3-D numerical models - Computational River Dynamics - page 316

Figure 7.12 Localized dynamic pressure due to jet impingement.

motion. Using Eqs. (7.64) and (3.1) yields the following relation for K p :

1

g ∂

p d
∂

K p = 1 + (7.65)

(ρ − ρ) z

s

where p d is the dynamic (non-hydrostatic) pressure. Because the effect of the hydro-
static pressure has already been considered in general sediment transport formulas,
only the effect of the dynamic pressure needs to be considered in K p .
The downward flow increases the acting area of tractive force on sediment particles
and then decreases the critical shear stress for sediment incipient motion. Therefore,
the correction factor K d can be determined by

1

K d = (7.66)

1 + sin β

where is the impact angle of flow to the bed, defined as the angle between the

near-bed resultant flow and the bed.
As discussed in Section 3.7, gravity affects the incipient motion of sediment on a
steep slope. The correction factor K g is defined as

β

sin (φ − ϕ)

r

K g = (7.67)

sin φ

r

ϕ

where is the streamwise bed slope angle with the horizontal (positive values denoting

downslope beds), and

r is the repose angle of submerged bed material. It should be
noted that when the bed slope angle is close to the repose angle, K g is close to zero.
This must be limited by imposing a small lower bound, such as 0.1, to K g .

φ