Transport modes. Basic concepts of sediment transport.
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:
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.
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) :
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:
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:
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.