 Transport modes. Basic concepts of sediment transport.

There are 3 kinds of sediment transport:

It's made of the particles moving and keeping contact with the bed.

It's mainly made of sediment rolling, sliding or jumping just over the bed.

As a consequence, this transport is mainly determined by the forces existing t the bed level..

These category moves above the bed because of turbulence an buyoncy, but also tend to deposit over it.

The very thin particles of the wash-load are dominated by the current and don't encounter the bed.

Sediment properties:

Diameter: Here we'll talk about particles with a diameter over 0.06 mm. A granulometric study leads to the following density of probability: specific gravity:

the specific gravity is define as: The sediment will be caracterise by the ratio between its spécific gravity and the water one: For natural sediments, a common value for s is 2.65.

Settling velocity:

The settling velocity is written ws. It depends on the particle size, its specific gravity, its shape and the caracteristics of tha fluid.

The drag force over the particle is: c (cd = the drag coefficient, V = relative velocity, A = surface opposed to the current) : with The settling force ( combinig gravity and flottability) is: As the 2 forces are supposed to balance, ws can be determined: Cd depends only on the reynold number calculated with the particle diameter: Experiments have shown that the drag can be approximated by: And finally the settling velocity ws is known..

Vertical distribution of sediments suspensionin steady fows or current flows. Firtly, let's examine the steady problem.:

When a given sand has a settling velocity equal to ws, that means that in a turbulent flow they settle at this speed.

According to the mixing-length theory, the fluid particles and sand particles move:

from a level 1 where the concentration of sediment is to a level 2 above where concentration is .( Indeed, as the concentration is increasing with depth, the second conentration is lower than the first one, see fig a:). The flux in a vertical direction is then: By analogy, this flux has an opposite flux, given by: To be in a steady situation, thes 2 flux are the same, so the result is (*): Then let's apply the mixing lenght theory, using the expression of vertical shear stress and an approximation of the velocity derivate: (*) can now be changed in: Eventually, an integration gives the distribution of Vanoni: In this second part the flow is purely harmonic:

As the concentrations and flux are now time-dependant, the governing equation is less simple: The left member is the rate of concentration évolution, the first right member is due to settling, the last two terms are relative to horizontal and verical diffusion. ( generaly, horizontal diffusion is considered minor in front of vertical one)

The left term is then roughly approximated by: and: The problem is now that any parameter is function of time, even the boudary conditions!!

For example, the Eddy viscosity is expressed by: The solving conditions are:

Periodic variations: flux=0 at the surface: Condition limite en concentration ( not completely satisfactory ) .

The explicit expression for is in the 3rd volume of 'Advanced series on Ocean Engineering', .

Solving the problem further needs modeling, as no alnalytic solution is available.