water into the burrow and filtering organic particles.

Introduction Definition of mud Mud clay cohesive 2 m silt pseudo-cohesive 63 m Sand non-cohesive 2000 m Gravel

Introduction sand mud Definition of mud Modelling of sand and mud require a fundamentally different approach Bedload transport Bed material sand Suspended sediment transport Total transport mud washload Suspended sediment transport

Introduction sand mud Definition of mud Modelling of sand and mud require a fundamentally different approach Several conceptually different approach to modelling of mud exist: supply-limited (washload) or erosion-rate limited (bed material) Bedload transport Bed material sand Suspended sediment transport Total transport mud washload Suspended sediment transport

Sand transport and morphology Sand is deposited (almost) instantaneously when bed shear stress < critical bed shear stress, and eroded when bed shear stress > critical bed shear stress

Sand transport and morphology Sand is deposited (almost) instantaneously when bed shear stress < critical bed shear stress, and eroded when bed shear stress > critical bed shear stress Transport of sand can be well predicted using empirical sediment transport formula Van Rijn (1993) Bed load + suspended Engelund-Hansen (1967) Total transport Meyer-Peter-Muller (1948) Total transport General formula Total transport Bijker (1971) Bed load + suspended By default, the formula of Van Rijn (1993) is applied in Delft3D. T = f(u3, 1/h, 1/D50, …)

Sand transport and morphology Sand is deposited (almost) instantaneously when bed shear stress < critical bed shear stress, and eroded when bed shear stress > critical bed shear stress Transport of sand can be well predicted using empirical sediment transport formula Sand morphology can be predicted with reasonable accuracy Advanced coupling with wave modules (wave-generated bed shear stress and flows)

Sand transport and morphology Sand is deposited (almost) instantaneously when bed shear stress < critical bed shear stress, and eroded when bed shear stress > critical bed shear stress Transport of sand can be well predicted using empirical sediment transport formula Sand morphology can be predicted with reasonable accuracy Advanced coupling with wave modules (wave-generated bed shear stress and flows) Note the use of ‘well predicted’ and ‘reasonable accuracy’!

Mud transport and morphology General formulations Transport of mud Transport of silt: in-between mud and sand Transport of sand-mud mixtures

Mud transport: general formulations 3D advection-diffusion equation with erosion and deposition terms as bed boundary conditions

Mud transport: general formulations 3D advection-diffusion equation Erosion and deposition: But: critical shear stress for deposition does probably not exists (although sometimes useful)

Mud transport: general formulations 3D advection-diffusion equation Erosion and deposition: But: critical shear stress for deposition does probably not exists (although sometimes useful) ws depends on sediment concentration and turbulence Mud modelling: define settling velocity (flocculation?), critical shear stress for erosion, and erosion parameter

Transport of mud Transport of mud depends on Fluid dynamics (bed shear stress AND flow velocity profile) Availability of sediment: sediment concentration depends on the erosion rate of sediments or the availability of sediments Age of the sediment deposit (consolidation increases the critical shear stress of the sediment)

Transport of mud: fluid dynamics Sediment density coupling Suspended sediment influences the density of water Water density influences mixing of turbulence Turbulent mixing influences the sediment concentration profile (upward sediment transport by turbulent mixing and downward transport by settling)  positive feedback loop resulting in deposition Accurate 3D flow and sediment concentration Net transport of mud is often a delicate balance between phasing in flow velocity and sediment concentration vertical and horizontal distribution (of velocity and sediment) example: harbour dock sedimentation

Example: harbour sedimentation Minimizing harbor siltation: Deurganckdok.

Example: harbour sedimentation Minimizing harbor siltation: Deurganckdok.

Example: harbour sedimentation Minimizing harbor siltation: Deurganckdok.

Transport of mud: erosion rate vs sediment availability Mud transport limited by sediment availability Sediment enters model domain through open boundaries, no initial amount of sediment!!! Concentration in water column and sediment on the bed is limited by sediment influx and outflux imposed by hydrodynamics Low critical shear stress for erosion (0.05-0.3 Pa) and high erosion parameter M (0.1-0.001 kg/m2/s) Dynamic equilibrium  suitable for long-term simulation and process studies Very long initialisation (spin-up)

Transport of mud: erosion rate vs sediment availability Mud transport limited by sediment availability Mud transport limited by erosion rate Sediment in water column generated by erosion of bed sediment C=f(u) Short-term, ‘engineering-type’ studies or erosion of consolidated bed sediment High critical shear stress for erosion (0.5-1 Pa) and low erosion parameter (1 10-5 – 1 10-6 kg/m2/s) Requires map of initial sediment availability Sediment concentration based on initial conditions, no dynamic equilibrium!

Transport of mud: erosion rate vs sediment availability Initial sediment bed NO YES Boundaries YES/NO Critical shear stress LOW HIGH Erosion parameter M Dynamic equilibrium Timescales LONG SHORT

Mud transport: consolidation Compaction of sediment in time through pressure exerted by overlying grains and resulting expulsion of interstitual pore water Decrease of erosion rate with time and with depth Modelling consolidation requires high vertical resolution and small timesteps  not useful for long-term large-scale simulations (Delft3D research version) ‘Simple’ consolidation model needed

Mud transport: sand-mud Mud in sand matrix: mud gradually released by bed reworking during storm season (Netherlands: gradual increase offshore sediment concentration during winter) Sand-mud mixture: Sand transport strongly reduced when bed consists of 5-10 % clay ( ≈ 20-40% mud) Few models simulate interaction, several research versions of Delft3D

Mud transport: silt Increase of critical shear stress due to shear dilatance

Modelling: Delft3D Hydrodynamics Sediment transport Advantages / disadvantages + Accurate morphological feedback + Sediment-density coupling + Easy to use, flexible + DLL ‘open source’ parts for sediment transport module, and erosion / deposition terms - relatively slow: for each sediment the computationally expensive hydrodynamics need to be re-run Delft3D flow with online sediment + Less computationlly expensive (especially with aggregation) + Mud-buffer model (and future sand-mud?) + Not easy to learn Delft3D flow Delft3D WAQ

Modelling: Delft3D Exercise 6: ETM formation

Modelling: Delft3D Exercise 7: Mudflat sedimentation