Sediment transport modes ___ Sediment properties ___ Vertical distribution of sediment

There are 3 kinds of sediment transport:

- the 'Bed load'

- the 'Suspended load'

- the 'Wash load':

*The bed-load 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..

*The suspended load:*

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

*The 'wash load':*

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

` 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..

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 foris in the 3rd volume of 'Advanced series on Ocean Engineering', .

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