Non-cohesive sediments (sands and gravel) are perfect candidates for particle models by default. They are readily available for transport in the aquatic environment, their dynamics are well-studied and their coupling with hydrodynamic models is generally straightforward. The hydrodynamic model provides currents, bottom stress and turbulence. The sediment particle is either stationary or moving, depending on turbulence levels. The movement occurs as bed-load (rolling, sliding or saltating) or suspended load. Dispersion is 3D. The law of the wall governs the boundary layer. There are four states and corresponding transition rates as shown in the accompanying figure. The distinction between different modes of transport is not needed in this framework: they are natural outcomes of the simulation and do not need specific transport relationships. The statistically significant number of particles that we are able to track on parallel processors provides pathways towards addressing problems such as sediment availability and bedform development.

The two representative animations of 2.5 M2 cycles given here show sand transport in a mesotidal New England estuary. There are two classes of sand, fine (0.1mm –blue) and coarse (1mm –red). Each class consists of approximately 400,000 particles. Particles obey the flow chart given in the corresponding Figure on the right. They may move as bed-load, suspended-load or just rest at the bottom according to the Shields’ criteria. The velocity gradient in the vertical is represented by the Rouse centroid height concept. Horizontal and vertical dispersion are modeled using \(A_{h,v}=A_{h0,v0}\bullet Hu_*\). Here \(A_{h,v}\) is the horizontal (\({h}\)) or vertical (\({v}\)) dispersion coefficient, \({H}\) is flow depth and \({u{}_{*}}\) is the shear velocity, characterizing the intensity of turbulence. The value \({A{}_{ho}}\) is 0.22, while \({A{}_{vo}}\) is 0.067. Figures accompanying the animation show simulation results with 5 sand classes and the resulting steady-state sediment accumulation potentials.

Flow chart for non-cohesive sediment particle simulations.


Four-state, 3-D particle model for non-cohesive sediments. P is Pelagic state; Mf is Mixing state, free to move; Mt is Mixing state, trapped; B is Burial state. α and β are the rates of trapping of free particles and freeing of trapped particles respectively. The rate of particle entrainment is re. μ is the rate of burial.

2.5 tidal cycle long animation of sand transport in a mesotidal estuary. There are two classes of sand, fine (0.1mm –blue) and coarse (1mm –red). Blue particles are below the red ones and they may be hidden if there is overlap.

Same as to the left, except zoomed in for clarity.


Progression of five sand classes during flood tide. There are approximately 400,000 particles in each class. Red: 1 mm; Blue: 0.8 mm, Yellow: 0.5 mm; Cyan: 0.3 mm; Green: 0.1 mm.

This picture zooms in to show detail. Note bedform formation, a direct effect of using a large number of particles.

Another zoom in to show detail.


Accumulation potential for coarse (D = 1 mm) sands. The color bar gives accumulation potential in percentage terms.

Accumulation potential for fine (D = 0.1 mm) sands.