Yang (1973, 1984) is a total load transport equation which bases transport on Stream Power, the product of velocity and shear stress. The function was developed and tested over a variety of flume and field data. The equation includes two separate relations for sand and gravel transport. Yang tends to be very sensitive to stream velocity, and it is more sensitive to fall velocity than most.
Yang is fundamentally a power law equation where Concentration (Ct) is a function of excess stream power (VS-VScr):
|
C_t = a \left( VS - VS_{cr} \right) ^b |
The log-transformed version of that equation is:
The actual form of the Yang (1973) sand (particle size, d<2mm) equation is:
Where the power and coefficient are functions that include dimensionless parameters (e.g. the classic ratio of shear velocity and fall velocity that is often used to determine if a grain class can be suspended.
The variables are:
Ct = Total sediment concentration
ω = Particle fall velocity
dm = Median particle diameter
ν = Kinematic viscosity
u* = Shear velocity
V = Average channel velocity
S = Energy gradient
This transport function switches to Yang's (1984) gravel equation for grain classes larger than 2 mm.
|
logC_t = 6.681 - 0.633log \frac{\omega d_m}{v} - 0.282log \frac{u_s}{\omega} + \left( 2.784 - 0.305 \frac{\omega d_m}{v} - 0.282log \frac{u_s}{\omega} \right) log \left( \frac{VS}{\omega} - \frac{V_{cr}S}{\omega} \right) |
The transition between the sand and gravel equations is not always smooth. If results have counter intuitive results around the sand-gravel boundary, investigate the computed potential across that transition.