Statement of the Model

where vsi denotes the fall velocity of the ith size, denotes the Karman constant and zr denotes a reference elevation.

The basic relation is

The sediment entrainment formulation of Garcia-Parker (1991) is as follows, where us denotes shear velocity due to skin friction.

The parameters kr and us are evaluated from Engelund-Hansen (1967) as

Flow velocity is evaluated as

- Implementation
- Water discharge per unit width qw = UH is held constant at 15 m2/s. For a width of 200 m, this corresponds to the bankfull discharge of the Middle Fly River of 3000 m3/s.
- The grain size distribution of the imposed load is held constant at the illustrated distribution, which consists of 8.51% sand and 91.49% mud.
- The imposed sediment concentration in the water in mg/liter C = 106x(R+1)qT/(qT+qw) is allowed to vary between 442 to 68806 mg/liter
- The resulting grain size distribution of the bed material and equilibrium depth H and slope S are back-calculated from the above formulation.

Bed gets muddier as C increases!

Note how the fraction of mud in the bed increases and the geometric mean size of the bed material decreases as concentration increases!

What is the effect of the mud on channel morphology?

In the diagram below equilibrium depth H and slope S are computed for a base case C = 4409 mg/l, but with the load truncated below sizes ranging from 1.95 m to 125 m (and the load concentration adjusted accordingly). The model predicts a WEAK but DISCERNIBLE effect of “wash load” on channel morphology!

Is this effect real?

We suspect not completely so. If the material below a given truncation size is present in such small quantities in the bed that it can comfortably fit within the pores of the coarser material, it should no longer have a discernible effect on channel morphology. We thus (somewhat arbitrarily) define a CUTOFF SIZE FOR WASHLOAD AS ONE SUCH THAT THE FINER MATERIAL WOULD OCCUPY 5% OF THE PORE SPACE OF THE COARSER MATERIAL.

Relation for porosity versus arithmetic standard deviation of bed material (adapted from Beard and Weyl, 1973)

OUR RESULT!!!

We can define a mechanistically consistent, dynamically varying cutoff size for washload that can fall below 62.5 m if, for example, the imposed load is sufficiently high!