Modeling Bedload Transport

Why model bedload transport?

Part of my thesis entails modeling bedload transport in Portsmouth Harbor. But why? Sandwave fields in the harbor clearly indicate that bottom sediments are mobile, but without further understanding the controls on this movement, it’s very difficult to determine how/when/where/why the sediment is moving. Bedload transport models (e.g. Van Rijn 1984, 1993, 2007) predict bedload transport as a function of controlling factors such as grain size distributions, changes in fluid density, and current and wave observations. Understanding the link between controlling factors and bedload transport allows the following questions to be answered:

• are tidal currents alone enough to initiate bedload transport?
• are tidal currents, waves, or both (e.g. wind- and wave- reinforced tidal currents) primarily responsible for the movement?
• are sands being transported into, or out of, the harbor?

Shear stresses and bedload transport

Hydrodynamic forcing agents (i.e. currents and waves) influence sediment dynamics via the frictional forces they exert on the seabed. These frictional forces are expressed in terms of the bed shear stress, which is the frictional force exerted by the flow per unit area of bed. Much of the work in modeling bedload sediment transport is concerned with calculating bed shear stresses, and to methods of determining their effects on the sediments. The total bed-shear stress acting on the seabed is comprised of three contributions:

• skin friction (τs), produced by (and acting on) the sediment grains
• form drag (τf), produced by the pressure field associated with the flow over ripples and/or larger bed features (e.g. dunes)
• a sediment-transport contribution (τt), caused by momentum transfer to mobilize the grains

Van Rijn (1993) refers to the skin friction component as the “grain-related” contribution, since this contribution is calculated using a logarithmic current velocity profile that is based on grain-related roughness elements (e.g. the Nikuradse roughness). If the bed is flat and sediment transport is not intense, then total roughness is assumed equal to the skin friction. As Soulsby (1997) notes, it’s important to be aware that only the skin friction contribution acts directly on the sediment grains, and it is therefore this contribution which is used to calculate the threshold of motion and bedload transport (with a few exceptions).

If this isn’t confusing enough, each of three contributions (skin friction, form drag, and the sediment-transport contribution) can be forced by currents, waves, or both. Soulsby (1997) provides the following diagram to help sort out the different contributions to shear stress:

[Insert Table I from Soulsby (1997), p. 12]

Procedure

The following procedure for modeling bedload sediment transport is proposed by Soulsby (1997):

1. Determine water properties: depth, temperature, salinity, and density.
2. Determine bed material properties: grain size distribution, median grain diameter, and sediment density.
3. Calculate the following parameters for initiation of motion: dimensionless grain size, threshold Shields parameter, threshold shear stress, and settling velocity.
4. Decide on prevailing flow conditions: currents, waves, or combined currents and waves. Since wind and wave conditions in Portsmouth Harbor were calm during the study period, I will assume currents alone for my thesis.
5. For currents alone, obtain measures of current speed through one tidal cycle each of mean spring and mean neaptides. Use a current meter or a numerical model. The depth-averaged current, which is approximately the value measured by a current meter mounted at a height of 0.32 x depth, is the value required for most of the subsequent formulae. This assumption is not necessarily valid for estuaries with density stratification; I have to work this out further.
6. Calculate the skin-friction bed shear stress, skin-friction velocity, and skin-friction Shields parameter.
7. Calculate the height and wavelength of ripples and dunes.
8. Calculate effective total roughness, total bed shear stress, and total friction velocity.
9. Calculate bedload transport rate, taking account of bed slope if appropriate.